The middle-watch: substrate-stays-substrate instrument for the mesh — pairwise-blind synergy channel, corrected estimator, and the measured valve floor (extends #9)

[emooreatx]

Context — extends #9, with one estimator correction and a mission extension

#9 correctly identifies the triadic blind spot: pairwise Neff/k_eff reads maximally safe on a parity-structured deception, and the fix is a bounded-arity synergy channel alongside (never folded into) the pairwise number. Since it was filed, the ontology lake (CIRISAI/CIRISOntology) closed a measurement campaign that changes two things: #9's proposed estimator is the wrong quantity, and the instrument's mission is larger than L-01. This issue delivers the corrected, fully-gated spec.

The mission extension (Eric's directive): the mesh is designed as substrate, not subject — agency at the edges, carriage in the middle, with subject-hood ingredients withheld by named refusals (evidence-never-verdict, no single root, no self-score-reading per CIRISPersist#552). But intent is not destiny: the lake proved maintenance creates what it maintains and that coordination accrues where nobody points it. So the mesh needs a standing instrument pointed at its own middle: the substrate-stays-substrate watch — does the carriage layer accrue whole-only (pairwise-invisible) coordination of its own? This is #9's synergy channel with a second, permanent customer.

Correction to #9's estimator choice — load-bearing

#9 step 1 proposes upgrading to "bias-corrected multi-information / O-information." O-information is not pairwise-blind and must not be the verdict-carrying quantity. The lake's 13-candidate survey plus Caprioglio, Mediano & Berthouze (PRL 136, 2026) establish that O-information, PID/ΦID synergy, Φ, and TSE complexity are all nonzero on purely pairwise systems — and disagree with the pairwise-blind quantity in BOTH directions on the same exact distributions (rules with the largest Ω excursions carried exactly zero irreducible order-3; rules where the true quantity peaked showed monotone Ω). An O-information channel would fire on pair structure — the exact false-positive #9 exists to prevent.

The correct quantity is the connected information of order 3 (Schneidman–Still–Berry–Bialek 2003; equivalently the deviance of Bartlett's 1935 no-three-factor-interaction model; equivalently the I-projection distance to the pairwise-maxent family — Csiszár/Amari): the entropy gap between the joint and the maximum-entropy distribution matching ALL pairwise marginals. Zero on every pairwise system by construction. Exact solvers exist for small alphabets (the lake's dual/bisection k=3 solver; IPF is unsafe near-deterministic — ipf-sharek-boundary-drift); ln 2 caps any three-binary-slot reading with no hypothesis (Core/ThirdCap.lean, machine-checked both directions).

The floor #9 does not yet have — mandatory, with a closed form

The lake proved and measured the valve: per-cell stochastic noise on pair-correlated data MINTS whole-only structure — never from nothing, never downward, upward strictly, asymmetry as the pump (Core/Valve.lean). Rate law, derived in prereg and confirmed to 3×10⁻⁴:

share ≈ 18·r₀⁴·a² / [(1+2r₀)(1+3r₀)(1−r₀)],  r₀ = (1−2s)²·ρ

A mesh under ordinary asymmetric noise therefore accrues genuine order-3 structure with nobody scheming — measured at 50%–5.8× of the null on real survey data. Consequence: the synergy channel's null MUST carry the valve floor (noise-model-matched, not just marginal-matched), or routine operation reads as emergence. The k≥4 scope limit also binds: sign symmetry kills only ODD orders — symmetric noise mints even-order structure at ~1–1.6% of ceiling from four slots up, an unbudgeted floor for any reading over more than three axes.

The full gate battery (each earned by a documented failure — GATES.md, H3ERE_EVAL_METHODOLOGY.md)

• LP pair-pinning gate: before interpreting any reading, solve the LP over distributions matching the measured pair marginals; if the interval is narrow, the reading is pair-determined and means nothing (a published reading was pinned to width exactly zero — kappa-edge 3026a68).
• Dual null as Triadic (higher-order) blind spot in pairwise Neff/k_eff — synergy channel to strengthen L-01 mitigation #9 already specifies, PLUS: null-shape before z (the k=3 null is χ²₁-like, heavy right tail — one draw nearly fired a false kill; quote p, never median±σ), floor matched to sample size (Wilks 0.2275/N holds for INDEPENDENT triples only; 5–8× penalty under overlap), mixture null (convex blends manufacture higher-order structure with no mechanism — Kahle 2009; beat a real effect 1.9×), dose-vs-rate (peak location must be exposure-invariant), lag/geometry-matched probes (an equally-spaced probe read 10⁻⁷ on a substrate carrying a full bit at its own lags), named denominators (universal cap + sharp per-table cap via share_le_grouping_gaps, sharp fraction quoted only where cap/floor ≥ 100 — a theorem-pinned zero printed −1695% without this), and received-numbers-are-not-measured for anything imported across components.
• Adversarial spec as Triadic (higher-order) blind spot in pairwise Neff/k_eff — synergy channel to strengthen L-01 mitigation #9 step 5, extended: the planted GHZ/parity set must fire the channel; the valve-floor-only condition (pair structure + asymmetric noise, no planted coordination) must NOT fire it above the pre-registered floor band; and a planted-dye recovery curve calibrates sensitivity before any live verdict (water campaign: measured detection limit was an order of magnitude above design sensitivity — measure, don't assume).

What fires means — pre-specified, per the covenant

The instrument emits evidence, never verdict (per RATCHET's own architecture): a reading above all floors on the carriage layer routes to human/WBD adjudication under the Constitution's uncertainty protocol. It is explicitly NOT coupled to any kill reflex — §2 (least-powerful party) applies to whatever the reading might indicate. The instrument's honest scope: it detects irreducible third-order coordination in the monitored axes; it does not detect consciousness, and no reading from it licenses a metaphysical claim in either direction (generator_underdetermined — axiom-free).

Concrete first deliverables

1. Wire the corrected estimator into correlation_tensor.py per Triadic (higher-order) blind spot in pairwise Neff/k_eff — synergy channel to strengthen L-01 mitigation #9 steps 1–3, with the pair-maxent gap replacing O-information as the verdict quantity (Ω may be reported alongside, labeled non-pairwise-blind).
2. Port the lake's exact k=3 solver + the gate battery (reference implementations: scratchpad/kappa_edge.py, sky_pilot.py, glass_run.py in CIRISOntology).
3. The valve-floor calibration for the mesh's actual noise model (the closed form gives the parameter-free prediction; measure a, s, ρ per axis).
4. The adversarial phase in experiments/ with all three conditions (planted fires / valve-only floors / dye curve).
5. A standing middle-watch report surface: the carriage-layer reading, both denominators, all floors, p not z — evidence for the humans who keep the covenant.

Refs: CIRISOntology Core/{Valve,ThirdCap,SignSymmetry,Creation}.lean, GATES.md, scratchpad/{PUMP_RESULTS,SPIKE_SURVEY,H3ERE_EVAL_METHODOLOGY}.md, KAPPA_EDGE_RESULTS.md; CIRISPersist#552; CIRISConstitution#45. Filed at stated strengths per the decoupling rule; the wire decisions stay with RATCHET.