diff --git a/WORKSPACE.md b/WORKSPACE.md
index a393f0f6..419a2754 100644
--- a/WORKSPACE.md
+++ b/WORKSPACE.md
@@ -3,45 +3,45 @@
 <a id="mandate"></a>
 
 Work only in **GoGoKo699/Hopf-Frame-Compilation**. Modification and merge
-are authorized. The destination is optimal general native T-depth for
-complete Hopf frames, with simultaneous count, width, precision and work return.
+are authorized. The destination is optimal general native T-depth for complete
+Hopf frames, with simultaneous count, width, precision and work return.
 Manuscript drafting and the changed-decoder supplement are separate tasks.
 
+This checkpoint owns the current question and next action. Replace it when
+the question changes; proofs and route assessments stay in their linked homes.
+
 <a id="current-checkpoint-native-source-scope-and-complete-readout"></a>
 
 ## Current checkpoint
 
-Verified baseline: [PR #269](https://github.com/GoGoKo699/Hopf-Frame-Compilation/pull/269),
-`5867adce7db176dc9983db851df451123ab9d272`, 29 October 2026.
-Its reviewed tree passed 2,054 tests locally and in both CI versions, plus the full gate and presentation checks.
+Scientific baseline: [PR #270](https://github.com/GoGoKo699/Hopf-Frame-Compilation/pull/270),
+merged as `30dc60d31e252d135327d0384af3311b4741414e`, 29 October 2026.
+Its reviewed tree `fc1fb46d64268a0cb8cf9694f36a9ac45dfb9e37` passed
+2,087 tests, the ten-command local gate and all five head checks; the PR
+retains exact receipts. Later maintenance commits may leave this scientific
+baseline unchanged: inspect the actual branch and intervening diff.
 
-Read the [resource frontier](docs/OPEN_PROBLEM.md) for general theorems and the
-[route decisions](research/ROUTE_DECISIONS.md) for the chosen mechanism.
-Use the [research catalogue](research/README.md) to find its proof dependencies.
+**Current bottleneck:** the augmented field recoupler pays uniform decoding
+and complete helper return, but its depth is linear in the address length.
+Compress the complete source beyond the fixed-frame helper-affine stage
+grammar. Helper-basis motion or non-Clifford sector intermediates remain
+eligible; weaker complete-probe and joint seed/copy routes remain open.
 
 <a id="current-depth-frontier"></a>
 
 ## Destination and strongest established statements
 
-For $`N=2^n`$, integers $`n\ge1,L\ge6`$, the strongest unconditional
-research upper theorem remains [R96](research/depth/ALL_PRECISION_LINEAR_DEPTH.md):
-
-```math
-D_T=O(NL/b^2+L+\log_2(n+2)),\qquad
-T=O(\sqrt{NL}+L+NL/b),\qquad G=O(NL).
-```
-
-One clean qubit suffices at real width $`b\ge17(L+n+7)`$ or
-complex-magnitude width $`b\ge17(L+n+8)`$, with complete initialized-isometry
-error at most $`2^{-L}`$, including arbitrary dirty/reference inputs and work return.
-[Selected Result D remains R79](manuscript/PUBLICATION_SCOPE.md).
-At fixed accuracy and square-root dirty width, logarithmic upper versus
-constant lower native T-depth remains open. The [frontier](docs/OPEN_PROBLEM.md)
-owns the other bounds, matching ranges and special-family qualifications.
+[R96](research/depth/ALL_PRECISION_LINEAR_DEPTH.md) remains the strongest
+unconditional general research upper. The [resource frontier](docs/OPEN_PROBLEM.md#large-width-t-depth)
+owns formulas, real/complex dirty reservations, precision ranges and matching
+intervals. At fixed accuracy and square-root dirty width, logarithmic upper
+versus constant lower native T-depth remains open.
+[Selected Result D remains R79](manuscript/PUBLICATION_SCOPE.md);
+Result C's one-clean count frontier is established.
 
 ## Main unfinished route and exact missing operation
 
-For p address bits and $`m=2^p`$, construct the complete dirty indicator
+For p address bits and $`m=2^p`$, the sufficient source target is
 
 ```math
 I_p|x,Y,w\rangle=|x,Y\mathbin\oplus e_x,w\rangle
@@ -49,123 +49,65 @@ I_p|x,Y,w\rangle=|x,Y\mathbin\oplus e_x,w\rangle
 
 at every fixed requested tolerance tau, with zero clean inputs,
 $`T,b_{\rm dirty}=O_\tau(m)`$, $`G=O_\tau(m^2)`$ and
-$`D_T=o(\log(p+2))`$. Every address, output, work and reference input is
-arbitrary. Intermediate register motion is permitted; full operator error
-includes every return error. This is a sufficient route, not a necessary
-representation of an unrestricted frame compiler.
+$`D_T=o(\log(p+2))`$. All address, output, work and reference inputs are
+arbitrary; full operator error includes every return error. Intermediate
+register motion is permitted. This sufficient route does not restrict an
+unrestricted frame compiler's representation.
 
 [Polynomial-overhead fusion](research/depth/POLYNOMIAL_OVERHEAD_INDICATOR_FUSION.md)
-allows discovery at fixed polynomial overhead on a smaller address;
+permits discovery at fixed polynomial overhead on a smaller address;
 [bounded-clean promotion](research/depth/DIRTY_PROMOTION_OF_CLEAN_QUERIES.md)
-pays leakage and off-code cancellation. The
-[R98 transfer](research/depth/QUERY_DEPTH_FRAME_TRANSFER.md) and its
-[constant-accuracy extension](research/depth/APPROXIMATE_QUERY_FRAME_TRANSFER.md)
+pays leakage and off-code cancellation. [R98 transfer](research/depth/QUERY_DEPTH_FRAME_TRANSFER.md)
+and its [constant-accuracy extension](research/depth/APPROXIMATE_QUERY_FRAME_TRANSFER.md)
 retain a log-log contribution. Constant source depth alone does not settle
 optimal frame depth or give a new all-precision theorem.
 
+### Latest substantive outcomes and resumption question
+
+| Open for the current task | What it settles or constrains |
+| --- | --- |
+| [Augmented recoupler](research/depth/AUGMENTED_FIELD_RECOUPLER.md) | Paid moving-helper decoder and complete echo. At most $`16(p-1)`$ decoder bands and $`64(p-1)+16`$ indicator bands; count, width and gates fit relaxed fusion budgets, depth does not. |
+| [Sector-degree barrier](research/depth/FIELD_SECTOR_DEGREE_BARRIER.md) | Clifford-sector intertwiners need helper-tableau degree at least $`p-1`$; fixed-frame helper-affine words need at least $`p-1`$ stages. This does not bound unrestricted native depth. |
+| [Field decisions](research/ROUTE_DECISIONS.md#field-recoupling) and [finite calibrations](research/ROUTE_DECISIONS.md#finite-field-calibrations) | Uniform recoupling dependencies and the retained four/eight-address words. |
+| [Decoder screens](research/ROUTE_DECISIONS.md#field-decoder-screens) | Full-intertwiner and weaker complete-probe domains; independent-cell and disjoint-span exclusions with their exact hypotheses. |
+| [Seed/copy decisions](research/ROUTE_DECISIONS.md#seed-and-copy) | Complete carrier equation, grading and seed restrictions for the alternative joint construction. |
+
+**Next action:** write a complete candidate relation outside the blocked stage
+grammar, specifying helper motion and the actual inverse before optimizing
+its native word. Derive uniform depth, count, simultaneous width, gates and
+error/return. Compare against the source target and charge frame transfer
+before claiming an improvement. Uniform field division and recovery are no
+longer the unpaid step of the augmented route; the earlier identity-helper
+decoder retains its separate scope.
+
 <a id="the-two-useful-source-interfaces"></a>
 
 ### Choose a complete source interface
 
-| Interface | First unpaid operation |
-| --- | --- |
-| [Complete Pauli derivative](research/depth/BANK_MIXING_AND_LOOKUP_PHASE.md#rank-one-indicator-equivalence) | Synthesize a native source with the required full-space derivative. Two actual source/adjoint calls extract the indicator; its canonical diagonal phase is an equivalent target. |
-| [Encoded dirty copy](research/depth/ENCODED_DIRTY_COPY_INTERFACE.md) | Jointly synthesize the encoded bank transition and its complete copy interaction with a physical output bank. Their echo returns the carrier; no physical implementation of its abstract decoder is required. |
-| [Accepted projector Gram](research/depth/NILPOTENT_PENCIL_OBSERVABLE_SOURCE.md#paired-projector-readout) | Synthesize a normalized source with $`K^\dagger K\approx\Pi_{\rm eq}/2`$ on every data/dirty input. Accepted fibers and intermediate address motion may be arbitrary. |
-
-Use the proof home's [one-clean](research/depth/NILPOTENT_PENCIL_OBSERVABLE_SOURCE.md#four-call-gram-readout)
+The [interface register](research/ROUTE_DECISIONS.md#complete-interfaces)
+retains [complete Pauli derivatives](research/depth/BANK_MIXING_AND_LOOKUP_PHASE.md#rank-one-indicator-equivalence)
+and [encoded dirty copies](research/depth/ENCODED_DIRTY_COPY_INTERFACE.md).
+The latter needs a jointly paid transition and physical copy, but no physical
+implementation of the abstract decoder. The [Gram interface](research/ROUTE_DECISIONS.md#gram-interfaces)
+needs a normalized complete-input source; use its actual-accuracy
+[one-clean](research/depth/NILPOTENT_PENCIL_OBSERVABLE_SOURCE.md#four-call-gram-readout)
 or [joint two-clean](research/depth/NILPOTENT_PENCIL_OBSERVABLE_SOURCE.md#two-clean-joint-gram-readout)
-recovery ledger at the actual requested Gram accuracy. The wrappers are paid;
-they do not construct the source.
+recovery ledger. Paid wrappers do not construct their source.
 
-### Latest substantive outcomes and resumption question
-
-The [tree-probe algebra](research/depth/INTERLEAVED_TREE_PROBE_SOURCE.md),
-[Clifford-orbit rank](research/depth/CLIFFORD_ORBIT_QUERY_RANK.md) and
-[non-Clifford seed spread](research/depth/NONCLIFFORD_SEED_SPREAD.md) retain their exact query/seed scopes.
-Target coordinates and support do not pay decoding.
-
-The [field shear](research/depth/FIELD_SHEAR_INTERTWINER.md) has a paid eight-band query.
-The [augmented recoupler](research/depth/AUGMENTED_FIELD_RECOUPLER.md) replaces the
-original decoder's unpaid division maps with two multiplication-XOR batches per level.
-A moving Pauli helper query appears on both sides; the complete indicator echo returns every helper.
-The paid decoder has at most $`16(p-1)`$ bands, and the indicator has at most $`64(p-1)+16`$.
-Its $`O(mp^3)`$ T count, $`O(mp^2)`$ dirty width and $`O(m^2p^2)`$ gates fit the relaxed fusion budgets;
-its linear depth does not. Invariant-stabilizer-diagonal seeds and Bell-zero-fiber preservation still fail.
-
-The [three-band source theorem](research/depth/THREE_BAND_LOOKUP_SOURCE_OBSTRUCTION.md)
-excludes every zero-clean native source of depth at most three for p at least
-seven below complete observable error $`\sin(\pi/8)/(2\sqrt2)`$.
-The proof forces the final two absorbed Pauli bands to preserve the address,
-with arbitrary Clifford interlayers, register motion and dirty width.
-This is a constant source-depth bound, not a growing frame-depth lower bound.
-
-The [copy-grading criterion](research/depth/DIRTY_COPY_GRADING.md) now
-characterizes exact copying of arbitrary unitary families: every word with
-nonzero occurrence parity must have zero trace. Spectral multiplicity yields
-constant robust word tests. Field-orbit reflection pairs have a common
-same-sign sector and cannot approximate an anticommuting pair below
-$`\sqrt{2-\sqrt2}`$. Nevertheless a copyable all-size noncommuting family
-exists. Its wire-translation query retains linear depth; moving it to the
-field query leaves its seed and copy unpaid.
-
-[Native copy components](research/depth/NATIVE_COPY_INTERACTION.md) retain
-their one-band component, dual-support bounds and product/coded-family screens.
-The [affine Pauli-query screen](research/depth/PAULI_ORBIT_COPY_SCREEN.md)
-has a quarter-error floor with Clifford dual probes; it does not cover the
-non-Pauli field shear or exclude all one-band field copies.
-
-The [copy-axis bound](research/depth/COPY_AXIS_SPAN.md) requires extensive
-physical-X span, compatible with linear count. The
-[seed-mixing bound](research/depth/MONOMIAL_QUERY_SEED_OBSTRUCTION.md)
-requires strong cross-commutators on every independent address pair;
-monomial query-eigenbasis seeds have a half-error floor. The full-Hadamard
-field seed passes the mixing test but still has a half-error spectral floor.
-
-The [flat four-address pilot](research/depth/FLAT_FIELD_BANK_PILOT.md) retains its six-T decoder and complete 72-T indicator.
-The [projective recoupler](research/depth/PROJECTIVE_FIELD_RECOUPLER.md) retains two exact eight-address allocations:
-172 T gates and at most 83 bands without extra helpers, or 148 T gates and at most 39 bands with six returned dirty helpers.
-Common reflection selection and private quartic batching pay the second word. Exponential line enumeration remains a finite-size limit.
-
-[Pauli-domain rigidity](research/depth/FIELD_DECODER_PAULI_DOMAIN.md) requires absorbed-axis rank at least $`2m-2`$,
-including moving Clifford helpers. Independent finite cells fail even with joint outer Clifford walls.
-The [weak-probe domain](research/depth/WEAK_PROBE_PAULI_DOMAIN.md) also excludes independent four-wire cells:
-complete-probe error is at least $`1/12`$ for p at least three, and $`1/4`$ for p at least five.
-It permits arbitrary joint Clifford walls and moving decoded helpers; extensive axis rank alone is not a depth bound.
-The [two-band screen](research/depth/TWO_BAND_FIELD_DECODER_OBSTRUCTION.md) excludes disjoint
-absorbed spans at fixed error; shared-span collisions and coupled three-band words remain open.
-The [scalar-field radical model](research/depth/SCALAR_FIELD_RADICAL_COPY_SCREEN.md)
-has a four-address identity for every address embedding; changing its address space does not repair it.
-The [sector-degree barrier](research/depth/FIELD_SECTOR_DEGREE_BARRIER.md) requires helper-tableau degree at least
-$`p-1`$ for Clifford-sector field intertwiners. The augmented construction attains it.
-Fixed-frame helper-affine stage words need at least $`p-1`$ stages; this does not bound unrestricted native T-depth.
-
-The [Clifford-seed bounds](research/depth/CLIFFORD_SEED_COPY_STRUCTURE.md) retain their commuting-orbit and one-band-copy scopes.
-The [seed fingerprint](research/depth/NATIVE_COPY_INTERACTION.md#seed-coefficient-rigidity) excludes product THT-dagger seeds below 3/32 for one-band field copies at p at least two.
-[Complete copy feasibility](research/depth/ONE_BAND_COPY_FEASIBILITY.md) still requires
-the carrier equation; triple-axis joint walls have zero full seed space.
-[Clifford-dual grading](research/depth/CLIFFORD_DUAL_COPY_GRADING.md) requires binary
-abelianization rank at least $`m-p-1`$; explicit relation words give robust floors.
-**Next question:** compress the complete source while leaving the fixed-frame helper-affine stage grammar,
-allowing helper-basis motion or non-Clifford sector intermediates, with a complete native return ledger.
-The weaker complete-probe and joint seed/copy alternatives remain open. R96 is unchanged.
-
-The [four-band Clifford front end](research/depth/CLIFFORD_INVOLUTION_SOURCE.md) and
-[weighted outer-phase route](research/depth/JOINT_ADDRESS_HELPER_SOURCE.md),
-[reduced central gauge](research/depth/COHERENT_CENTRAL_TRANSPORT.md#reduced-carrier-gauge) and
-[minimal-tree probe](research/depth/ORDERED_MATCHING_PROBE_SOURCE.md#minimal-tree-source) remain component alternatives under their separate screens.
-In the [precision route](research/depth/JOINT_PRECISION_ROTATION.md), joint recovery beyond the separately paid two-path pilots remains open.
-
-A finite-size identity needs a uniform all-size rule; serial grade computations retain the old cost. Any gain
-needs a fresh complete-circuit ledger, including transfer, precision words,
-actual inverses, leakage and work return.
+Retained alternatives: [four-band front end](research/depth/CLIFFORD_INVOLUTION_SOURCE.md),
+[weighted outer phases](research/depth/JOINT_ADDRESS_HELPER_SOURCE.md),
+[reduced central gauge](research/depth/COHERENT_CENTRAL_TRANSPORT.md#reduced-carrier-gauge),
+[minimal-tree probe](research/depth/ORDERED_MATCHING_PROBE_SOURCE.md#minimal-tree-source),
+and [joint precision recovery](research/ROUTE_DECISIONS.md#joint-precision-route)
+beyond the separately paid two-path pilots. Consult their route screens before resuming.
 
 ## Stopped routes, reopening conditions and superseded instructions
 
-The [route decisions](research/ROUTE_DECISIONS.md) own each failed mechanism and its reopening condition.
-Detailed proofs and unique counterexamples stay in their linked homes. Old instructions to add another mixer,
-improve a scalar filter, or pay the rank-one phase do not override those complete-action screens.
-A scoped failure does not retire the unrestricted destination.
+[Route decisions](research/ROUTE_DECISIONS.md) own the exact excluded class
+and reopening condition for each mechanism. Proofs, counterexamples and unique
+unfinished attempts remain in their linked homes. Historical prompts are
+records, not current work orders. A scoped failure does not retire the
+unrestricted destination; a finite pilot is not an all-size construction.
 
 <a id="research-decision-and-stopping-rules"></a>
 <a id="continuing-toward-the-general-answer"></a>
@@ -173,48 +115,40 @@ A scoped failure does not retire the unrestricted destination.
