Authors: Carmen N. Wrede, Lino P. Casu AI Assistants: Bingsi, Akira Status: Canonical Reference — Single Source of Truth Last Updated: 2026-10-11 (inventory audit: file counts corrected, 12 unlisted files added to index, 2 dead LIGO links resolved openly, new sections for animations + pipeline + research repos; previous content update 2026-05-19)
Segmented Spacetime (SSZ) is a falsifiable extension of General Relativity (GR) built around a single additional quantity: a dimensionless segment density field Ξ(r). SSZ reproduces GR exactly in weak fields while producing systematic, testable deviations in strong fields — especially around neutron stars and compact objects.
Core equation:
D_SSZ(r) = 1 / (1 + Ξ(r))
At the Schwarzschild radius: D(r_s) = 0.55503 (finite!) vs GR: D(r_s) = 0 (singularity).
| # | Section | Contents |
|---|---|---|
| 00 | Index | Master index, completeness assessment |
| 01 | Overview | What is SSZ, core postulates, relation to GR |
| 02 | Foundations | Ξ(r), D(r), regimes, φ-geometry, φ-lattice, scaling factor |
| 03 | Formulas | Complete compendium, PPN, worked examples, special values, units |
| 04 | Kinematics | Dual velocities, geodesics, orbital mechanics, frame dragging |
| 05 | Electromagnetism | Maxwell gauge, group velocity, energy, Shapiro delay, lensing |
| 06 | Strong Field | BH metric, singularities, ISCO, QNM, Penrose, Lagrangian |
| 07 | Validation | GPS, Cassini, Mercury, NS redshift, power law, GR vs SSZ |
| 08 | Falsification | Testable predictions, instruments, falsification criteria |
| 09 | Papers | All 25 papers, bibliography, preprints + 64 mirrored paper markdown files (markdown/, PDFs in pdf/) |
| 10 | Repositories | All 37 repos, test index, reproducibility |
| 11 | Guardrails | Prime directive, method assignment, confusion prevention |
| 12 | Glossary | EN/DE terminology |
| 13 | Frequency Framework | Holonomy invariants, frequency curvature, experimental prospects |
- repo_index of documentation — master index
- BOOK_TO_DOC_GAP_ANALYSIS.md — (deprecated) Gap analysis book → docs
- DOCUMENTATION_COMPLETENESS.md — Documentation completeness assessment
- ssz_overview.md — What is SSZ, executive summary
- core_postulates.md — The 5 core postulates
- relation_to_gr.md — How SSZ relates to GR
- authors.md — Carmen N. Wrede, Lino P. Casu
- segment_density.md — Xi(r): weak, strong, blend formulas
- time_dilation.md — D(r) = 1/(1+Xi)
- scaling_factor.md — s(r) = 1+Xi = 1/D
- regime_definitions.md — 5 regimes, transition radii, two-layer coherence collapse clarification
- regime_and_formula_domain_clarification.md — Formula domains vs physical regimes, numerical table, 6 common misunderstandings
- phi_geometry.md — Golden ratio in SSZ
- phi_lattice_discretization.md — φ-lattice x_k=φ^k, bracket theorem, QNM connection
- intersection_invariance.md — two mass-independent r*/r_s comparisons: 1.594811 and 1.386562
- coherence_collapse.md — g1→g2 irreversible transition
- energy_conditions.md — WEC/DEC/SEC/NEC in SSZ, SEC violation
- emergent_axes.md — Emergent coordinate axes
- euler_derivation.md — Euler identity connection
- fine_structure.md — alpha = 1/137 derivation
- structural_constants.md — phi, alpha_SSZ, r*/r_s
- temporal_growth.md — Temporal growth rate
- space_and_path.md — Space, path, and emergence in SSZ theory
- formula_compendium.md — Complete formula list with origin + domain
- quick_reference.md — Top-10 formulas on one page
- symbol_table.md — All symbols defined
- ppn_formulas.md — PPN gamma=1, lensing, Shapiro — CRITICAL
- worked_examples.md — Cassini, Mercury, GPS, NS calculations
- unit_conversion_table.md — SI/CGS/Natural units
- special_values.md — Xi(r_s)=0.80171, D(r_s)=0.55503, r*/r_s, phi-table
- phi_beta_calibration.md — Calibration curves
- forbidden_formulas.md — Deprecated/wrong formulas to avoid
- DISCRETE_SSZ_STATE_FORMULATION.md — Discrete SSZ state formulation: canonical technical reference
- DISCRETE_SSZ_STATE_FORMULATION_DE.md — Deutsche Fassung der diskreten SSZ-Zustandsformulierung
- dual_velocities.md — v_coord vs v_physical
- lorentz_v0.md — Lorentz factor at v=0
- kinematic_closure.md — Kinematic closure condition
- frame_dragging.md — Lense-Thirring, Gravity Probe B
- geodesics.md — Geodesic equations, radial free-fall