 
 ## Working contract and reading map
 
-Prefer analytic identities and a few exact fixtures. Preserve literal phases, every logical column,
-coherent address and arbitrary dirty/reference inputs, actual native adjoints, and all clean leakage and work return.
-No QRAM, free loading or precision states, unpriced clean history, resets or postselection.
-A suffix is clean only on its active sector; inactive action needs its own proof.
-Separate general theorems, conditional interfaces, useful components and
+Prefer analytic identities and a few exact fixtures. Preserve literal phases,
+every logical column, coherent address and arbitrary dirty/reference inputs,
+actual native adjoints, and all clean leakage and work return. No QRAM, free
+loading or precision states, unpriced clean history, resets or postselection.
+A suffix is clean only on its active sector; inactive action needs its own
+proof. Separate general theorems, conditional interfaces, components and
 representation limits. Internal audits and finite checks do not replace
 analytic proof or external technical review.
 
-| Need | Authoritative home |
+| Information that changed | Update its authoritative home |
 | --- | --- |
-| Selected A–D claims and allocations | [Publication scope](manuscript/PUBLICATION_SCOPE.md) |
-| Core argument and dependencies | [Review](REVIEW.md), [documentation map](docs/README.md) |
-| Strongest general resource statements | [Resource frontier](docs/OPEN_PROBLEM.md) |
-| Mechanism decisions and proof locations | [Route decisions](research/ROUTE_DECISIONS.md), [research catalogue](research/README.md) |
-| Attribution and executable evidence | [Source catalogue](docs/reference/SOURCE_CATALOGUE.md), [verification catalogue](docs/reference/VERIFICATION_CATALOGUE.md) |
+| Construction or proof | Existing proof home; [research catalogue](research/README.md) locates it. Change the index only for a new home or changed role. |
+| Mechanism assessment or reopening condition | [Route decisions](research/ROUTE_DECISIONS.md), linked to the proof. |
+| Bottleneck or next action | Replace this checkpoint; keep detailed outcomes in existing proof/route homes. |
+| General theorem or global gap | [Resource frontier](docs/OPEN_PROBLEM.md). Selected A–D statements belong in [publication scope](manuscript/PUBLICATION_SCOPE.md); [proof map](docs/README.md) owns dependencies. |
+| Evidence or attribution | Relevant tests and [verification catalogue](docs/reference/VERIFICATION_CATALOGUE.md); [source catalogue](docs/reference/SOURCE_CATALOGUE.md) owns attribution and stable IDs. |
+| Validation procedure or upstream baseline | [Research validation](scripts/README.md#research-validation) or [SYNC](SYNC.md), respectively. |
 
 <a id="refurnishing-policy"></a>
 
-Each claim has one proof home. Preserve unique attempts, stable identifiers, inbound anchors, tests and receipt hashes; change mechanisms when complete synthesis restores the old cost.
+Update only affected homes. Keep summaries as links plus decision-relevant
+scope. Preserve unique attempts, stable identifiers, inbound anchors, tests
+and receipt hashes; change mechanisms when complete synthesis restores the old cost.
 
 ## Restore and verify
 
 Check worktree status and remote, fetch main, and inspect changes since the
-baseline. Preserve unrelated work. [SYNC](SYNC.md) owns upstream versions.
-For a proof move, compare the mathematics and audit old and new links.
-Run the complete local gate on the final reviewed tree:
-
-```bash
-python -m compileall -q compiler_robust_hopf scripts tests validate.py
-python scripts/reviewer_walkthrough.py
-python scripts/coarse_frame_native_example.py
-python scripts/complex_coarse_native_example.py
-python scripts/residual_qbp_native_example.py --q 16
-python validate.py --quiet
-python scripts/verify_fault_tolerant.py
-python scripts/check_upstream_sync.py --offline
-python scripts/unified_resource_ledger.py --n 12 --format json
-python scripts/strict_zero_echo_ledger.py --n 12 --format json
-```
-
-Use the [presentation guide](assets/README.md#rendering-checks) for changed
-mathematics and reader-facing pages. Complete focused visual checks before the
-memory-heavy numerical suite; use full presentation CI for the complete corpus.
-Record exact-tree receipts in the review record and merge after required checks pass.
-A fixture is not an asymptotic proof or a scalable native emitter.
+scientific baseline. Preserve unrelated work. Read the checkpoint and the
+dependency branch needed for the next action; use catalogues for targeted
+lookup rather than replaying session history.
+
+[Research validation](scripts/README.md#research-validation) owns focused
+iteration checks and the complete ten-command final gate. Complete focused
+[visual checks](assets/README.md#rendering-checks) before the memory-heavy
+numerical suite; full presentation CI covers the corpus. For proof moves,
+compare mathematics and audit old and new links. Record exact-tree receipts
+in the review record and merge after required checks pass.
diff --git a/llms.txt b/llms.txt
index fe6866d2..5edaaa04 100644
--- a/llms.txt
+++ b/llms.txt
@@ -6,12 +6,13 @@ Canonical repository: https://github.com/GoGoKo699/Hopf-Frame-Compilation
 
 ## Start by task
 
-- Continuing research: fetch current main, then read [WORKSPACE](https://raw.githubusercontent.com/GoGoKo699/Hopf-Frame-Compilation/main/WORKSPACE.md) and its current proof-home links. Historical session prompts do not override that checkpoint.
+- Continuing research: inspect the worktree, fetch current main and compare intervening changes, then read [WORKSPACE](https://raw.githubusercontent.com/GoGoKo699/Hopf-Frame-Compilation/main/WORKSPACE.md). Follow its current dependency branch and next unpaid operation; historical session prompts do not override the checkpoint.
 - Understanding the result: [README](https://raw.githubusercontent.com/GoGoKo699/Hopf-Frame-Compilation/main/README.md) gives the target and selected A–D claims; [REVIEW](https://raw.githubusercontent.com/GoGoKo699/Hopf-Frame-Compilation/main/REVIEW.md) explains their mechanisms.
 - Checking a theorem: [PUBLICATION_SCOPE](https://raw.githubusercontent.com/GoGoKo699/Hopf-Frame-Compilation/main/manuscript/PUBLICATION_SCOPE.md) owns selected statements and literal reservations; [docs/README](https://raw.githubusercontent.com/GoGoKo699/Hopf-Frame-Compilation/main/docs/README.md) maps proof dependencies.
 - Checking the current frontier: [OPEN_PROBLEM](https://raw.githubusercontent.com/GoGoKo699/Hopf-Frame-Compilation/main/docs/OPEN_PROBLEM.md) owns general resource bounds, their matching intervals and scoped lower bounds.
 - Choosing a mechanism: [ROUTE_DECISIONS](https://raw.githubusercontent.com/GoGoKo699/Hopf-Frame-Compilation/main/research/ROUTE_DECISIONS.md) owns failed mechanisms and their reopening conditions. [research/README](https://raw.githubusercontent.com/GoGoKo699/Hopf-Frame-Compilation/main/research/README.md) is the complete proof-home catalogue.
 - Reproducing evidence: [VERIFICATION](https://raw.githubusercontent.com/GoGoKo699/Hopf-Frame-Compilation/main/docs/VERIFICATION.md) routes to tests and receipts; [the finite-evidence catalogue](https://raw.githubusercontent.com/GoGoKo699/Hopf-Frame-Compilation/main/docs/reference/VERIFICATION_CATALOGUE.md) records their exact scopes.
+- Running checks: [research validation](https://raw.githubusercontent.com/GoGoKo699/Hopf-Frame-Compilation/main/scripts/README.md#research-validation) owns the focused test map and complete final gate. Use the evidence catalogue for other components; keep exact-tree receipts in the review record.
 - Checking attribution: [SOURCE_MAP](https://raw.githubusercontent.com/GoGoKo699/Hopf-Frame-Compilation/main/docs/SOURCE_MAP.md), [RELATED_WORK](https://raw.githubusercontent.com/GoGoKo699/Hopf-Frame-Compilation/main/docs/RELATED_WORK.md) and machine-readable provenance distinguish imported premises from local contributions.
 
 ## Scientific contract
@@ -39,6 +40,6 @@ The [state-based QBP supplement](https://raw.githubusercontent.com/GoGoKo699/Hop
 
 Finite checks support named identities, phases, inverses, work return and ledgers. They do not prove universal asymptotic claims. Internal audits are not external peer review or formal proof certification; no general native emitter is claimed.
 
-Preserve one proof home per claim, stable identifiers and inbound anchors. Front pages route; they do not accumulate session histories. Keep useful component proofs and scoped failed attempts when a stronger headline supersedes their old benchmark.
+Preserve one proof home per claim, stable identifiers and inbound anchors. Follow WORKSPACE's update-ownership map: replace its checkpoint when the next action changes, revise the affected route assessment, and index new proof homes without copying their outcome inventories across maps. Keep useful component proofs, scoped failed attempts and unfinished records when a stronger headline supersedes an old benchmark. This guide retains stable contracts; WORKSPACE owns the live research choice.
 
 Use the exact consulted commit and CITATION.cff for attribution. MIT licensed. Contact: gogoko699@gmail.com.
diff --git a/research/README.md b/research/README.md
index ca7c1f6a..47259f1a 100644
--- a/research/README.md
+++ b/research/README.md
@@ -2,12 +2,12 @@
 
 [Selected claims](../manuscript/PUBLICATION_SCOPE.md) · [Resource frontier](../docs/OPEN_PROBLEM.md) · [Core proof map](../docs/README.md) · [Working checkpoint](../WORKSPACE.md)
 
-This is a topic catalogue, not a second frontier statement or a sequence of
-research instructions. Each claim has one proof home; that home supplies its
-hypotheses, resource/error ledger, literal phases, actual inverses and return
-contract. A method-specific obstruction is not a lower bound for every compiler.
-Stopped and superseded routes are assessed once in the
-[route decisions](ROUTE_DECISIONS.md).
+Use this catalogue to locate a proof or recover a dependency without replaying
+sessions. Entries give the mathematical role and limiting scope; the linked
+proof owns the hypotheses, formulas, resource/error ledger, phases, inverses
+and return contract. Keep route assessments and reopening conditions in
+[route decisions](ROUTE_DECISIONS.md), and the active task in WORKSPACE.
+A method-specific obstruction is not a lower bound for every compiler.
 
 Use the [minimal count-proof chain](../docs/README.md#c-one-clean-compilation-and-its-corollaries)
 for selected dependencies. Use the [working checkpoint](../WORKSPACE.md)
@@ -20,6 +20,7 @@ has a separate task-level guarantee.
 | One-clean count and earlier endpoint methods | [Endpoint results](#endpoint-results) |
 | General depth constructions and promised families | [Large-workspace T-depth](#large-workspace-t-depth) |
 | Complete indicator interfaces and paid promotion | [Query transfers](#complete-query-transfers-and-clean-source-promotion) |
+| Encoded copy, field decoders and their screens | [Copy interfaces](#encoded-copy-and-field-bank-tools) · [Field source chain](#field-query-and-decoder-chain) |
 | Source mechanisms and their limitations | [Components](#constructive-components-and-source-candidates) · [Scoped limits](#source-specific-limits-and-failed-compositions) |
 | Native lower bounds and the focused scout | [Boolean rigidity](#native-boolean-rigidity-and-clean-code-structure) · [Physical pairs](#original-physical-pairs-and-the-four-band-scout) |
 | Restricted query/source grammars | [Read-only transport](#read-only-queries-and-source-transport-classes) |
@@ -187,24 +188,30 @@ These are complete interfaces and conditional transfers, not constructions of th
 - [Clean-sector parallelism: what the native schedule actually buys](depth/CLEAN_SECTOR_PARALLELISM_AUDIT.md)
 - [Dirty-tree compilation from complete branch differences](depth/DIRTY_TREE_DIFFERENTIAL_RECURRENCE.md)
 - [Which incomplete indicator interfaces still contain the full operation](depth/WEAKER_INDICATOR_INTERFACES.md)
-- [Bank mixing and the complete lookup phase](depth/BANK_MIXING_AND_LOOKUP_PHASE.md) — scoped mixing screens and the rank-one phase/indicator resource equivalence, including arbitrary address/work motion within the derivative gauge
+- [Bank mixing and the complete lookup phase](depth/BANK_MIXING_AND_LOOKUP_PHASE.md) — Complete phase/indicator equivalence; derivative gauge permits address/work motion.
 - [Table-specific probes and the remaining joint-word freedom](depth/TABLE_SPECIFIC_INDICATOR_INTERFACES.md)
-- [Encoded dirty copy without a synthesized decoder](depth/ENCODED_DIRTY_COPY_INTERFACE.md) — jointly paid carrier/copy interactions supply a physical indicator; an address-independent Clifford copy has a uniform error floor for one field-query orbit
-- [Exact dirty copying as a parity grading](depth/DIRTY_COPY_GRADING.md) — a complete criterion for arbitrary unitary families, robust word tests, field-pair rigidity and a noncommuting all-size calibration
-- [Native copy interactions and dual readout](depth/NATIVE_COPY_INTERACTION.md) — paid components, extensive copy T count, support screens, and a width-independent 3/32 floor for product THT-dagger seeds with Clifford output duals
-- [Complete one-band copy feasibility](depth/ONE_BAND_COPY_FEASIBILITY.md) — signed Walsh support spaces and spectra, the exact carrier fixed-point criterion, and a native triple-axis joint-wall family with zero complete seed space and a $`1/\sqrt6`$ copy-error floor despite passing the tensor screen
-- [Clifford output-dual grading](depth/CLIFFORD_DUAL_COPY_GRADING.md) — every exact one-band copy, even with an arbitrary unitary seed, requires an extensive binary abelianization of each dual's symplectic orbit group; explicit relation words give robust certificates
-- [Affine Pauli-orbit copy screen](depth/PAULI_ORBIT_COPY_SCREEN.md) — a one-quarter error floor with Clifford dual probes, the native one-bit endpoint and the paid dirty-mask gauge
-- [Extensive non-Clifford copy-axis span](depth/COPY_AXIS_SPAN.md) — quotient-sector weight gives a robust output-axis and T-count requirement, with no growing depth conclusion
-- [Monomial query-seed copy obstruction](depth/MONOMIAL_QUERY_SEED_OBSTRUCTION.md) — commuting original and seed-conjugated query algebras force a four-word identity and copy error at least one half, even with an arbitrary physical copy
-- [Four-address Clifford seed and physical copy](depth/FIELD_COPY_CLIFFORD_PILOT.md) — a noncommuting central-sector grading, a paid native copy and a complete 288-T, 96-band finite indicator with seven arbitrary dirty wires
-- [Flat-seed field bank and six-T decoder](depth/FLAT_FIELD_BANK_PILOT.md) — a genuinely non-Clifford graded four-address bank, a three-band decoder with a full Clifford intertwiner completion, and a complete 72-T, 28-band indicator with three returned dirty wires; no all-size depth improvement
-- [Projective field recoupler](depth/PROJECTIVE_FIELD_RECOUPLER.md) — complete eight-address native decoders: 172 T gates and at most 83 bands without extra helpers, or 148 T gates and at most 39 bands with six returned dirty helpers; shared reflection phases and private quartic batching retain every zero-fiber column, while line enumeration remains exponential
-- [Complete field decoder Pauli domain](depth/FIELD_DECODER_PAULI_DOMAIN.md) — robust absorbed-axis rank and T-count floor $`2m-2`$ for complete field intertwiners, including moving Clifford target helpers; independent finite cells fail after arbitrary joint outer Clifford walls
-- [Weak complete-probe Pauli domain](depth/WEAK_PROBE_PAULI_DOMAIN.md) — degree-sensitive Reed--Muller domain and axis bounds for the transported probe alone; a low-weight field-kernel argument yields independent-cell error floor $`1/12`$ from three address bits, improved to $`1/4`$ from five bits, including linear Pauli helper queries and moving decoded helpers
-- [Disjoint-span two-band field decoders](depth/TWO_BAND_FIELD_DECODER_OBSTRUCTION.md) — a uniform error floor for partial or full bands with zero span intersection, including arbitrary source identity helpers and Clifford target-helper motion; shared-span cancellation remains outside the theorem
-- [Scalar-field radical copy screen](depth/SCALAR_FIELD_RADICAL_COPY_SCREEN.md) — algebra-automorphism equivariance forces a square-zero shear image and a four-address relation for every address embedding, giving direct-copy error at least one half and output-dual copy error at least one quarter
-- [Clifford seed copy structure](depth/CLIFFORD_SEED_COPY_STRUCTURE.md) — projectively involutive seeds with commuting symplectic orbits have a 1/64 field-copy floor at p at least seven for arbitrary copies; every Clifford seed has a $`\sin(\pi/8)`$ floor at p at least nine when the copy has one physical T band
+### Encoded copy and field-bank tools
+
+The interface, copy feasibility and decoder contracts are distinct. Use the
+linked scopes before combining a seed, query and physical copy. Numerical
+allocations stay in their proof homes; finite pilots establish no all-size gain.
+
+- [Encoded dirty copy without a synthesized decoder](depth/ENCODED_DIRTY_COPY_INTERFACE.md) — Physical indicator from jointly paid carrier transition and copy; the abstract decoder need not be synthesized.
+- [Exact dirty copying as a parity grading](depth/DIRTY_COPY_GRADING.md) — Exact parity grading for arbitrary unitary families, robust word tests, and a noncommuting calibration.
+- [Native copy interactions and dual readout](depth/NATIVE_COPY_INTERACTION.md) — Native components, copy count/support screens, and product-seed rigidity with Clifford output duals.
+- [Complete one-band copy feasibility](depth/ONE_BAND_COPY_FEASIBILITY.md) — Walsh support plus the carrier fixed point; the triple-axis joint-wall family fails despite passing the tensor screen.
+- [Clifford output-dual grading](depth/CLIFFORD_DUAL_COPY_GRADING.md) — Extensive dual-orbit abelianization for one-band copies with arbitrary seeds; robust relation-word certificates.
+- [Affine Pauli-orbit copy screen](depth/PAULI_ORBIT_COPY_SCREEN.md) — Clifford-dual error floor, one-bit endpoint and paid dirty-mask gauge; field shear has a different scope.
+- [Extensive non-Clifford copy-axis span](depth/COPY_AXIS_SPAN.md) — Robust output-axis and T-count requirement; no growing depth conclusion.
+- [Monomial query-seed copy obstruction](depth/MONOMIAL_QUERY_SEED_OBSTRUCTION.md) — Commuting query and seed-conjugated algebras fail even with an arbitrary physical copy.
+- [Four-address Clifford seed and physical copy](depth/FIELD_COPY_CLIFFORD_PILOT.md) — Four-address central-sector grading and complete native indicator; finite construction.
+- [Flat-seed field bank and six-T decoder](depth/FLAT_FIELD_BANK_PILOT.md) — Four-address non-Clifford bank, six-T decoder and complete indicator; finite construction.
+- [Projective field recoupler](depth/PROJECTIVE_FIELD_RECOUPLER.md) — Eight-address decoders with and without returned helpers; exponential line enumeration limits scaling.
+- [Complete field decoder Pauli domain](depth/FIELD_DECODER_PAULI_DOMAIN.md) — Full-intertwiner axis/count bound; independent cells fail even with joint Clifford walls and moving helpers.
+- [Weak complete-probe Pauli domain](depth/WEAK_PROBE_PAULI_DOMAIN.md) — Weaker complete-probe domain and independent-cell error floors, including moving decoded helpers.
+- [Disjoint-span two-band field decoders](depth/TWO_BAND_FIELD_DECODER_OBSTRUCTION.md) — Disjoint absorbed spans fail at fixed error; overlapping spans remain outside the screen.
+- [Scalar-field radical copy screen](depth/SCALAR_FIELD_RADICAL_COPY_SCREEN.md) — Scalar-shear algebra-automorphism model fails for every address embedding.
+- [Clifford seed copy structure](depth/CLIFFORD_SEED_COPY_STRUCTURE.md) — Separate commuting-symplectic-orbit and one-band-copy screens for Clifford seeds.
 - [Joint bank routing and the complete dirty indicator](depth/JOINT_ROUTING_INDICATOR_INTERFACES.md)
 
 ## Constructive components and source candidates
@@ -212,15 +219,15 @@ These are complete interfaces and conditional transfers, not constructions of th
 Each home separates its paid native operations from its first unpaid conversion. A scalar predicate, forward XOR query, inverse-column formula or trace character is not by itself a normalized complete indicator.
 
 - [Exact two-layer quadratic queries with one returned dirty qubit](depth/QUADRATIC_NATIVE_QUERY.md)
-- [Parallel weighted-cubic phases with returned dirty work](depth/DIRTY_CUBIC_PHASE_COMPILER.md) — an exact thirteen-band compiler with shared logical controls and paid coefficient-cube parity layers
-- [Local HRT operations and complete coherent feedback](depth/COHERENT_FEEDBACK_SOURCES.md) — exact local encoded Hadamards, [twenty-four-band pair-star fusion](depth/COHERENT_FEEDBACK_SOURCES.md#pair-star-hadamard-fusion), and complete feedback repairs that retain the forward/inverse-coordinate mismatch
+- [Parallel weighted-cubic phases with returned dirty work](depth/DIRTY_CUBIC_PHASE_COMPILER.md) — Paid parallel cubic phase compiler with shared controls and coefficient-cube parity layers.
+- [Local HRT operations and complete coherent feedback](depth/COHERENT_FEEDBACK_SOURCES.md) · [twenty-four-band pair-star fusion](depth/COHERENT_FEEDBACK_SOURCES.md#pair-star-hadamard-fusion) — Encoded Hadamards and complete feedback repairs; forward/inverse-coordinate mismatch remains.
 - [Balanced native compilation of the HRT algebra permutations](depth/BALANCED_ALGEBRA_PERMUTATION.md)
 - [Full-input algebra queries and fast returned multiplication](depth/ALGEBRA_QUERY_EXTRACTION.md)
 - [A complete bank from one nonlinear algebra source](depth/FULL_BANK_CHARACTER_TRANSPORT.md) — [quadratic-inverse component](depth/FULL_BANK_CHARACTER_TRANSPORT.md#5-the-quadratic-inverse-has-a-paid-xor-query-not-a-paid-in-place-map) · [coherent-correction audit](depth/FULL_BANK_CHARACTER_TRANSPORT.md#6-the-choi-basis-is-paid-its-coherent-x-correction-is-not)
 - [Direct output readout and the weaker algebra-source contract](depth/OUTPUT_ALIASED_CHARACTER_SOURCE.md) — [direct output version](depth/OUTPUT_ALIASED_CHARACTER_SOURCE.md#3-the-arbitrary-key-correction-has-the-same-weaker-return-interface)
 - [Complete observable transport and the shared-key source limit](depth/OBSERVABLE_TRANSPORT_SOURCE.md)
 - [A nonhomomorphic affine-pencil source for the complete bank](depth/NILPOTENT_PENCIL_OBSERVABLE_SOURCE.md) — [paired projector-Gram interface](depth/NILPOTENT_PENCIL_OBSERVABLE_SOURCE.md#paired-projector-readout) · [one-clean two-band case](depth/NILPOTENT_PENCIL_OBSERVABLE_SOURCE.md#two-band-projector-gram-gap) · [four-call recovery](depth/NILPOTENT_PENCIL_OBSERVABLE_SOURCE.md#four-call-gram-readout) · [joint two-clean recovery](depth/NILPOTENT_PENCIL_OBSERVABLE_SOURCE.md#two-clean-joint-gram-readout) · [latent-center interface](depth/NILPOTENT_PENCIL_OBSERVABLE_SOURCE.md#latent-center-readout)
-- [A paid constant-depth approximate zero reflection](depth/EXPANDER_ZERO_REFLECTION.md) — [exact shared address stage](depth/EXPANDER_ZERO_REFLECTION.md#synchronized-anchored-generator-stage), [mixed-selector return failure](depth/EXPANDER_ZERO_REFLECTION.md#mixed-selector-commutator), [paid quarter-phase stage](depth/EXPANDER_ZERO_REFLECTION.md#quarter-phase-selector-stage), and [actual one-clean source](depth/EXPANDER_ZERO_REFLECTION.md#quarter-phase-flip-difference-source) with a nontrivial accepted fiber but wrong complete-bank Gram
+- [A paid constant-depth approximate zero reflection](depth/EXPANDER_ZERO_REFLECTION.md) · [exact shared address stage](depth/EXPANDER_ZERO_REFLECTION.md#synchronized-anchored-generator-stage) · [mixed-selector return failure](depth/EXPANDER_ZERO_REFLECTION.md#mixed-selector-commutator) · [paid quarter-phase stage](depth/EXPANDER_ZERO_REFLECTION.md#quarter-phase-selector-stage) · [actual one-clean source](depth/EXPANDER_ZERO_REFLECTION.md#quarter-phase-flip-difference-source) — Paid zero reflection and quarter-phase source; complete-bank Gram remains wrong.
 - [Coherent counters: an exact odd-key code and the missing native schedule](depth/COHERENT_COUNTER_SOURCE.md) — [counter revision](depth/COHERENT_COUNTER_SOURCE.md#9-one-pass-row-filters-clean-dimension-error-and-dirty-mixing)
 - [Exact arithmetic with virtual Boolean functions and dirty work](depth/VIRTUAL_FUNCTION_ARITHMETIC.md)
 - [Complete bank difference: a paid nonlinear merge and its depth cost](depth/COMPLETE_BANK_DIFFERENCE.md)
@@ -238,6 +245,8 @@ Each home separates its paid native operations from its first unpaid conversion.
 
 Use these only with their stated actual-boundary, fiber, normalization or source-call premises. The read-only two-band compression bound differs from the one-clean two-band Gram screen in the pencil proof; neither is a dimension-growing unrestricted depth theorem.
 
+### Band, selector and transport screens
+
 - [Complete two-band sources with native read-only address](depth/READ_ONLY_TWO_BAND_SOURCE_GAP.md)
 - [A Clifford-sum gap excludes bounded-clean two-band indicator sources](depth/FIXED_CLIFFORD_SUM_SOURCE_GAP.md) — [rank--norm refinement](depth/FIXED_CLIFFORD_SUM_SOURCE_GAP.md#10-rank-norm-bounds-sharpen-the-exact-and-finite-error-source-screen) · [bounded-clean projector-Gram screen](depth/FIXED_CLIFFORD_SUM_SOURCE_GAP.md#bounded-clean-two-band-gram-screen)
 - [Clifford averages cannot select the complete lookup eigenspace](depth/CLIFFORD_LOOKUP_FIXED_SPACE.md)
@@ -246,52 +255,61 @@ Use these only with their stated actual-boundary, fiber, normalization or source
 - [Simultaneous output parities and native support rank](depth/SIMULTANEOUS_OUTPUT_PARITY_LIMITS.md)
 - [Limits of structured frames for spectral promotion](depth/SPECTRAL_PROMOTION_FRAME_LIMITS.md)
 - [Crossed cubic kernels and complete observable transport](depth/CROSSED_CUBIC_KERNEL_SOURCE.md) — [normalized forward source](depth/CROSSED_CUBIC_KERNEL_SOURCE.md#normalized-forward-gram-source) · [Clifford signal-image gap](depth/CROSSED_CUBIC_KERNEL_SOURCE.md#clifford-signal-gram-gap) · [normalized half-bilinear trial](depth/CROSSED_CUBIC_KERNEL_SOURCE.md#normalized-half-bilinear-source) · [XOR-carry trial and changed acceptance question](depth/CROSSED_CUBIC_KERNEL_SOURCE.md#normalized-xor-carry-source); constructed words retain wrong lookup sectors
-- [Signal-interleaved kernel sources](depth/SIGNAL_INTERLEAVED_KERNEL_SOURCE.md) — complete native Grams, unequal-branch rejection, all-call tail-bank commutant obstruction, and a changed-bank three-query finite failure
-- [Coupled quarter-phase sources](depth/COUPLED_QUARTER_PHASE_SOURCE.md) — paid two-stage and four-path words, full-bank relative action, scalar-filter collision, coherent Gram defect and exact row-selective partial source
-- [Quarter-phase matching limits](depth/QUARTER_PHASE_MATCHING_LIMITS.md) — simultaneous matching ledger, row covariance, heterogeneous-signature and bipartition invariants, and a uniform one-row dressed-expander gap
-- [Complete bank response and row isolation](depth/BANK_BIT_RESPONSE_AND_ROW_ISOLATION.md) — surviving background conjugation, exact two-row defect, fixed-row SELECT, aggregation costs and the restricted affine-cube collision
-- [Co-moving lookup stages](depth/CO_MOVING_LOOKUP_STAGE.md) — paid charge-preserving bank motion, exact global echo, even-bank and transplanted four-path failures, and the remaining complete acceptance identity
-- [Co-moving selector readout](depth/CO_MOVING_SELECTOR_READOUT.md) — paid address-relative Hadamard tags and their controlled sources, full-bank sector identity, covariant orbit-pair singlet limit, and affine singleton transport
-- [Entangling selector acceptance](depth/ENTANGLING_SELECTOR_ACCEPTANCE.md) — paid Clifford/non-Clifford selector controls; complete-call and cell-crossing rank limits; retained finite nonlocal evidence, sector separator, fixed-row central word, paid address-transport boundary and square-stage affine-Pauli limit
-- [Bank-coupled selector dynamics](depth/BANK_COUPLED_SELECTOR_DYNAMICS.md) — paid bank swaps/Hadamards and their signal controls, complete principal-work dynamics, an all-size Bell-cell witness for the specified nonlocal frames, and a finite bank-Hadamard source excluded by its complete marked path Gram
-- [MOD3 zeta transport](depth/MOD3_ZETA_TRANSPORT.md) — binary order-three blocks, paid native baselines and shared cleanup, a native two-band exclusion, and exactness of three-layer observable approximation below the fixed gap; sublogarithmic joint transport remains unpaid
-- [Weak Pauli orbit compression](depth/WEAK_PAULI_ORBIT_COMPRESSION.md) — native single-coordinate and joint two-coordinate sources, complete two-address lookup, four-band nested coefficients, [two-band coefficient shear and complete assembly](depth/WEAK_PAULI_ORBIT_COMPRESSION.md#complete-coefficient-shear) with a paused linear-depth recurrence, and scoped product/prefix-rank/final-block limits
-- [Native fusion of complete coefficient shears](depth/COEFFICIENT_SHEAR_NATIVE_FUSION.md) — exact completed exchanges, failed half-band regrouping, a uniform-angle bipartite word gap, and scoped common-Clifford-basis and dirty-replica screens
-- [Coordinate-weighted pulse limits](depth/COORDINATE_WEIGHTED_PULSE_LIMITS.md) — paid coordinate and tail-dependent quarter angles, robust signature collisions, and the directed-filtration lower bound on total pulses; Clifford pulses are not charged as T layers
-- [Clifford-interleaved lookup](depth/CLIFFORD_INTERLEAVED_LOOKUP.md) — the two-block gap, sharp Clifford-fiber block count, and a three-block requirement for later key mixing even with an arbitrary global third-level prefix; the long physical Clifford-zeta frame remains failed
-- [Unrestricted three-band lookup sources](depth/THREE_BAND_LOOKUP_SOURCE_OBSTRUCTION.md) — point-mask rank and native-axis independence force the last two absorbed bands to preserve the address for p at least five; the degree-six boundary excludes every three-layer source for p at least seven, with a uniform complete-error floor
-- [Clifford involution source](depth/CLIFFORD_INVOLUTION_SOURCE.md) — four native bands, linear T count and no helpers for every traceless Hermitian Clifford; two-outer-conjugation reduction and an exact Galois symmetry screen
-- [Complete Clifford symmetries of lookup](depth/LOOKUP_CLIFFORD_SYMMETRIES.md) — exact normal form, uniform operator-norm rounding and address-algebra preservation for p at least three, with arbitrary dirty helpers and a genuine two-bit address/bank-mixing exception
-- [Joint address, carrier and helper source](depth/JOINT_ADDRESS_HELPER_SOURCE.md) — paid quartic-face trials and repair, a nonmonomial Hadamard-pair gap with a weighted-phase escape, and the fixed-coefficient versus arbitrary-coefficient boundary; no all-size shallow source
-- [Coherent central transport](depth/COHERENT_CENTRAL_TRANSPORT.md) — [reduced pair-register gauge](depth/COHERENT_CENTRAL_TRANSPORT.md#reduced-carrier-gauge), general carrier-linear root criterion, four-band root completion, partial character basis, and sharp scoped polarization-query bounds
-- [Ordered-matching probe source](depth/ORDERED_MATCHING_PROBE_SOURCE.md) — one matching per subset, common-point native fusion, and a minimal-tree specialization with linear T count and no private work; depth remains linear
-- [Fixed-readout syndrome bound](depth/FIXED_READOUT_SYNDROME_BOUND.md) — complete lookup requires near-full syndrome dimension after low-degree Pauli transport, even with an arbitrary fixed non-Clifford readout; a query-grammar bound, not native-depth optimality
-- [Interleaved tree-probe algebra](depth/INTERLEAVED_TREE_PROBE_SOURCE.md) — paid later-address wall, literal Pauli phases, full commutation rank, and one-query error floors allowing arbitrary non-Clifford probes; two opposite queries leave those premises
-- [Clifford-orbit query rank](depth/CLIFFORD_ORBIT_QUERY_RANK.md) — faithful normal-Pauli phase lift and multiplicative group rank require at least ceiling(p/8) literal affine queries for a Clifford starting reflection and arbitrary fixed decoder, even at small fixed error
-- [Two-address interleaved pilot](depth/TWO_ADDRESS_INTERLEAVED_PILOT.md) — a complete controlled-Hadamard family with a paid fixed Clifford decoder, native source and actual inverse; a finite benchmark, not an asymptotic gain
-- [Non-Clifford seed spread](depth/NONCLIFFORD_SEED_SPREAD.md) — exact Pauli-algebra and robust quantum random-access bounds force a broad seed for bounded affine queries; a paid extensive seed and its local-decoder limit separate seed count from native depth
-- [Field-shear intertwiner](depth/FIELD_SHEAR_INTERTWINER.md) — paid query and native two-bit decoder, spectator count, Bell-fiber redistribution, helper-valued probe freedom, and exclusion of exact seeds diagonal in any query-invariant stabilizer basis
-- [Recursive field-shear decoder](depth/RECURSIVE_FIELD_SHEAR_DECODER.md) — all-size identity-helper algebraic intertwiner with full zero sectors, dense native queries and paid multiplication-XOR batches; the original in-place maps remain uncompiled, while the augmented helper-query construction pays a different complete decoder
-- [Augmented field recoupler](depth/AUGMENTED_FIELD_RECOUPLER.md) — uniform native field-plus-Pauli-helper intertwiner with shared moving helpers and complete indicator return; two multiplication-XOR batches per level give $`16(p-1)`$ decoder bands and the specific relaxed fusion count/width/gate budgets, but depth still fails the discovery target
-- [Clifford-sector degree barrier](depth/FIELD_SECTOR_DEGREE_BARRIER.md) — helper shift rank and helper-tableau degree at least $`p-1`$ for full field intertwiners with Clifford sectors; the augmented construction attains the degree, so fixed-frame helper-affine stages cannot compress to a bounded number, while unrestricted native words remain outside the screen
-- [Dirty Choi teleportation and a sufficient residual probe](depth/DIRTY_CHOI_OBSERVABLE_SOURCE.md) — complete standard/group Bell diagnostics and four-phase/eight-source extraction, with one-bank polarization and safe output/carrier aliases reducing dirty width
-- [Coupled final encoders](depth/COUPLED_FINAL_ENCODER.md) — paid address/tag and bank-motion sources, scoped three-layer boundaries, the corrected relative involution, and complete-transition failures of retained repairs
-- [Coupled order interference](depth/COUPLED_ORDER_GRAM_SOURCE.md) — actual joint word, robust direct square readout for balanced two-unitary sources, paid anchors and two distinct finite failed bank-moving trials
-- [Affine orbit reflection source](depth/AFFINE_ORBIT_REFLECTION_SOURCE.md) — paid fixed-point-free charge-preserving motion and orbit coordinates, exact diagonal phase cochains, sharp phase-degree scope and a failed local anchor
-- [Transverse orbit reflections](depth/TRANSVERSE_ORBIT_REFLECTION_SOURCE.md) — arbitrary controlled-dressing normalization, a paid non-diagonal square-root trial and its all-size sector error; the affine orbit is a charge-preserving native change of coordinates
-- [Boolean reflection Gram sources](depth/BOOLEAN_REFLECTION_GRAM_SOURCE.md) — exact spectral Boolean queries without clean work, paid controlled quarter phases, full reflection-product Gram criterion and the flat-mixer sector obstruction
-- [A normalized scalar-kernel partial source](depth/SCALAR_KERNEL_FILTER_SOURCE.md) — correct-charge support, native/error ledger and fixed-diagonal rigidity; a paid rank-one determinant query still has a thin, wrong-sector scalar echo
-- [Corank-one Fourier kernels and Bell acceptance](depth/CORANK_FOURIER_BELL_SOURCE.md) — complete Bell dilation, normalized thin and broad sources, coherent-sector failures, and transfer of the complete charge-readout error to auxiliary acceptance
+- [Signal-interleaved kernel sources](depth/SIGNAL_INTERLEAVED_KERNEL_SOURCE.md) — Complete Grams and tail-bank commutant screen; changed-bank three-query trial fails.
+- [Coupled quarter-phase sources](depth/COUPLED_QUARTER_PHASE_SOURCE.md) — Paid path words, complete relative action and row-selective partial source; scalar and Gram defects remain.
+- [Quarter-phase matching limits](depth/QUARTER_PHASE_MATCHING_LIMITS.md) — Matching/row-covariance invariants and the one-row dressed-expander gap.
+- [Complete bank response and row isolation](depth/BANK_BIT_RESPONSE_AND_ROW_ISOLATION.md) — Two-row defect, fixed-row SELECT and aggregation costs; affine-cube collision is scoped.
+- [Co-moving lookup stages](depth/CO_MOVING_LOOKUP_STAGE.md) — Paid bank motion and global echo; retained trials fail complete acceptance.
+- [Co-moving selector readout](depth/CO_MOVING_SELECTOR_READOUT.md) — Address-relative tags and full-bank sectors; covariant orbit-pair singlet limit.
+- [Entangling selector acceptance](depth/ENTANGLING_SELECTOR_ACCEPTANCE.md) — Paid selector controls, call/crossing-rank limits and retained nonlocal components; affine-Pauli screen is scoped.
+- [Bank-coupled selector dynamics](depth/BANK_COUPLED_SELECTOR_DYNAMICS.md) — Paid bank/signal controls and Bell-cell witness; the bank-Hadamard trial fails its full Gram.
+- [MOD3 zeta transport](depth/MOD3_ZETA_TRANSPORT.md) — Paid order-three baselines and two-band/three-layer screens; sublogarithmic joint transport remains unpaid.
+- [Weak Pauli orbit compression](depth/WEAK_PAULI_ORBIT_COMPRESSION.md) · [two-band coefficient shear and complete assembly](depth/WEAK_PAULI_ORBIT_COMPRESSION.md#complete-coefficient-shear) — Paid coefficient shears and complete assembly; the paused recurrence has linear depth and scoped rank limits.
+- [Native fusion of complete coefficient shears](depth/COEFFICIENT_SHEAR_NATIVE_FUSION.md) — Complete exchanges; regrouping, fixed-angle and common-basis/replica screens.
+- [Coordinate-weighted pulse limits](depth/COORDINATE_WEIGHTED_PULSE_LIMITS.md) — Paid quarter angles and total-pulse bounds; Clifford pulses are not T layers.
+- [Clifford-interleaved lookup](depth/CLIFFORD_INTERLEAVED_LOOKUP.md) — Clifford-fiber block limits and later-key-mixing requirement; the long Clifford-zeta trial fails.
+- [Unrestricted three-band lookup sources](depth/THREE_BAND_LOOKUP_SOURCE_OBSTRUCTION.md) — Unrestricted zero-clean three-band source screen with a fixed complete-error floor; no growing frame-depth bound.
+### Probe and orbit mechanisms
+
+- [Clifford involution source](depth/CLIFFORD_INVOLUTION_SOURCE.md) — Paid four-band traceless Hermitian-Clifford source and scoped conjugation/Galois screens.
+- [Complete Clifford symmetries of lookup](depth/LOOKUP_CLIFFORD_SYMMETRIES.md) — Exact lookup normal form, robust rounding and address preservation; two-bit mixing exception.
+- [Joint address, carrier and helper source](depth/JOINT_ADDRESS_HELPER_SOURCE.md) — Paid quartic trials/repair and weighted-phase alternative; fixed and arbitrary coefficients have different scope.
+- [Coherent central transport](depth/COHERENT_CENTRAL_TRANSPORT.md) · [reduced pair-register gauge](depth/COHERENT_CENTRAL_TRANSPORT.md#reduced-carrier-gauge) — Carrier-linear root criterion, four-band completion and scoped polarization-query bounds.
+- [Ordered-matching probe source](depth/ORDERED_MATCHING_PROBE_SOURCE.md) — Paid matching fusion and minimal-tree query; depth remains linear.
+- [Fixed-readout syndrome bound](depth/FIXED_READOUT_SYNDROME_BOUND.md) — Near-full syndrome requirement after low-degree Pauli transport; query grammar, not unrestricted depth.
+- [Interleaved tree-probe algebra](depth/INTERLEAVED_TREE_PROBE_SOURCE.md) — Paid later-address wall and one-query error floors with arbitrary probes; opposite-query words lie outside.
+- [Clifford-orbit query rank](depth/CLIFFORD_ORBIT_QUERY_RANK.md) — Literal affine-query lower bound with a Clifford starting reflection and arbitrary fixed decoder.
+- [Two-address interleaved pilot](depth/TWO_ADDRESS_INTERLEAVED_PILOT.md) — Complete controlled-Hadamard source, paid decoder and actual inverse; finite benchmark.
+- [Non-Clifford seed spread](depth/NONCLIFFORD_SEED_SPREAD.md) — Exact and robust seed-spread bounds; extensive paid seed does not imply shallow decoding.
+### Field query and decoder chain
+
+The algebraic decoder, augmented native decoder and sector-degree screen use
+different helper contracts. Follow those contracts through the complete echo.
+
+- [Field-shear intertwiner](depth/FIELD_SHEAR_INTERTWINER.md) — Paid field query, two-bit decoder and helper-valued probe freedom; invariant-stabilizer seeds fail.
+- [Recursive field-shear decoder](depth/RECURSIVE_FIELD_SHEAR_DECODER.md) — All-size algebraic intertwiner and paid XOR batches; original in-place maps remain uncompiled.
+- [Augmented field recoupler](depth/AUGMENTED_FIELD_RECOUPLER.md) — Uniform paid field/helper intertwiner and full return within relaxed fusion budgets; linear depth remains.
+- [Clifford-sector degree barrier](depth/FIELD_SECTOR_DEGREE_BARRIER.md) — Sharp helper-tableau degree requirement for Clifford sectors; fixed-frame affine-stage screen only.
+### Gram, Bell and scalar-source screens
+
+- [Dirty Choi teleportation and a sufficient residual probe](depth/DIRTY_CHOI_OBSERVABLE_SOURCE.md) — Complete Bell diagnostics and residual-probe extraction; paid polarization and width reductions.
+- [Coupled final encoders](depth/COUPLED_FINAL_ENCODER.md) — Paid address/tag and bank-motion components; retained repairs fail complete transition.
+- [Coupled order interference](depth/COUPLED_ORDER_GRAM_SOURCE.md) — Balanced two-unitary square readout and paid anchors; two finite bank-moving trials fail.
+- [Affine orbit reflection source](depth/AFFINE_ORBIT_REFLECTION_SOURCE.md) — Paid charge-preserving motion and phase cochains; scoped degree bound and failed local anchor.
+- [Transverse orbit reflections](depth/TRANSVERSE_ORBIT_REFLECTION_SOURCE.md) — Controlled-dressing normalization; paid non-diagonal trial has an all-size sector error.
+- [Boolean reflection Gram sources](depth/BOOLEAN_REFLECTION_GRAM_SOURCE.md) — Paid spectral queries/quarter phases and full Gram criterion; flat-mixer sector obstruction.
+- [A normalized scalar-kernel partial source](depth/SCALAR_KERNEL_FILTER_SOURCE.md) — Normalized partial source and fixed-diagonal rigidity; paid determinant query has the wrong scalar sector.
+- [Corank-one Fourier kernels and Bell acceptance](depth/CORANK_FOURIER_BELL_SOURCE.md) — Complete Bell dilation and normalized sources; coherent-sector failures and acceptance-error transfer.
 - [Two complete key-mixing tests for observable transport](depth/KEY_MIXING_OBSERVABLE_SCREENS.md)
 - [Gaussian compression with a small clean signal](depth/GAUSSIAN_COMPRESSION_SOURCE_LIMITS.md)
-- [Clifford projector-Gram rigidity](depth/CLIFFORD_PROJECTOR_GRAM.md) — singular accepted Grams of fully interleaved Clifford fibers; clean-signal rigidity and a separate read-only affine-query count boundary
+- [Clifford projector-Gram rigidity](depth/CLIFFORD_PROJECTOR_GRAM.md) — Interleaved Clifford-fiber Gram rigidity; separate read-only affine-query bound.
 - [Involutory Gaussian loops and their unsquared scalar limit](depth/INVOLUTORY_GAUSS_SOURCE_LIMITS.md)
 - [Scalar phases of closed Gaussian circuits have bounded degree](depth/GAUSSIAN_SCALAR_LOOP_OBSTRUCTION.md)
 - [Complete-input limits of two approximate equality filters](depth/APPROXIMATE_INDICATOR_FILTER_LIMITS.md)
 - [Phase-signal and coherent-frame interfaces for complete queries](depth/PHASE_SIGNAL_QUERY_LIMITS.md)
 - [Dirty geometric phase loops and the complete-bank cost](depth/DIRTY_GEOMETRIC_PHASE_LOOPS.md)
 - [Joint detuning and the cost of independent fine-angle replacement](depth/JOINT_DETUNING_PRECISION_LIMITS.md)
-- [Native sharing and complete-probe support](depth/NATIVE_INDICATOR_SHARING.md) — unrestricted incidence and robust linear source-count constraints; no growing-depth conclusion
+- [Native sharing and complete-probe support](depth/NATIVE_INDICATOR_SHARING.md) — Incidence and robust linear source-count constraints; no growing-depth conclusion.
 - [The count cost of replacing two indicators by many](depth/MULTIWAY_QUERY_COST_BARRIER.md)
 - [A source-count barrier for symplectic commutator readout](depth/SYMPLECTIC_MODULE_QUERY_BARRIER.md) — [universal-probe conversion](depth/SYMPLECTIC_MODULE_QUERY_BARRIER.md#6-universal-pauli-probes-contain-a-complete-dirty-indicator) · [all R98 word-query budgets](depth/SYMPLECTIC_MODULE_QUERY_BARRIER.md#7-the-complete-r98-word-query-interface-follows-conditionally) · [Walsh phase attempt](depth/SYMPLECTIC_MODULE_QUERY_BARRIER.md#71-a-dense-walsh-phase-program-does-not-supply-the-faster-source)
 - [An exact T-count barrier for the separate Walsh dual readout](depth/DUAL_FRAME_READOUT_BARRIER.md)
@@ -404,90 +422,111 @@ individual limitations do not obstruct the later complete-column compiler.
 
 ## Session records and designs
 
-These records preserve decisions, failed attempts, supporting derivations and
-the scope known at each checkpoint. Their next-step instructions are historical
-unless reaffirmed in the working checkpoint. A design prompt is not a theorem.
-The records below keep every retained outcome and design discoverable from
-this catalogue.
-
-- [Continuation: amplitude-uniform source limits and a paid joint detuning](depth/AMPLITUDE_UNIFORM_SOURCE_RESULT.md)
-- [Revision: complete bank motion is paid; a shallow source remains missing](depth/BANK_MOTION_CONTINUATION_RESULT.md)
-- [Five-hour design: move precision into borrowed work](depth/BORROWED_PRECISION_BRIDGE_PROMPT.md)
-- [Borrowed precision and direct programming: execution outcome](depth/BORROWED_PRECISION_BRIDGE_SESSION_RESULT.md)
-- [Branch-orientation depth session](depth/BRANCH_ORIENTATION_SESSION_RESULT.md)
-- [Five-hour design: carry the workspace through the catalogue](depth/CATALOGUE_BOOTSTRAP_PROMPT.md)
-- [Catalogue bootstrap session: the local compiler carries its workspace](depth/CATALOGUE_BOOTSTRAP_SESSION_RESULT.md)
-- [Revision: constant translations and approximate query transfer](depth/CENTRAL_COCYCLE_SESSION_RESULT.md)
-- [Revision: fix one genuine parity before counting matrix features](depth/CENTRAL_PARITY_REVISION_RESULT.md)
-- [Revision: one algebra source serves the whole indicator bank](depth/CHARACTER_SOURCE_REVISION_RESULT.md)
-- [Clean-code revision and a paid algebra recovery](depth/CLEAN_CODE_ALGEBRA_SESSION_RESULT.md)
-- [Revision: a paid clean-source route to the dirty indicator](depth/CLEAN_PROMOTION_SESSION_RESULT.md)
-- [Revision: clean-transition phase and representation cost](depth/CLEAN_TRANSITION_PHASE_SESSION_RESULT.md)
-- [Revision: weaker coherent sources and uniform all-active one-pair closure](depth/COHERENT_SOURCE_AND_ONE_PAIR_RESULT.md)
-- [Product-coin continuation: causal batching and recursive depth](depth/COIN_CONTINUATION_SESSION_RESULT.md)
-- [Revision: the computational phase and the complete native source](depth/COMPUTATIONAL_PHASE_SESSION_RESULT.md)
+Consult these when a proof or route decision leaves an unresolved derivation,
+failed attempt or design choice to recover. They retain the scope known at the
+time; their instructions are historical unless WORKSPACE reaffirms them.
+Prompts are labelled **design**, and do not establish results. Cross-topic
+records are filed under their principal mechanism; original filenames remain
+searchable. Every retained record is linked below.
+
+[Sources/readout](#source-acceptance-and-readout-records) ·
+[Transfers](#transfer-and-promotion-records) ·
+[Depth/precision](#complete-frame-depth-and-precision-records) ·
+[Native transport](#read-only-query-and-native-transport-records) ·
+[Clean codes/pairs](#clean-code-and-physical-pair-records)
+
+### Source, acceptance and readout records
+
+- [Amplitude-uniform source limits and a paid joint detuning](depth/AMPLITUDE_UNIFORM_SOURCE_RESULT.md)
+- [Complete bank motion is paid; a shallow source remains missing](depth/BANK_MOTION_CONTINUATION_RESULT.md)
+- [One algebra source serves the whole indicator bank](depth/CHARACTER_SOURCE_REVISION_RESULT.md)
+- [Weaker coherent sources and uniform all-active one-pair closure](depth/COHERENT_SOURCE_AND_ONE_PAIR_RESULT.md)
 - [Coupled incidence, signed normalization and a complete inverse query](depth/COUPLED_INCIDENCE_SESSION_RESULT.md)
-- [Joint encodings: unrestricted one-clean two-layer Boolean rigidity](depth/DIAGONAL_ENCODING_SESSION_RESULT.md)
-- [Revision: pay the readout before claiming a shallower source](depth/DIRTY_KEY_REVISION_RESULT.md)
+- [Pay the readout before claiming a shallower source](depth/DIRTY_KEY_REVISION_RESULT.md)
+- [Spectral promotion, zero tests and complete sources](depth/EXPANDER_AND_SOURCE_SCOPE_REVISION_RESULT.md)
+- [Gaussian readout, scalar phases and physical-center transport](depth/GAUSSIAN_AND_CENTER_REVISION_RESULT.md)
+- [Complete joint indicators and growing native displacement](depth/JOINT_INDICATOR_SESSION_RESULT.md)
+- [The complete selective word remains unpaid](depth/JOINT_SELECTIVE_CONTINUATION_RESULT.md)
+- [Native sharing and table-specific indicator probes](depth/NATIVE_SHARING_SESSION_RESULT.md)
+- [Keep the destination, change the source mechanism](depth/OBSERVABLE_SOURCE_REVISION_RESULT.md)
+- [Complete transitions from overlapping two-band sources](depth/OVERLAPPING_SOURCE_SESSION_RESULT.md)
+- [Parallel access is paid; selective dynamics remain missing](depth/PARALLEL_ACCESS_REVISION_RESULT.md)
+- [Pay parallel promotion, then test the complete source](depth/PARALLEL_PROMOTION_AND_KERNEL_REVISION_RESULT.md)
+- [Native source scope and complete projector readout](depth/READOUT_AND_NATIVE_SOURCE_REVISION_RESULT.md)
+- [Two-band source obstruction and the continuing physical-pair scout](depth/TWO_BAND_SOURCE_GAP_SESSION_RESULT.md)
+- [Zero-character source certificates and an intrinsic transport test](depth/ZERO_CHARACTER_SESSION_RESULT.md)
+
+### Transfer and promotion records
+
+- [A paid clean-source route to the dirty indicator](depth/CLEAN_PROMOTION_SESSION_RESULT.md)
 - [Dirty-query reformulation: execution outcome](depth/DIRTY_QUERY_SESSION_RESULT.md)
-- [Revision: spectral promotion, zero tests and complete sources](depth/EXPANDER_AND_SOURCE_SCOPE_REVISION_RESULT.md)
-- [Revision: retain the native middle and bound its probe action](depth/EXTERNAL_CENTER_SESSION_RESULT.md)
-- [Five-layer query continuation: a normalizer gap and two mechanism tests](depth/FIVE_LAYER_QUERY_SESSION_RESULT.md)
-- [Four-layer query closure: follow-up outcome](depth/FOUR_LAYER_QUERY_SESSION_RESULT.md)
-- [Five-hour design: read the complete flag and pay precision once](depth/FULL_FLAG_DEPTH_PROMPT.md)
+- [Keep the depth destination, relax the source count requirement](depth/INDICATOR_FUSION_REVISION_RESULT.md)
+- [Restored-address queries and the complete-frame transfer](depth/RESTORED_ADDRESS_SESSION_RESULT.md)
+
+### Complete-frame depth and precision records
+
+- [Runnable prompt for a five-hour depth research session](depth/RESEARCH_SESSION_PROMPT.md) — design
+- [Fixed-accuracy depth research session: execution record](depth/RESEARCH_SESSION_RESULT.md)
+- [Read the complete flag and pay precision once](depth/FULL_FLAG_DEPTH_PROMPT.md) — design
 - [Complete flags and local precision: execution outcome](depth/FULL_FLAG_DEPTH_SESSION_RESULT.md)
-- [Revision: Gaussian readout, scalar phases and physical-center transport](depth/GAUSSIAN_AND_CENTER_REVISION_RESULT.md)
-- [Five-hour design: general magnitudes from exposed clean space](depth/GENERAL_MAGNITUDE_RECOVERY_PROMPT.md)
+- [General magnitudes from exposed clean space](depth/GENERAL_MAGNITUDE_RECOVERY_PROMPT.md) — design
 - [General-magnitude recovery: session result](depth/GENERAL_MAGNITUDE_RECOVERY_SESSION_RESULT.md)
-- [Revision: keep the depth destination, relax the source count requirement](depth/INDICATOR_FUSION_REVISION_RESULT.md)
-- [Five-hour design: factor the interval recovery](depth/INTERVAL_RECOVERY_FACTORIZATION_PROMPT.md)
-- [Interval-recovery factorization: session result](depth/INTERVAL_RECOVERY_FACTORIZATION_SESSION_RESULT.md)
-- [Joint decoder and terminal depth session](depth/JOINT_DEPTH_SESSION_RESULT.md)
-- [Revision: complete joint indicators and growing native displacement](depth/JOINT_INDICATOR_SESSION_RESULT.md)
-- [Revision: joint defects, bounded relations, and the complete probe task](depth/JOINT_NONPAULI_TRANSPORT_SESSION_RESULT.md)
-- [Algebraic side results from the joint orientation session](depth/JOINT_ORIENTATION_DISCOVERY_NOTES.md)
-- [Five-hour design: joint orientation and recovery](depth/JOINT_ORIENTATION_RECOVERY_PROMPT.md)
+- [Branch-orientation depth session](depth/BRANCH_ORIENTATION_SESSION_RESULT.md)
+- [Joint orientation and recovery](depth/JOINT_ORIENTATION_RECOVERY_PROMPT.md) — design
 - [Joint orientation and recovery: session result](depth/JOINT_ORIENTATION_RECOVERY_SESSION_RESULT.md)
-- [Revision: the complete selective word remains unpaid](depth/JOINT_SELECTIVE_CONTINUATION_RESULT.md)
+- [Algebraic side results from the joint orientation session](depth/JOINT_ORIENTATION_DISCOVERY_NOTES.md)
+- [Joint decoder and terminal depth session](depth/JOINT_DEPTH_SESSION_RESULT.md)
+- [Factor the interval recovery](depth/INTERVAL_RECOVERY_FACTORIZATION_PROMPT.md) — design
+- [Interval-recovery factorization: session result](depth/INTERVAL_RECOVERY_FACTORIZATION_SESSION_RESULT.md)
+- [Product-coin continuation: causal batching and recursive depth](depth/COIN_CONTINUATION_SESSION_RESULT.md)
+- [Move precision into borrowed work](depth/BORROWED_PRECISION_BRIDGE_PROMPT.md) — design
+- [Borrowed precision and direct programming: execution outcome](depth/BORROWED_PRECISION_BRIDGE_SESSION_RESULT.md)
+- [Carry the workspace through the catalogue](depth/CATALOGUE_BOOTSTRAP_PROMPT.md) — design
+- [Catalogue bootstrap session: the local compiler carries its workspace](depth/CATALOGUE_BOOTSTRAP_SESSION_RESULT.md)
+- [Precision without repeated long-prefix work](depth/PRECISION_TERMINAL_PROMPT.md) — design
+- [Precision-terminal session: grouping the noncommuting middle](depth/PRECISION_TERMINAL_SESSION_RESULT.md)
+- [Compose the terminal with returned borrowed work](depth/TERMINAL_SOURCE_GAUGE_PROMPT.md) — design
+- [Whole-terminal session: logarithmic general depth](depth/TERMINAL_SOURCE_GAUGE_SESSION_RESULT.md)
+- [Precision-uniform follow-up: execution record](depth/UNIFORM_PRECISION_SESSION_RESULT.md)
+
+### Read-only query and native transport records
+
 - [Unrestricted two-layer queries: joint constraints and native return](depth/JOINT_TRANSFER_SESSION_RESULT.md)
-- [Revision: where the remaining native cubic defect can live](depth/MIDDLE_DEFECT_SESSION_RESULT.md)
+- [Three-layer queries: execution outcome](depth/THREE_LAYER_QUERY_SESSION_RESULT.md)
+- [Three-layer revision: a native degree invariant and a paid cubic query](depth/THREE_LAYER_NATIVE_SESSION_RESULT.md)
+- [Four-layer query closure: follow-up outcome](depth/FOUR_LAYER_QUERY_SESSION_RESULT.md)
+- [Five-layer query continuation: a normalizer gap and two mechanism tests](depth/FIVE_LAYER_QUERY_SESSION_RESULT.md)
 - [Native defects close the five-layer read-only degree gap](depth/NATIVE_DEFECT_SESSION_RESULT.md)
-- [Native partial conjugation: cube relations and returned phase mechanisms](depth/NATIVE_PARTIAL_ACTION_SESSION_RESULT.md)
-- [Revision: native sharing and table-specific indicator probes](depth/NATIVE_SHARING_SESSION_RESULT.md)
-- [Native Clifford transport and nonlinear returned characters](depth/NATIVE_TRANSPORT_SESSION_RESULT.md)
-- [Revision: non-Pauli clean codes and the cost of changing representations](depth/NONPAULI_BOUNDARY_SESSION_RESULT.md)
-- [Revision: keep the destination, change the source mechanism](depth/OBSERVABLE_SOURCE_REVISION_RESULT.md)
-- [Revision: logical transport, native algebra costs, and the remaining depth question](depth/OCCUPIED_TRANSPORT_SESSION_RESULT.md)
-- [Five-hour design: the unrestricted one-clean four-layer gap](depth/ONE_CLEAN_FOUR_LAYER_PROMPT.md)
-- [One-clean four-layer session: outer misalignment and the remaining gap](depth/ONE_CLEAN_FOUR_LAYER_SESSION_RESULT.md)
-- [Overlap-one closure and the cost of the cycle source](depth/ONE_OVERLAP_SESSION_RESULT.md)
-- [Revision: use Booleanity before resynthesizing negative singletons](depth/ORIGINAL_PAIR_COLLAPSE_RESULT.md)
-- [Continuation: complete transitions from overlapping two-band sources](depth/OVERLAPPING_SOURCE_SESSION_RESULT.md)
-- [Revision: parallel access is paid; selective dynamics remain missing](depth/PARALLEL_ACCESS_REVISION_RESULT.md)
-- [Revision: pay parallel promotion, then test the complete source](depth/PARALLEL_PROMOTION_AND_KERNEL_REVISION_RESULT.md)
-- [The in-place permutation checkpoint](depth/PERMUTATION_BRIDGE_SESSION_RESULT.md)
-- [Five-hour design: precision without repeated long-prefix work](depth/PRECISION_TERMINAL_PROMPT.md)
-- [Precision-terminal session: grouping the noncommuting middle](depth/PRECISION_TERMINAL_SESSION_RESULT.md)
-- [Historical revision: native source scope and complete projector readout](depth/READOUT_AND_NATIVE_SOURCE_REVISION_RESULT.md)
-- [Runnable prompt for a five-hour depth research session](depth/RESEARCH_SESSION_PROMPT.md)
-- [Fixed-accuracy depth research session: execution record](depth/RESEARCH_SESSION_RESULT.md)
-- [Restored-address queries and the complete-frame transfer](depth/RESTORED_ADDRESS_SESSION_RESULT.md)
-- [Returned-query invariants: execution outcome](depth/RETURNED_QUERY_SESSION_RESULT.md)
-- [Native axes, scalar return and the missing relation](depth/RETURNED_RELATIONS_SESSION_RESULT.md)
-- [Revision: global native matching and the exact readout cost](depth/SHARED_CENTER_SESSION_RESULT.md)
 - [Six-layer Pauli comparisons and diagonal-source bounds](depth/SIX_LAYER_TRANSPORT_SESSION_RESULT.md)
 - [Span-preserving comparisons and the cost of returned sources](depth/SPAN_PRESERVING_SESSION_RESULT.md)
-- [Revision: remove the matrix core before counting its features](depth/STRUCTURAL_PAIR_REVISION_RESULT.md)
-- [Five-hour design: compose the terminal with returned borrowed work](depth/TERMINAL_SOURCE_GAUGE_PROMPT.md)
-- [Whole-terminal session: logarithmic general depth](depth/TERMINAL_SOURCE_GAUGE_SESSION_RESULT.md)
+- [Returned-query invariants: execution outcome](depth/RETURNED_QUERY_SESSION_RESULT.md)
+- [Native axes, scalar return and the missing relation](depth/RETURNED_RELATIONS_SESSION_RESULT.md)
+- [Native partial conjugation: cube relations and returned phase mechanisms](depth/NATIVE_PARTIAL_ACTION_SESSION_RESULT.md)
+- [Native Clifford transport and nonlinear returned characters](depth/NATIVE_TRANSPORT_SESSION_RESULT.md)
 - [Three native bands and a noncommutative return mechanism](depth/THREE_BAND_NONLINEAR_SESSION_RESULT.md)
-- [Three-layer revision: a native degree invariant and a paid cubic query](depth/THREE_LAYER_NATIVE_SESSION_RESULT.md)
-- [Three-layer queries: execution outcome](depth/THREE_LAYER_QUERY_SESSION_RESULT.md)
-- [Two-band source obstruction and the continuing physical-pair scout](depth/TWO_BAND_SOURCE_GAP_SESSION_RESULT.md)
+- [Overlap-one closure and the cost of the cycle source](depth/ONE_OVERLAP_SESSION_RESULT.md)
 - [Overlap-two sources, bounded-core transport, and commuting inverse pivots](depth/TWO_OVERLAP_SESSION_RESULT.md)
 - [Unbounded paired cores and controlled-Pauli transport](depth/UNBOUNDED_CONTROL_SESSION_RESULT.md)
-- [Precision-uniform follow-up: execution record](depth/UNIFORM_PRECISION_SESSION_RESULT.md)
-- [Zero-character source certificates and an intrinsic transport test](depth/ZERO_CHARACTER_SESSION_RESULT.md)
+- [The in-place permutation checkpoint](depth/PERMUTATION_BRIDGE_SESSION_RESULT.md)
+
+### Clean-code and physical-pair records
+
+- [The unrestricted one-clean four-layer gap](depth/ONE_CLEAN_FOUR_LAYER_PROMPT.md) — design
+- [One-clean four-layer session: outer misalignment and the remaining gap](depth/ONE_CLEAN_FOUR_LAYER_SESSION_RESULT.md)
+- [Joint encodings: unrestricted one-clean two-layer Boolean rigidity](depth/DIAGONAL_ENCODING_SESSION_RESULT.md)
+- [Clean-code revision and a paid algebra recovery](depth/CLEAN_CODE_ALGEBRA_SESSION_RESULT.md)
+- [Non-Pauli clean codes and the cost of changing representations](depth/NONPAULI_BOUNDARY_SESSION_RESULT.md)
+- [Logical transport, native algebra costs, and the remaining depth question](depth/OCCUPIED_TRANSPORT_SESSION_RESULT.md)
+- [Clean-transition phase and representation cost](depth/CLEAN_TRANSITION_PHASE_SESSION_RESULT.md)
+- [The computational phase and the complete native source](depth/COMPUTATIONAL_PHASE_SESSION_RESULT.md)
+- [Constant translations and approximate query transfer](depth/CENTRAL_COCYCLE_SESSION_RESULT.md)
+- [Joint defects, bounded relations, and the complete probe task](depth/JOINT_NONPAULI_TRANSPORT_SESSION_RESULT.md)
+- [Global native matching and the exact readout cost](depth/SHARED_CENTER_SESSION_RESULT.md)
+- [Retain the native middle and bound its probe action](depth/EXTERNAL_CENTER_SESSION_RESULT.md)
+- [Where the remaining native cubic defect can live](depth/MIDDLE_DEFECT_SESSION_RESULT.md)
+- [Fix one genuine parity before counting matrix features](depth/CENTRAL_PARITY_REVISION_RESULT.md)
+- [Remove the matrix core before counting its features](depth/STRUCTURAL_PAIR_REVISION_RESULT.md)
+- [Use Booleanity before resynthesizing negative singletons](depth/ORIGINAL_PAIR_COLLAPSE_RESULT.md)
 
 ## Attribution and reproducibility
 
diff --git a/research/ROUTE_DECISIONS.md b/research/ROUTE_DECISIONS.md
index 5e9c40e2..4888a406 100644
--- a/research/ROUTE_DECISIONS.md
+++ b/research/ROUTE_DECISIONS.md
@@ -8,45 +8,111 @@ operation or hypothesis needed to reopen it. Proofs, exact counterexamples
 and unique failed attempts remain in the linked homes. A representation
 limit, oracle-call bound or failed word is not an unrestricted depth bound.
 
+## Find the decision for the proposed operation
+
+Use [WORKSPACE](../WORKSPACE.md) to select the live question. Then read the
+relevant section here and its proof home before trying a variant. The sections
+below organize existing decisions by operation; their order is not a research
+priority or a claim that every route must be revisited.
+
+| Proposed work | Decision section |
+| --- | --- |
+| Complete indicator, encoded copy or rank-one phase | [Complete interfaces](#complete-interfaces) |
+| Field query, recursive decoder or helper motion | [Field recoupling](#field-recoupling) |
+| Small field pilot or a coupled decoder | [Finite calibrations](#finite-field-calibrations) · [decoder/probe screens](#field-decoder-screens) |
+| Joint seed and physical copy | [Seed/copy criteria and screens](#seed-and-copy) |
+| Gram recovery, clean promotion or weak fibers | [Paid interfaces](#gram-interfaces) · [candidate sources](#conditional-gram-sources-and-scalar-or-selector-components) |
+| Few native bands or Clifford block structure | [Native source screens](#native-source-screens) |
+| Pauli transport, tree probes or fixed decoding | [Transport components](#transport-components) |
+| A variant of a previously paid source word | [Stopped words and repairs](#stopped-source-words) |
+| Restricted two-band, query or acceptance grammar | [Representation limits](#source-specific-representation-limits) |
+| Physical-pair or other lower-bound scout | [Settled branches and reopening conditions](#lower-scouts-and-settled-earlier-questions) |
+| Joint precision synthesis | [Precision route](#joint-precision-route) |
+
+When a mechanism changes, revise its existing row and linked proof home.
+Keep the exact screened class and reopening condition together. WORKSPACE owns
+the live choice and next operation; this map owns reusable route assessments.
+A paid component can remain useful after its recorded complete word fails.
+
 ## Complete sources and promotion
 
 Start with a complete interface; consult component families only when the proposed source uses them.
 
+<a id="complete-interfaces"></a>
+
 ### Complete interfaces and resource-preserving reductions
 
 | Route | Present assessment | What would justify continuing |
 | --- | --- | --- |
 | [Polynomial-overhead complete source](depth/POLYNOMIAL_OVERHEAD_INDICATOR_FUSION.md) | Fusion, controlled use, return and count normalization are paid; the known source retains logarithmic depth. | A complete sublogarithmic source with uniform precision and simultaneous polynomial budgets. A single-output predicate is insufficient. |
 | [Encoded dirty copy](depth/ENCODED_DIRTY_COPY_INTERFACE.md) | A joint transition/copy echo gives the physical indicator while cancelling an abstract encoding on its returned dirty carrier. Polynomial-overhead fusion and R98 then apply. | Pay the encoded bank transition and its physical copy interaction, including actual inverses and full operator error. The abstract decoder need not be implemented, but its existence does not price either word. Use the grading and native-copy screens below before tuning a candidate. |
-| [Exact copy grading](depth/DIRTY_COPY_GRADING.md) | Vanishing traces of all nonzero-parity words exactly characterize copyable unitary families. Noncommuting examples exist; field-orbit reflections nevertheless have a common same-sign sector and a sharp pairwise anticommuting-target gap. | Supply a jointly paid seed and copy in the same coordinates. The explicit noncommuting example has a Clifford seed/copy but linear-depth wire translations; moving it to the cheap field query leaves those two operations unpaid. Arbitrary identity helpers cannot remove word-trace obstructions. |
-| [Native copy and dual support](depth/NATIVE_COPY_INTERACTION.md) | A native one-band non-Clifford component exists. General copy needs extensive T count for one field shear; exact dual readout needs extensive orbit support. Output-only Clifford mixing of product magic and the specified coded two-band family fail at growing size, including untouched helpers in the latter class. | Change the interaction beyond these classes, for example by mixing carrier and output before the phase gates or using noncommuting carrier phase axes. Prove complete dual readout and grade relations before claiming a scalable seed/copy pair. Extensive count fits the discovery budget and is not a depth obstruction. |
-| [Complete one-band copy feasibility](depth/ONE_BAND_COPY_FEASIBILITY.md) | Signed Walsh blocks give exact coefficient support spaces and spectra; complete copying also requires a carrier fixed point. All output duals can agree while the carrier action is wrong. The explicit triple-axis joint walls pass the tensor screen but have zero complete seed space for p at least two. Their full copy error is at least $`1/\sqrt6`$ for every unitary seed, with arbitrary dirty helpers. | Stop that family below its error floor. Choose changed uniform joint walls, solve the complete reduced equations, and exhibit a native seed. The bounded two-band seed-generator / one-band copy target would give a 42-band indicator if it succeeds. For other walls, empty kernels reject exact instances; approximation needs its own quantitative bounds. A finite fit or another necessary screen does not supply the all-size construction. |
-| [Affine Pauli-orbit copy](depth/PAULI_ORBIT_COPY_SCREEN.md) | At p at least two, Clifford dual output probes force copy error at least one quarter for an affine Pauli-query orbit; native one-band copies are included. The one-bit endpoint has a paid two-T, one-band copy and a complete returned-work echo. | Leave the affine Pauli-query or Clifford-dual-probe hypotheses. A dirty-mask extension of the field query has a paid gauge to Pauli translations, but that gauge can change copy depth; it does not transfer the one-band exclusion to the field shear. |
-| [Localized non-Clifford copy repair](depth/COPY_AXIS_SPAN.md) | A one-shear orbit requires at least $`m-p-1`$ independent physical-X directions in the copy rotation-axis span exactly, and an extensive span at constant error below square root two. | This span bound alone does not exclude a broad one-band copy; pay it jointly with the seed. This is a count/span screen, not a growing depth obstruction. |
-| [Monomial seed in query eigen-coordinates](depth/MONOMIAL_QUERY_SEED_OBSTRUCTION.md) | Copy error is at least one half for p at least two, even for arbitrary non-Clifford copies. The broader screen is commutation of original and seed-conjugated query algebras. | Break that algebra condition with genuine eigenspace mixing and certify the complete copy. Nonlinear reversible permutations or phases in the same query eigenbasis do not suffice. The all-Hadamard field seed passes the quantitative mixing test but still has a half-error floor from an order-three orbit-pair product. |
+| [Rank-one phase and complete indicator](depth/BANK_MIXING_AND_LOOKUP_PHASE.md#rank-one-indicator-equivalence) | Two-call reductions in both directions preserve the target resource orders, with a paid four-T-band control bank and arbitrary returned auxiliary work. General source representatives have the full commutant freedom of the probe X. | Treat the phase as an equivalent target, not an easier compiler. Seek a paid native representative with the complete derivative and return promise, possibly using address/work motion or synthesis across coordinate rounds. The linear T-count consequence gives no growing depth bound. |
+
+<a id="gram-interfaces"></a>
+
+### Gram recovery, clean promotion and weak-fiber interfaces
+
+| Route | Present assessment | What would justify continuing |
+| --- | --- | --- |
+| [Projector-Gram readout](depth/NILPOTENT_PENCIL_OBSERVABLE_SOURCE.md#paired-projector-readout) | Four-call recovery and serial promotion are paid: complete error $`64\sqrt\delta`$ for one clean signal, $`128\sqrt\delta`$ for two jointly accepted signals. The six-call block-error alternative remains. | A normalized native Gram source, allowing arbitrary accepted private fibers; actual source synthesis remains essential. |
+| [Spectral clean promotion](depth/MSS_SPECTRAL_PROMOTION.md) | Qualifies conditionally at $`k=o(\log(p+2))`$; uniform source accuracy and native address sharing are still required. | Supply an actual eligible source. Endpoint address return does not establish native sharing. |
+| [Exact packing and virtual arithmetic](depth/PARALLEL_CLEAN_PROMOTION.md), [arithmetic](depth/VIRTUAL_FUNCTION_ARITHMETIC.md) | Exact packing has a smaller sufficient window. Addition/multiplication/interval components do not pay full in-place radix compression; the spectral wrapper no longer needs it. | A complete rectangle-to-rank conversion whose total ledger improves on the paid wrapper, not another arithmetic component alone. |
+| [Balanced two-unitary acceptance](depth/COUPLED_ORDER_GRAM_SOURCE.md#balanced-two-unitary-gram-readout) | Gram error delta already gives a direct zero-clean squared relative word with error at most four delta plus four square-root delta. No control or promotion is needed for this extraction. | Supply that complete unitary identity, or change the balanced two-unitary interface. Other coefficients and genuine multipath acceptance retain their own obligations. |
+| [Four-path accepted fibers](depth/COUPLED_ORDER_GRAM_SOURCE.md#four-path-accepted-fibers) | A three-qubit native example has an exact half-projector Gram, nontrivial accepted polar motion and no cancelling pair of paths. The calibrated nonrectangular two-involution family instead forces its second involution to be identity below Gram error $`1/32`$. With the diagnostic phases, three independent Hermitian reflections also collapse to its original anticommuting pair under exact flatness, even with arbitrary block mixing. | Build the complete lookup Gram by joint cross-term interference; the one-qubit diagnostic is not lookup, and pairwise collapse cannot be assumed for arbitrary four-path sources. The exact three-reflection obstruction does not prove approximate rigidity; a different exact ansatz must change weights, phases or branch structure. Pay controls, normalization and every accepted fiber. |
+| [Output-alias weak fiber source](depth/OUTPUT_ALIASED_CHARACTER_SOURCE.md) | Four-call extraction cancels arbitrary private unitary fibers; the known source is not sublogarithmic. | A new weak fiber source, paired transform or whole extraction within the full polynomial budgets. |
+| [Single HRT residual probe](depth/DIRTY_CHOI_OBSERVABLE_SOURCE.md#one-bank-polarization) | Four residual-phase or eight probe-source calls suffice through one-bank quadratic polarization, with $`3m-2`$ principal dirty wires plus the private pool. A direct top phase needs $`2m-2`$. Standard/group Choi completions retain unpaid key conversion; parallel carrier-only readout loses input dependence. | The [paid feedback trial](depth/COHERENT_FEEDBACK_SOURCES.md) now tests one such coupling and fails. Restore its missing key response through a genuinely changed joint word, or synthesize the top phase directly. Its cubic bent dual is a dense kernel, not a diagonal implementation. The reduction is sufficient, not a converse or a new depth upper bound. |
+| [Approximate address-blind cache](depth/SHARED_PREFIX_QUERY_AUDIT.md#approximate-cache-capacity) | With bank-independent encoding and actual inverse decoding, the full bank needs $`2^c\ge2^p(1-\varepsilon^2/2)^2`$ initialized capacity below square-root-two error, even with arbitrary dirty and bank mixing. The small-clean spectral-promotion window does not repair this interface. | Retain address access during the bank operation, encode jointly with the bank, or establish another complete word. A smaller equality fingerprint or faster isolated zero test does not implement the arbitrary bank. |
+| [Clean-sector parallelism](depth/CLEAN_SECTOR_PARALLELISM_AUDIT.md) | A clean bank fixed at every native boundary can already be removed by restriction. General black-box promotion needs exponentially many source occurrences in clean count. | A genuinely different native schedule; logical call counts alone do not bound native depth. |
+
+<a id="field-recoupling"></a>
+
+## Field queries and recoupling
+
+| Route | Present assessment | What would justify continuing |
+| --- | --- | --- |
+| [Field-shear intertwiner](depth/FIELD_SHEAR_INTERTWINER.md) | The paid query has the full lookup character. Monomial/Clifford decoders and a preserved physical Bell zero fiber fail. An exact seed diagonal in any query-invariant stabilizer basis fails at p at least two, even with arbitrary helpers and a non-Clifford decoder. | Jointly design a seed outside those preserved diagonal algebras and its physical decoder or encoded copy companion. Exact output-probe gauge freedom cancels from the seed; source-centralizer freedom and a changed pencil remain possible. A zero-branch basis repair alone cannot work. |
+| [Recursive field-shear decoder](depth/RECURSIVE_FIELD_SHEAR_DECODER.md) | The identity-helper algebraic decoder includes every zero sector, with paid dense queries and multiplication-XOR batches but unpaid uniform in-place coordinate maps. Separately implemented levels retain a depth contribution. | The augmented source below changes the helper query and pays a different uniform decoder. Neither its linear stage count nor a faster isolated arithmetic call meets the sublogarithmic-depth target. |
+| [Augmented field recoupler](depth/AUGMENTED_FIELD_RECOUPLER.md) | An explicit moving Pauli helper query permits two native multiplication-XOR batches per level, shared helpers, and complete readout return. The decoder uses at most $`16(p-1)`$ bands; the direct indicator uses at most $`64(p-1)+16`$, with $`O(mp^3)`$ T count, $`O(mp^2)`$ dirty width and $`O(m^2p^2)`$ gates. | The specific relaxed fusion budgets are paid, but depth remains linear in p. Compress the complete source across levels while retaining the source helper query and every actual inverse; omitting that query breaks the identity. |
+| [Clifford-sector degree barrier](depth/FIELD_SECTOR_DEGREE_BARRIER.md) | A linear Pauli helper query needs shift rank at least $`p-1`$ for a Clifford-sector field intertwiner. Its helper-dependent symplectic matrix has degree at least $`p-1`$, including moving Clifford core spectators. The augmented construction attains that degree. | A fixed helper frame with helper-affine symplectic stages needs at least $`p-1`$ stages. Leave that grammar through paid helper motion or non-Clifford sector intermediates, or use only the weaker complete-probe endpoint. This is not a native T-depth lower bound for unrestricted circuits. |
+
+<a id="finite-field-calibrations"></a>
+
+### Finite field calibrations
+
+| Route | Present assessment | What would justify continuing |
+| --- | --- | --- |
 | [Finite Clifford field copy](depth/FIELD_COPY_CLIFFORD_PILOT.md) | A noncommuting four-address Clifford orbit has a central-sector grading and a paid physical copy. Its indicator uses 288 T gates, at most 96 bands and seven arbitrary dirty wires. The same cheaper query improves the direct decoder to 300 T, 160 bands and three dirty wires; the copy's depth gain costs more workspace and total gates. | Use its explicit sector-control construction as a component, not an all-size compiler. Its Pauli-valued commutators fall under the eventual obstruction below. |
 | [Flat field bank and shallow finite decoder](depth/FLAT_FIELD_BANK_PILOT.md) | A genuinely non-Clifford four-address seed has full commuting-bank grading. A six-T three-band decoder yields a 12-T six-band complete copy and a direct indicator with 72 T gates, at most 28 bands, 350 total gates and three returned dirty wires. A separate Clifford completion makes it a full field intertwiner. The same seed has one-band copy error at least $`1/(2\sqrt2)`$. | Extend the decoder uniformly within polynomial discovery budgets and sublogarithmic depth, allowing the complete probe's commutant freedom. The finite words establish no asymptotic bound or minimum cost; full-intertwiner restrictions are separated below from the weaker probe contract. |
 | [Projective field recoupler](depth/PROJECTIVE_FIELD_RECOUPLER.md) | Exact eight-address decoders retain two allocations: 172 T gates and at most 83 bands without extra helpers, or 148 T gates and at most 39 bands with six returned dirty helpers. A common reflection selector and a private quartic batch pay the latter word, including its zero fiber and actual inverse. | The finite OR selector becomes a growing-degree nonzero predicate, and projective-line enumeration is exponential in bank width. Use the coupled word as a finite calibration; a uniform route must change that enumeration and pay the full return ledger. |
+
+<a id="field-decoder-screens"></a>
+
+### Complete-intertwiner and probe screens
+
+| Route | Present assessment | What would justify continuing |
+| --- | --- | --- |
 | [Full decoder Pauli domain](depth/FIELD_DECODER_PAULI_DOMAIN.md) | At p at least three, absorbed axes must span at least $`2m-2`$ directions below error $`\sqrt2/6`$ with arbitrary Clifford target-helper motion, or below one-third for identity and residual-field helpers. Independent finite cells fail even after joint outer Clifford mixing. | Extensive T count fits the discovery budget and is not a depth obstruction. The weaker probe contract has its own domain screen below; merely replacing the full endpoint by that contract does not rescue independent cells. |
 | [Weak complete-probe domain](depth/WEAK_PROBE_PAULI_DOMAIN.md) | Degree-d Clifford queries restrict image-domain X masks to a Reed--Muller code below error $`2^{-d-1}`$. Full-rank field queries, including Pauli helper queries, force pure-Z kernel masks to be constant below $`1/(3m)`$. Independent four-wire cells have probe-error floor $`1/12`$ for p at least three and $`1/4`$ for p at least five. | Couple the non-Clifford operations or change the domain; arbitrary joint outer Clifford walls and moving decoded helpers do not repair tensor cells. The domain and absorbed-axis bounds do not lower-bound unrestricted native depth. |
 | [Disjoint-span two-band decoder](depth/TWO_BAND_FIELD_DECODER_OBSTRUCTION.md) | Partial or full bands whose absorbed spans have zero intersection have full-intertwining error at least $`\frac12\sqrt{1-1/\sqrt2}`$ for p at least two, including enlarged sources and arbitrary Clifford target-helper action. Intrinsic two-term Pauli images recover the outer axis list. | An eligible two-band word must exploit actual shared-span collisions; general overlapping bands remain open. A coupled three-band word or a non-Clifford endpoint satisfying only the complete-probe equation also leaves this screen. |
+
+<a id="seed-and-copy"></a>
+
+## Encoded seed and copy criteria
+
+| Route | Present assessment | What would justify continuing |
+| --- | --- | --- |
+| [Exact copy grading](depth/DIRTY_COPY_GRADING.md) | Vanishing traces of all nonzero-parity words exactly characterize copyable unitary families. Noncommuting examples exist; field-orbit reflections nevertheless have a common same-sign sector and a sharp pairwise anticommuting-target gap. | Supply a jointly paid seed and copy in the same coordinates. The explicit noncommuting example has a Clifford seed/copy but linear-depth wire translations; moving it to the cheap field query leaves those two operations unpaid. Arbitrary identity helpers cannot remove word-trace obstructions. |
+| [Native copy and dual support](depth/NATIVE_COPY_INTERACTION.md) | A native one-band non-Clifford component exists. General copy needs extensive T count for one field shear; exact dual readout needs extensive orbit support. Output-only Clifford mixing of product magic and the specified coded two-band family fail at growing size, including untouched helpers in the latter class. | Change the interaction beyond these classes, for example by mixing carrier and output before the phase gates or using noncommuting carrier phase axes. Prove complete dual readout and grade relations before claiming a scalable seed/copy pair. Extensive count fits the discovery budget and is not a depth obstruction. |
+| [Complete one-band copy feasibility](depth/ONE_BAND_COPY_FEASIBILITY.md) | Signed Walsh blocks give exact coefficient support spaces and spectra; complete copying also requires a carrier fixed point. All output duals can agree while the carrier action is wrong. The explicit triple-axis joint walls pass the tensor screen but have zero complete seed space for p at least two. Their full copy error is at least $`1/\sqrt6`$ for every unitary seed, with arbitrary dirty helpers. | Stop that family below its error floor. Choose changed uniform joint walls, solve the complete reduced equations, and exhibit a native seed. The bounded two-band seed-generator / one-band copy target would give a 42-band indicator if it succeeds. For other walls, empty kernels reject exact instances; approximation needs its own quantitative bounds. A finite fit or another necessary screen does not supply the all-size construction. |
+| [Affine Pauli-orbit copy](depth/PAULI_ORBIT_COPY_SCREEN.md) | At p at least two, Clifford dual output probes force copy error at least one quarter for an affine Pauli-query orbit; native one-band copies are included. The one-bit endpoint has a paid two-T, one-band copy and a complete returned-work echo. | Leave the affine Pauli-query or Clifford-dual-probe hypotheses. A dirty-mask extension of the field query has a paid gauge to Pauli translations, but that gauge can change copy depth; it does not transfer the one-band exclusion to the field shear. |
+| [Localized non-Clifford copy repair](depth/COPY_AXIS_SPAN.md) | A one-shear orbit requires at least $`m-p-1`$ independent physical-X directions in the copy rotation-axis span exactly, and an extensive span at constant error below square root two. | This span bound alone does not exclude a broad one-band copy; pay it jointly with the seed. This is a count/span screen, not a growing depth obstruction. |
+| [Monomial seed in query eigen-coordinates](depth/MONOMIAL_QUERY_SEED_OBSTRUCTION.md) | Copy error is at least one half for p at least two, even for arbitrary non-Clifford copies. The broader screen is commutation of original and seed-conjugated query algebras. | Break that algebra condition with genuine eigenspace mixing and certify the complete copy. Nonlinear reversible permutations or phases in the same query eigenbasis do not suffice. The all-Hadamard field seed passes the quantitative mixing test but still has a half-error floor from an order-three orbit-pair product. |
 | [Scalar-field radical algebra](depth/SCALAR_FIELD_RADICAL_COPY_SCREEN.md) | Algebra-automorphism equivariance forces the shear image to be square-zero for every address embedding at p at least two. The resulting four-address identity gives direct-copy error at least one half or selected-output-dual copy error at least one quarter, with arbitrary identical field banks and fixed helpers. | Leave the associative-algebra realization or the scalar-shear automorphism assumptions. Changed address embeddings, including collision-free product spaces, do not repair this model. Arbitrary Clifford duals, general regular affine groups and non-scalar dressings remain outside the theorem. |
 | [Seed coefficient and fingerprint rigidity](depth/NATIVE_COPY_INTERACTION.md#seed-coefficient-rigidity) | A unique largest Pauli magnitude with gap g forces field-copy error at least g/2 for p at least two when a selected output dual is Clifford. Product THT-dagger seeds have the width-independent floor 3/32, even after an arbitrary Clifford embedding and with arbitrary identity helpers. | For a one-band copy, change the product seed and remove its distinguished Pauli witness; degeneracy alone is insufficient. Deeper copies with non-Clifford duals remain eligible, as the paid flat-bank pilot illustrates. This is a seed/readout restriction, not an all-two-band-seed or unrestricted-copy theorem. |
 | [Clifford seed copy structure](depth/CLIFFORD_SEED_COPY_STRUCTURE.md) | A projectively involutive Clifford seed with commuting symplectic orbit has field-copy error at least 1/64 for p at least seven, for an arbitrary copy. With one physical copy band, every Clifford seed has error at least $`\sin(\pi/8)`$ for p at least nine; no orbit commutation or seed-order assumption is needed. | A one-band field copy needs a genuinely non-Clifford seed at sufficiently small error. In $`R=VPV^\dagger`$, V must therefore use at least two T bands. A Clifford-seed route needs more copy bands and must still leave the older commuting-orbit class. Neither condition supplies a construction. |
 | [Clifford output-dual grading](depth/CLIFFORD_DUAL_COPY_GRADING.md) | Every exact one-band copy induces a copyable Clifford orbit at each physical output dual, even for an arbitrary unitary seed. Its symplectic orbit group needs elementary binary abelianization rank at least $`m-p-1`$ for the field query. Explicit symplectic relation words yield quantitative scalar-word tests; the rank bound alone has no uniform approximate gap. | Design a dual group that retains the required address grades, then satisfy the complete carrier equations and synthesize the seed. Noncommuting symplectic generators alone are insufficient. An odd-order orbit-pair product already gives a robust obstruction for p at least three, with its certified order in the denominator. |
-| [Projector-Gram readout](depth/NILPOTENT_PENCIL_OBSERVABLE_SOURCE.md#paired-projector-readout) | Four-call recovery and serial promotion are paid: complete error $`64\sqrt\delta`$ for one clean signal, $`128\sqrt\delta`$ for two jointly accepted signals. The six-call block-error alternative remains. | A normalized native Gram source, allowing arbitrary accepted private fibers; actual source synthesis remains essential. |
-| [Spectral clean promotion](depth/MSS_SPECTRAL_PROMOTION.md) | Qualifies conditionally at $`k=o(\log(p+2))`$; uniform source accuracy and native address sharing are still required. | Supply an actual eligible source. Endpoint address return does not establish native sharing. |
-| [Exact packing and virtual arithmetic](depth/PARALLEL_CLEAN_PROMOTION.md), [arithmetic](depth/VIRTUAL_FUNCTION_ARITHMETIC.md) | Exact packing has a smaller sufficient window. Addition/multiplication/interval components do not pay full in-place radix compression; the spectral wrapper no longer needs it. | A complete rectangle-to-rank conversion whose total ledger improves on the paid wrapper, not another arithmetic component alone. |
-| [Balanced two-unitary acceptance](depth/COUPLED_ORDER_GRAM_SOURCE.md#balanced-two-unitary-gram-readout) | Gram error delta already gives a direct zero-clean squared relative word with error at most four delta plus four square-root delta. No control or promotion is needed for this extraction. | Supply that complete unitary identity, or change the balanced two-unitary interface. Other coefficients and genuine multipath acceptance retain their own obligations. |
-| [Four-path accepted fibers](depth/COUPLED_ORDER_GRAM_SOURCE.md#four-path-accepted-fibers) | A three-qubit native example has an exact half-projector Gram, nontrivial accepted polar motion and no cancelling pair of paths. The calibrated nonrectangular two-involution family instead forces its second involution to be identity below Gram error $`1/32`$. With the diagnostic phases, three independent Hermitian reflections also collapse to its original anticommuting pair under exact flatness, even with arbitrary block mixing. | Build the complete lookup Gram by joint cross-term interference; the one-qubit diagnostic is not lookup, and pairwise collapse cannot be assumed for arbitrary four-path sources. The exact three-reflection obstruction does not prove approximate rigidity; a different exact ansatz must change weights, phases or branch structure. Pay controls, normalization and every accepted fiber. |
-| [Output-alias weak fiber source](depth/OUTPUT_ALIASED_CHARACTER_SOURCE.md) | Four-call extraction cancels arbitrary private unitary fibers; the known source is not sublogarithmic. | A new weak fiber source, paired transform or whole extraction within the full polynomial budgets. |
-| [Single HRT residual probe](depth/DIRTY_CHOI_OBSERVABLE_SOURCE.md#one-bank-polarization) | Four residual-phase or eight probe-source calls suffice through one-bank quadratic polarization, with $`3m-2`$ principal dirty wires plus the private pool. A direct top phase needs $`2m-2`$. Standard/group Choi completions retain unpaid key conversion; parallel carrier-only readout loses input dependence. | The [paid feedback trial](depth/COHERENT_FEEDBACK_SOURCES.md) now tests one such coupling and fails. Restore its missing key response through a genuinely changed joint word, or synthesize the top phase directly. Its cubic bent dual is a dense kernel, not a diagonal implementation. The reduction is sufficient, not a converse or a new depth upper bound. |
-| [Local HRT mixers and coherent feedback](depth/COHERENT_FEEDBACK_SOURCES.md) | Individual encoded Hadamards cost at most sixteen T layers without helpers; a pair star admits joint twenty-four-band fusion with returned dirty helpers. Disjoint pairs obstruct that regrouping. The both-label feedback is a quadratic-query conjugate of a fixed Clifford. A complete motion repair computes the inverse-coordinate phase, whereas the target uses the forward coordinate; its error is two for r at least three. | Change the forward-coordinate mechanism. Fixed-key Clifford bank repairs have error at least one over square root two; key mixing or nonlinear bank dynamics leaves that screen. Cancelling motion alone is now paid and insufficient. |
-| [Approximate address-blind cache](depth/SHARED_PREFIX_QUERY_AUDIT.md#approximate-cache-capacity) | With bank-independent encoding and actual inverse decoding, the full bank needs $`2^c\ge2^p(1-\varepsilon^2/2)^2`$ initialized capacity below square-root-two error, even with arbitrary dirty and bank mixing. The small-clean spectral-promotion window does not repair this interface. | Retain address access during the bank operation, encode jointly with the bank, or establish another complete word. A smaller equality fingerprint or faster isolated zero test does not implement the arbitrary bank. |
-| [Clean-sector parallelism](depth/CLEAN_SECTOR_PARALLELISM_AUDIT.md) | A clean bank fixed at every native boundary can already be removed by restriction. General black-box promotion needs exponentially many source occurrences in clean count. | A genuinely different native schedule; logical call counts alone do not bound native depth. |
-| [Rank-one phase and complete indicator](depth/BANK_MIXING_AND_LOOKUP_PHASE.md#rank-one-indicator-equivalence) | Two-call reductions in both directions preserve the target resource orders, with a paid four-T-band control bank and arbitrary returned auxiliary work. General source representatives have the full commutant freedom of the probe X. | Treat the phase as an equivalent target, not an easier compiler. Seek a paid native representative with the complete derivative and return promise, possibly using address/work motion or synthesis across coordinate rounds. The linear T-count consequence gives no growing depth bound. |
 
-### Conditional Gram sources and scalar or selector components
+## Conditional Gram sources and scalar or selector components
 
 | Route | Present assessment | What would justify continuing |
 | --- | --- | --- |
@@ -61,23 +127,30 @@ Start with a complete interface; consult component families only when the propos
 | [Forward affine-pencil XOR](depth/NILPOTENT_PENCIL_OBSERVABLE_SOURCE.md) | Eight-layer forward query and its converse are paid; coherent in-place or observable readout is not. Rebuilding from the old indicator retains its depth. | A genuinely quantum complete readout outside the proved fixed-address Clifford/monomial restrictions. |
 | [One-pass row filters and counters](depth/COHERENT_COUNTER_SOURCE.md) | Fixed-fiber and arbitrary dirty-mixing limits differ. The paid fully dirty counter echo retains linear depth. | Leave the actual one-pass/invariant-fiber or Majorana grammar and pay the complete source, not only the counter. |
 
-### Joint Pauli transport and native bank transitions
+## Joint Pauli transport and native bank transitions
+
+<a id="native-source-screens"></a>
+
+### Native source and Clifford-block screens
 
 | Route | Present assessment | What would justify continuing |
 | --- | --- | --- |
 | [MOD3 zeta transport](depth/MOD3_ZETA_TRANSPORT.md) | Shared cleanup uses two indicator calls for weak observable transport and four for the full batch. At most three source layers give either exact transport or observable error at least $`\tau_*=\sin(\pi/8)/(2\sqrt2)`$; the newer unrestricted source theorem excludes the exact case for p at least seven. | Use more than three source layers and meet the complete sublogarithmic-depth and polynomial-budget contract at every fixed tolerance. Controlled $`P_0`$ suffices; no controlled source or full-batch approximation is required. The constant-call equivalence uses quadratic Clifford count and retains the transfer's log-log term. R96 remains unchanged. |
 | [Unrestricted three native source bands](depth/THREE_BAND_LOOKUP_SOURCE_OBSTRUCTION.md) | At p at least five, point-mask rank rigidity forces the last two pure bands in every exact source to preserve the address. The retained degree-six theorem excludes complete lookup at p at least seven, with the same tau_* floor by three-layer rounding. Arbitrary dirty width and register motion are included. | At least four native source layers below that error, or a different complete interface with separately paid recovery. This does not exclude arbitrary three third-level blocks, initialized-clean sources, or sublogarithmic depth with more bands. |
-| [Weak Pauli orbit compression](depth/WEAK_PAULI_ORBIT_COMPRESSION.md) | The one-coordinate product has error two. A separate twelve-T, three-layer source pays the complete two-address bank and lifts to joint two-coordinate transport at every bank size, with no extra work. Its final block commutes with the residual sign; that condition forces degree at most three and prevents extending this mechanism to p at least three. | Supply the remaining joint action with a changed final block or another complete source. The sequential prefix-rank requirement remains representation-specific. The two-coordinate identity is settled; repeating the independent single-mask product or extending the commuting final band is superseded. |
-| [Nested coefficients and complete shear assembly](depth/WEAK_PAULI_ORBIT_COMPRESSION.md#complete-coefficient-shear), [native fusion](depth/COEFFICIENT_SHEAR_NATIVE_FUSION.md) | Complete p=3 assembly and the exact all-size source with linear T-count are paid; the serial depth remains linear. The calibrated half-band palindrome has error two. Every word of the uniform-angle bipartite generators has error at least square root two, including arbitrary repetitions and per-occurrence angle choices; the two native calibrated words have error two. | Pause these schedules. A changed joint transition must distinguish the paired lookup sectors. Completed phase exchanges do not justify half-band exchanges; common Clifford diagonalization and independent affine-query replicas have separate scoped obstructions. Coordinate-only weights have the additional pulse-count boundary below. |
-| [Coordinate and tail-dependent bipartite pulses](depth/COORDINATE_WEIGHTED_PULSE_LIMITS.md) | Equal or nearby coordinate signatures retain their robust gap. More generally, arbitrary tail weights and mixed signed edges still have exact error two with fewer than p total pulses; a directed parity certificate also excludes longer words. Quarter-angle edge weights retain thirteen-band dirty-return compilation. | Clifford interlayers can cross the filtration at zero T-depth. Tail weights alone do not repair a short pulse-only source. Distinct signatures and successful propagation remain necessary conditions, not complete lookup. |
 | [Two cubic blocks with arbitrary Clifford frames](depth/CLIFFORD_INTERLEAVED_LOOKUP.md) | For p at least three, $`V=CDU`$, with C Clifford, D diagonal third-level and U any third-level unitary, has derivative error at least $`\sin(\pi/8)`$. All Clifford address/work mixing is allowed. This includes two weighted-cubic pulses and every native two-T-layer source. | Three broader third-level blocks or a changed final nonlinear class remain possible; three actual native bands are now separately excluded at p at least seven. The theorem supplies no growing native-depth bound. A nonmonomial final Clifford alone no longer reopens the two-block route. |
 | [Third-level blocks with Clifford fibers](depth/CLIFFORD_INTERLEAVED_LOOKUP.md#clifford-fiber-block-bound) | With held address and Clifford bank/work fibers, fewer than p blocks give complete derivative error at least square root two, even with arbitrary address-algebra-preserving Clifford interlayers. The gap and block count are sharp. | A shallow candidate must use non-Clifford fibers or leave the preserved address algebra. Bank Hadamards alone do not escape. The count is for specified source blocks, not their joint native synthesis. |
 | [Three blocks with later key preservation](depth/CLIFFORD_INTERLEAVED_LOOKUP.md#three-block-late-key-mixing) | An arbitrary global third-level prefix and two later diagonal third-level blocks give error at least one quarter for label degree above six when their Clifford walls preserve the key algebra. Lookup at p at least seven and the residual HRT probe at r at least eight are covered, including non-Clifford bank fibers. | Mix the relevant key in a later stage or change architecture. Initial key motion alone is insufficient. This is a three-block source boundary, not an unrestricted growing native-depth lower bound. |
-| [Long physical Clifford-zeta frame](depth/CLIFFORD_INTERLEAVED_LOOKUP.md#6-a-long-physical-clifford-frame-and-its-calibrated-repair) | The specified three-pulse source has a square-root-three gap. Its actual zero-address calibration has error two at native quarter angles, with a fused 38-band compiler; arbitrary real endpoint/middle angles retain a square-root-two gap. | Change the complete transition. Repeating the same frame with baseline calibration or angle tuning is closed; this does not exclude arbitrary three-block sources. |
-| [Clifford involution front end](depth/CLIFFORD_INVOLUTION_SOURCE.md) | Every traceless Hermitian Clifford has a four-band, linear-T-count Pauli source without helpers. Two outer conjugations reduce exact completion to a Clifford peeled target. Their combined Galois defect must be a signed lookup symmetry; fourth-root outer phases require even displacement rank. | Find and pay those outer factors with genuine later address participation. The arithmetic screen is exact, and constrains the combined defect rather than each wall. It supplies no approximate gap or complete lookup. |
 | [Complete Clifford lookup symmetries](depth/LOOKUP_CLIFFORD_SYMMETRIES.md) | For Clifford R and Boolean sign Q, QRQ strictly within $`1/\sqrt2`$ of a Clifford is exactly Clifford. Lookup then forces the hard-coordinate/monomial normal form and, for p at least three, address-algebra preservation, including arbitrary helpers; genuine address/bank mixing survives at p=2. | Screen qualifying intermediate images even at complete probe error below $`1/(2\sqrt2)`$. This does not fix each address value or force arbitrary three-block walls to preserve the address; only Clifford-to-Clifford images enter the screen. |
-| [Joint address/carrier/helper trial](depth/JOINT_ADDRESS_HELPER_SOURCE.md) | A literal twenty-band source creates the desired quartic-face sign and unwanted carrier translations. Two anticommuting Pauli coefficients give error at least 1/16 after any final Clifford. The actual carrier repair is paid, producing a complete finite-face phase at 136 T gates and at most 72 bands. | Change the earlier cubic/Clifford mechanism to cancel the translations while retaining the quartic sign. Changing only the final Clifford is closed for this word. The repair is a finite-face benchmark, not an all-size source or a general three-block obstruction. |
-| [Nonmonomial quartic-face sources](depth/JOINT_ADDRESS_HELPER_SOURCE.md#nonmonomial-hadamard-pair-screen) | The specified Hadamard-pair/CCZ coupling has error at least 1/16 for arbitrary later Cliffords and every cubic-sign last batch. A weighted escape breaks that coefficient ceiling but its specific word retains a 3/16 final-Clifford gap. The Fourier-swap fixed-coefficient source reduces to a quadratic finite difference, with a direct 28-T, eight-band phase and no helpers. A four-corner identity gives a 1/2 gap for its common-readout extension to arbitrary top coefficient. | Use a genuinely changed weighted coupling and later address participation. Nonmonomial first images alone do not complete the face; repeating the fixed-coefficient finite difference supplies no all-size gain. Each exclusion retains its stated first coupling or common-readout grammar. |
+| [Coupled final encoders](depth/COUPLED_FINAL_ENCODER.md) | The bank-fiber theorem excludes every three-layer completion with a bank-independent final one-band block at p at least three. A distinct full-bank X-motion encoder also fails. These scoped proofs retain their smaller-address coverage; the new unrestricted theorem excludes all three-band final encoders at p at least seven. | More source layers or a changed complete interface for growing p. A fixed output Clifford or private Z-tag decoration cannot repair the stated mechanisms. Finding another middle for either encoder is superseded. |
+
+<a id="transport-components"></a>
+
+### Transport components and orbit requirements
+
+| Route | Present assessment | What would justify continuing |
+| --- | --- | --- |
+| [Weak Pauli orbit compression](depth/WEAK_PAULI_ORBIT_COMPRESSION.md) | The one-coordinate product has error two. A separate twelve-T, three-layer source pays the complete two-address bank and lifts to joint two-coordinate transport at every bank size, with no extra work. Its final block commutes with the residual sign; that condition forces degree at most three and prevents extending this mechanism to p at least three. | Supply the remaining joint action with a changed final block or another complete source. The sequential prefix-rank requirement remains representation-specific. The two-coordinate identity is settled; repeating the independent single-mask product or extending the commuting final band is superseded. |
+| [Clifford involution front end](depth/CLIFFORD_INVOLUTION_SOURCE.md) | Every traceless Hermitian Clifford has a four-band, linear-T-count Pauli source without helpers. Two outer conjugations reduce exact completion to a Clifford peeled target. Their combined Galois defect must be a signed lookup symmetry; fourth-root outer phases require even displacement rank. | Find and pay those outer factors with genuine later address participation. The arithmetic screen is exact, and constrains the combined defect rather than each wall. It supplies no approximate gap or complete lookup. |
 | [Coherent central transport](depth/COHERENT_CENTRAL_TRANSPORT.md#reduced-carrier-gauge) | Only q pair controls and the carrier are needed for the exact central echo; four-band root completion replaces the full linear factor. Each pair factor has a four-band helper-free word, but overlapping factors have no shallow joint schedule. General carrier-linear gauges obey an exact root criterion and allow strictly more freedom; low-row degree must be at least floor(p/2). | Synthesize the joint echo or a weaker eligible probe. The [earlier gauge](depth/COHERENT_CENTRAL_TRANSPORT.md#weak-pair-gauge-source) separates unnecessary full-encoding corrections from failed truncations. Algebraic degree, hierarchy level and completed-shear rank do not lower-bound unrestricted native depth. |
 | [Ordered-matching and minimal-tree probes](depth/ORDERED_MATCHING_PROBE_SOURCE.md) | The matching representation has paid common-point fusion. Its sparse-tree specialization pays the complete coefficient probe with 6m−5 T gates, at most 4p bands and no private work. An eight-band complete forward XOR query is separately paid. | Synthesize the in-place map or complete readout faster. The cheap out-of-place query does not supply the inverse, and the linear-depth baseline does not improve the retained logarithmic indicator or R96. |
 | [Fixed final readout after Pauli transport](depth/FIXED_READOUT_SYNDROME_BOUND.md) | Even an arbitrary fixed non-Clifford carrier/helper unitary requires a near-full input syndrome space. After q affine-symplectic query stages, exact lookup requires q at least p; fixed error below $`\sqrt{2-\sqrt2}`$ requires q at least p/2 minus a square-root correction. | Make the readout participate in address-dependent processing, move the address, or leave the Pauli-image grammar. More expressive fixed decoding alone cannot help. Logical query stages do not lower-bound a jointly resynthesized native word. |
@@ -85,20 +158,35 @@ Start with a complete interface; consult component families only when the propos
 | [Clifford-orbit affine-query rank](depth/CLIFFORD_ORBIT_QUERY_RANK.md) | A faithful lift retains normal-Pauli signs. Its multiplicative rank forces $`q\ge\lceil p/8\rceil`$ literal affine XOR queries for a fixed Hermitian Clifford starting reflection, at error below $`\sqrt{2-\sqrt2}/4`$, with arbitrary fixed decoder and dirty width. | Use a genuinely non-Clifford first image, certify another query grammar, or jointly resynthesize the native word. Affine symplectic entries alone do not certify the sign lift. This logical query bound is not an unrestricted native-depth lower bound. |
 | [Two-address interleaved pilot](depth/TWO_ADDRESS_INTERLEAVED_PILOT.md) | Controlled Hadamards realize the complete four-member target algebra with a fixed Clifford decoder and a paid native source and inverse. | Find a uniform complete rule with a better total ledger. Serial controlled-Clifford extension retains the old cost; a finite exact family alone supplies no asymptotic improvement. |
 | [Non-Clifford seed spread](depth/NONCLIFFORD_SEED_SPREAD.md) | A bounded number of affine Clifford queries requires an exponentially broad seed Pauli-label span at fixed error, even with arbitrary fixed decoding. Native seed T count bounds that span. The extensive two-band tensor seed survives, while its plain local inverse decoder fails for the tree family. | Use extensive nonlinear structure and a jointly designed nonlocal decoder, or leave the orbit grammar. Neither seed count nor query count alone bounds native depth. |
-| [Field-shear intertwiner](depth/FIELD_SHEAR_INTERTWINER.md) | The paid query has the full lookup character. Monomial/Clifford decoders and a preserved physical Bell zero fiber fail. An exact seed diagonal in any query-invariant stabilizer basis fails at p at least two, even with arbitrary helpers and a non-Clifford decoder. | Jointly design a seed outside those preserved diagonal algebras and its physical decoder or encoded copy companion. Exact output-probe gauge freedom cancels from the seed; source-centralizer freedom and a changed pencil remain possible. A zero-branch basis repair alone cannot work. |
-| [Recursive field-shear decoder](depth/RECURSIVE_FIELD_SHEAR_DECODER.md) | The identity-helper algebraic decoder includes every zero sector, with paid dense queries and multiplication-XOR batches but unpaid uniform in-place coordinate maps. Separately implemented levels retain a depth contribution. | The augmented source below changes the helper query and pays a different uniform decoder. Neither its linear stage count nor a faster isolated arithmetic call meets the sublogarithmic-depth target. |
-| [Augmented field recoupler](depth/AUGMENTED_FIELD_RECOUPLER.md) | An explicit moving Pauli helper query permits two native multiplication-XOR batches per level, shared helpers, and complete readout return. The decoder uses at most $`16(p-1)`$ bands; the direct indicator uses at most $`64(p-1)+16`$, with $`O(mp^3)`$ T count, $`O(mp^2)`$ dirty width and $`O(m^2p^2)`$ gates. | The specific relaxed fusion budgets are paid, but depth remains linear in p. Compress the complete source across levels while retaining the source helper query and every actual inverse; omitting that query breaks the identity. |
-| [Clifford-sector degree barrier](depth/FIELD_SECTOR_DEGREE_BARRIER.md) | A linear Pauli helper query needs shift rank at least $`p-1`$ for a Clifford-sector field intertwiner. Its helper-dependent symplectic matrix has degree at least $`p-1`$, including moving Clifford core spectators. The augmented construction attains that degree. | A fixed helper frame with helper-affine symplectic stages needs at least $`p-1`$ stages. Leave that grammar through paid helper motion or non-Clifford sector intermediates, or use only the weaker complete-probe endpoint. This is not a native T-depth lower bound for unrestricted circuits. |
 | [Clique polarization and joint integration](depth/COHERENT_CENTRAL_TRANSPORT.md#clique-polarization-integration) | Desired and cheap transports have the same 32-band polarization; their ratio is the unpaid coherent zeta homomorphism. Direct and central half-Gram query costs are sharply floor(p/2) and ceiling(floor(p/2)/2), even with orbit-diagonal phases and controlled work. Fixed-first-argument queries lose the quadratic refinement under character-independent interlayers. | Use nonmonomial native bank dynamics or joint synthesis outside completed polarization queries, or meet only the weaker root-probe interface. These are oracle-query statements, not native-depth bounds; the central half-Gram is not the lookup projector. |
-| [Joint precision rotation](depth/JOINT_PRECISION_ROTATION.md) | A Clifford image of the actual signal forces unit acceptance below error 2sin(π/16). Separately paid balanced branches admit a direct alternating-word bypass; the paid 3:1 pilot admits a direct branch within 3√ε of the recovered unitary. Cheap joint completion need not supply those branches. | Seek joint synthesis or another accepted-source family with sublinear precision depth and linear count, then pay coherent chart selection and every remaining R96 serial word. The actual-signal premise and branch-resource premise have separate scopes. |
 | [Parallel weighted-cubic phases](depth/DIRTY_CUBIC_PHASE_COMPILER.md) | An exact thirteen-band compiler pays shared logical controls, arbitrary dirty helpers and actual inverses. It supplies the coefficient-cube parity layers with polynomial overhead and zero clean work. | Use this component inside a separately proved complete source. Its paid schedule does not repair the uniform-angle bipartite sector collision or establish complete lookup. |
-| [Coupled final encoders](depth/COUPLED_FINAL_ENCODER.md) | The bank-fiber theorem excludes every three-layer completion with a bank-independent final one-band block at p at least three. A distinct full-bank X-motion encoder also fails. These scoped proofs retain their smaller-address coverage; the new unrestricted theorem excludes all three-band final encoders at p at least seven. | More source layers or a changed complete interface for growing p. A fixed output Clifford or private Z-tag decoration cannot repair the stated mechanisms. Finding another middle for either encoder is superseded. |
+
+<a id="stopped-source-words"></a>
+
+### Stopped source words and retained repairs
+
+| Route | Present assessment | What would justify continuing |
+| --- | --- | --- |
+| [Local HRT mixers and coherent feedback](depth/COHERENT_FEEDBACK_SOURCES.md) | Individual encoded Hadamards cost at most sixteen T layers without helpers; a pair star admits joint twenty-four-band fusion with returned dirty helpers. Disjoint pairs obstruct that regrouping. The both-label feedback is a quadratic-query conjugate of a fixed Clifford. A complete motion repair computes the inverse-coordinate phase, whereas the target uses the forward coordinate; its error is two for r at least three. | Change the forward-coordinate mechanism. Fixed-key Clifford bank repairs have error at least one over square root two; key mixing or nonlinear bank dynamics leaves that screen. Cancelling motion alone is now paid and insufficient. |
+| [Nested coefficients and complete shear assembly](depth/WEAK_PAULI_ORBIT_COMPRESSION.md#complete-coefficient-shear), [native fusion](depth/COEFFICIENT_SHEAR_NATIVE_FUSION.md) | Complete p=3 assembly and the exact all-size source with linear T-count are paid; the serial depth remains linear. The calibrated half-band palindrome has error two. Every word of the uniform-angle bipartite generators has error at least square root two, including arbitrary repetitions and per-occurrence angle choices; the two native calibrated words have error two. | Pause these schedules. A changed joint transition must distinguish the paired lookup sectors. Completed phase exchanges do not justify half-band exchanges; common Clifford diagonalization and independent affine-query replicas have separate scoped obstructions. Coordinate-only weights have the additional pulse-count boundary below. |
+| [Coordinate and tail-dependent bipartite pulses](depth/COORDINATE_WEIGHTED_PULSE_LIMITS.md) | Equal or nearby coordinate signatures retain their robust gap. More generally, arbitrary tail weights and mixed signed edges still have exact error two with fewer than p total pulses; a directed parity certificate also excludes longer words. Quarter-angle edge weights retain thirteen-band dirty-return compilation. | Clifford interlayers can cross the filtration at zero T-depth. Tail weights alone do not repair a short pulse-only source. Distinct signatures and successful propagation remain necessary conditions, not complete lookup. |
+| [Long physical Clifford-zeta frame](depth/CLIFFORD_INTERLEAVED_LOOKUP.md#6-a-long-physical-clifford-frame-and-its-calibrated-repair) | The specified three-pulse source has a square-root-three gap. Its actual zero-address calibration has error two at native quarter angles, with a fused 38-band compiler; arbitrary real endpoint/middle angles retain a square-root-two gap. | Change the complete transition. Repeating the same frame with baseline calibration or angle tuning is closed; this does not exclude arbitrary three-block sources. |
+| [Joint address/carrier/helper trial](depth/JOINT_ADDRESS_HELPER_SOURCE.md) | A literal twenty-band source creates the desired quartic-face sign and unwanted carrier translations. Two anticommuting Pauli coefficients give error at least 1/16 after any final Clifford. The actual carrier repair is paid, producing a complete finite-face phase at 136 T gates and at most 72 bands. | Change the earlier cubic/Clifford mechanism to cancel the translations while retaining the quartic sign. Changing only the final Clifford is closed for this word. The repair is a finite-face benchmark, not an all-size source or a general three-block obstruction. |
+| [Nonmonomial quartic-face sources](depth/JOINT_ADDRESS_HELPER_SOURCE.md#nonmonomial-hadamard-pair-screen) | The specified Hadamard-pair/CCZ coupling has error at least 1/16 for arbitrary later Cliffords and every cubic-sign last batch. A weighted escape breaks that coefficient ceiling but its specific word retains a 3/16 final-Clifford gap. The Fourier-swap fixed-coefficient source reduces to a quadratic finite difference, with a direct 28-T, eight-band phase and no helpers. A four-corner identity gives a 1/2 gap for its common-readout extension to arbitrary top coefficient. | Use a genuinely changed weighted coupling and later address participation. Nonmonomial first images alone do not complete the face; repeating the fixed-coefficient finite difference supplies no all-size gain. Each exclusion retains its stated first coupling or common-readout grammar. |
 | [Syndrome-star pulse continuation](depth/COUPLED_FINAL_ENCODER.md#syndrome-star-pulse-boundaries) and [broad baseline](depth/COUPLED_FINAL_ENCODER.md#broad-baseline-syndrome-source) | The original pulse algebra retains kernel translations. Both the paid zero-baseline source and the changed normalized fixed-row baseline fail: the latter has ideal Gram distance exactly one half for p at least three, despite constant native depth at fixed precision. Fewer than $`(m-1)/4`$ thin controlled-reflection insertions cannot repair a word whose deletion baseline is that fixed-row source. | Pause fixed-call corrections of these baselines. Reopen with a lookup-dependent broad action or a jointly paid growing-call schedule, including aggregate precision and return. These are source/baseline and call restrictions, not unrestricted native-depth bounds. |
 | [Shifted-syndrome wide commutator](depth/COUPLED_FINAL_ENCODER.md#shifted-syndrome-wide-commutator) | Four actual T bands, 4m T gates and no helpers pay a different full-space word. A missing bank-row response gives complete lookup-image error at least square root two for p at least two, even at arbitrary angles on the same axes. The native p=1 coefficient gap is one quarter. No thin-reflection premise is used. | Pause this fixed-axis commutator, including angle or T-sign tuning. Change the middle action, axes, full word or accepted interface and derive the complete action. This is not a general four-layer or shifted-syndrome obstruction. |
 | [Common-probe pulses and third-frame repair](depth/COUPLED_FINAL_ENCODER.md#common-probe-wide-source) | The original four-band word retains separate covariance, singlet and relative-spectrum failures. The [corrected middle](depth/COUPLED_FINAL_ENCODER.md#relative-probe-involution-repair) now pays an exact Hermitian relative block with four native bands and zero clean work. | The earlier relative-involution step is settled for this partial construction; complete lookup is not. Preserve the original hypotheses rather than applying its old spectrum obstruction to the changed word. |
 | [Relative-block repair and complete lookup](depth/COUPLED_FINAL_ENCODER.md#relative-probe-involution-repair) | At fixed native angles, any static diagonal dressing has direct error above one third for p at least three; every nonempty Hadamard mask has error at least square root two. The specified cubic-phase/Hadamard word also fails analytically. Three separately paid asymmetric-fiber trials have exact p=3 failures. | Pause these tested single-dressing mechanisms. The next joint transition must also respect the broader mixing screens below. Hermiticity alone is no longer an unpaid step. Completed quadratic coordinate rounds retain a logarithmic round requirement, without excluding cross-round native synthesis. These are specified-word limits. |
 | [Affine/Fourier and two-Clifford mixing](depth/BANK_MIXING_AND_LOOKUP_PHASE.md#affine-fourier-complete-transition-gap) | Either affine/full-Fourier order has error at least square root two in the repaired word, including arbitrary X-diagonal pulses and diagonal middles. Exact monomial dressing also fails at the original native angles, without a uniform approximate gap. The bank-only two-Clifford grammar permits one aligned rank-one exception; common-affine-frame masks fail. | Angle tuning, diagonal-middle tuning and a shared affine exposure do not reopen these classes. The [rank-one phase is indicator-equivalent](depth/BANK_MIXING_AND_LOOKUP_PHASE.md#rank-one-indicator-equivalence), so its synthesis is the full task. Changed non-Clifford mixing, nondiagonal middles, active work or address motion remain possible within their complete native ledgers. |
 
+<a id="joint-precision-route"></a>
+
+### Joint precision route
+
+| Route | Present assessment | What would justify continuing |
+| --- | --- | --- |
+| [Joint precision rotation](depth/JOINT_PRECISION_ROTATION.md) | A Clifford image of the actual signal forces unit acceptance below error 2sin(π/16). Separately paid balanced branches admit a direct alternating-word bypass; the paid 3:1 pilot admits a direct branch within 3√ε of the recovered unitary. Cheap joint completion need not supply those branches. | Seek joint synthesis or another accepted-source family with sublinear precision depth and linear count, then pay coherent chart selection and every remaining R96 serial word. The actual-signal premise and branch-resource premise have separate scopes. |
+
 ## Source-specific representation limits
 
 Choose the row matching the actual proposed word. A failed nearby representation does not inherit these conclusions.
diff --git a/scripts/README.md b/scripts/README.md
index 3fd01853..a46341d9 100644
--- a/scripts/README.md
+++ b/scripts/README.md
@@ -6,6 +6,53 @@ The scripts provide a readable orientation, resource ledgers, source checks,
 exact verification receipts, and rendered presentation checks. They do not
 replace the analytic proof.
 
+## Research validation
+
+Run commands from the repository root. During an edit, select the affected
+modules below; the [verification catalogue](../docs/reference/VERIFICATION_CATALOGUE.md#catalogue-index)
+owns their detailed evidence contracts and maps the other research components.
+Use [WORKSPACE](../WORKSPACE.md) for the current question, not this command map.
+
+| Changed material | Focused checks |
+| --- | --- |
+| Working documents, links and mathematical syntax | [`test_repository_navigation`](../tests/test_repository_navigation.py), [`test_reviewer_narrative`](../tests/test_reviewer_narrative.py), [`test_presentation`](../tests/test_presentation.py) |
+| [Augmented field recoupler](../research/depth/AUGMENTED_FIELD_RECOUPLER.md) | [`test_augmented_field_recoupler`](../tests/test_augmented_field_recoupler.py) |
+| [Projective field recoupler](../research/depth/PROJECTIVE_FIELD_RECOUPLER.md), both native allocations | [`test_projective_field_recoupler`](../tests/test_projective_field_recoupler.py), [`test_coupled_projective_recoupler`](../tests/test_coupled_projective_recoupler.py) |
+| [Weak complete-probe domain](../research/depth/WEAK_PROBE_PAULI_DOMAIN.md) | [`test_weak_probe_pauli_domain`](../tests/test_weak_probe_pauli_domain.py) |
+| [Clifford-sector degree barrier](../research/depth/FIELD_SECTOR_DEGREE_BARRIER.md) and signed helper tableaux | [`test_field_sector_degree`](../tests/test_field_sector_degree.py), [`test_field_sector_tableaux`](../tests/test_field_sector_tableaux.py) |
+
+For example, the working-document checks run with:
+
+```bash
+python -m unittest tests.test_repository_navigation tests.test_reviewer_narrative tests.test_presentation
+```
+
+Use the same `python -m unittest tests.<module>` form for the affected scientific
+suites. A bounded fixture checks its stated identities and implementation;
+the linked proof retains responsibility for all-size claims and scope.
+
+Before merging, run the complete local gate on the final reviewed tree:
+
+```bash
+python -m compileall -q compiler_robust_hopf scripts tests validate.py
+python scripts/reviewer_walkthrough.py
+python scripts/coarse_frame_native_example.py
+python scripts/complex_coarse_native_example.py
+python scripts/residual_qbp_native_example.py --q 16
+python validate.py --quiet
+python scripts/verify_fault_tolerant.py
+python scripts/check_upstream_sync.py --offline
+python scripts/unified_resource_ledger.py --n 12 --format json
+python scripts/strict_zero_echo_ledger.py --n 12 --format json
+```
+
+Complete focused [visual checks](#visual-checks) for changed mathematics and
+pages before the memory-heavy numerical suite; full presentation CI covers
+the complete corpus. Focused tests support iteration and do not replace this
+final gate or required CI. Record the tested commit/tree and command results
+in the review record. Expected scientific receipts stay unchanged unless the
+underlying evidence is intentionally regenerated and reviewed.
+
 ## Technical walkthrough
 
 ```bash