- orbital_mechanics.md — ISCO, photon sphere, effective potential
- radial_scaling.md — Radial scaling gauge for Maxwell fields
- group_velocity.md — Group velocity in segment lattice
- light_travel_time.md — Additive travel time correction
- maxwell_rotating.md — Maxwell equations in rotating SSZ
- redshift.md — Gravitational redshift z = Delta_Xi
- energy_em_field.md — EM energy in segment lattice, u = s^2*u_flat
- shapiro_delay.md — Shapiro delay, PPN factor, Cassini
- gravitational_lensing.md — Lensing alpha=2r_s/b, Eddington, VLBI
- black_hole_metric.md — SSZ Schwarzschild metric
- singularities.md — Singularity resolution, D(r_s)=0.555
- dark_star.md — Dark star (no true horizon)
- cosmic_censorship.md — SSZ version of cosmic censorship
- infalling_matter.md — Infalling matter, no freezing
- superradiance.md — Wave amplification in ergosphere
- rotating_black_holes.md — Kerr-SSZ, ergosphere, frame dragging
- qnm_spectrum.md — QNM: f_SSZ/f_GR = 1.39, phi-lattice connection
- isco_comparison.md — ISCO: SSZ r_ISCO = 2.95 r_s vs GR 3 r_s
- penrose_process.md — Penrose efficiency: SSZ 21.4% vs GR 20.71%
- lagrangian_mechanics.md — Effective Lagrangian, Euler-Lagrange, orbit equations
- GR_SSZ_INTERSECTION_PHI_DISCRETIZATION.md — GR–SSZ intersection: derivation on the φ-lattice
- delta_a_derivation.md — deltaA_SSZ(f) derivation
- delta_psi_derivation.md — deltaPsi_SSZ(f) derivation
- epsilon_220_derivation_status.md — epsilon_220 derivation status
- h_ssz_v0_derivation.md — h_SSZ(f) V0 derivation
- all_tests_2026-05-07.md — Canonical all-tests snapshot: 1296/1296 PASS
- test_methodology.md — Forward-prediction test framework and method assignment
- consistency_checks.md — Formula and cross-repository consistency checks
- gr_vs_ssz_tables.md — Side-by-side comparison tables
- curvature_detection.md — Frequency curvature observables
- nebulae_validation.md — G79.29+0.46 LBV nebula (Cygnus X-1)
- gps_validation.md — GPS: +38.45 µs/day confirmed
- cassini_test.md — Cassini: gamma=1.000021±0.000023
- mercury_precession.md — Mercury: 42.98"/century confirmed
- neutron_star_redshift.md — NS: z_SSZ=0.173 vs z_GR=0.236
- power_law_universal.md — E/E_rest = 1+0.32*(r_s/R)^0.98, R²=0.997
- ligo_gw240925_v0_pipeline.md — GW240925 O4b forward model pipeline (EXPLORATORY, no claim) — data: Zenodo 18600070
- ligo_final_interpretation_lock.md — Locked interpretation of LIGO pipeline results
- ligo_artifact_gate_gw240925.md — L1 artifact gate: 20-40 Hz excess, kurtosis +44.9
- ligo_h1l1_mini_pipeline_test_plan.md — 10-phase hard-gate test plan; trigger vs off-source windows (±100/300/500 s), subband xcorr; Phase 3–10 PENDING
- ligo_h1l1_time_delay_replication.md — H1/L1 FFT xcorr lag scan ±50ms, COHERENT_WITH_SIGN_FLIP
- LIGO H1/L1 long-baseline extension (off-source windows, subband xcorr statistics; PENDING run) — planned as Phases 3–10 of ligo_h1l1_mini_pipeline_test_plan.md. (Listed as
ligo_h1l1_long_baseline_plan.mdin earlier README versions; no separate file exists.) - ligo_next_physics_derivation_tasks.md — LIGO next physics derivation tasks
- test_coverage_complete.md — SSZ complete test coverage
- falsification_criteria.md — When SSZ is falsified
- predictions.md — Quantitative predictions
- instruments.md — EHT, NICER, ET, LISA, Athena
- known_limitations.md — Known limitations and open questions
- ligo_open_data_position.md — Strain vs posteriors: model-bound self-confirmation problem
- ligo_physics_clarification.md — Chirp mass, posteriors, L1 anomaly, anti-circularity
- LIGO reproducibility critique — sourced critique: calibration gap, bilby migration, PB-scale data vs public release → hosted in ssz-ligo-tests/docs. (The relative link
08_FALSIFICATION/ligo_reproducibility_critique.mdused here was dead — target exists only in the external repo; flagged by the pipeline link check and openly re-pointed to the GitHub URL in the 2026-10-11 revision.) - LIGO open data full report (8 parts, 14 sources) — calibration chain, PCal/DARM gap, code provenance, template dependence, GW150914 reproduction failure, reproducibility standard → hosted in ssz-ligo-tests/docs. (Same dead relative link
08_FALSIFICATION/ligo_open_data_full_report.md— openly re-pointed 2026-10-11.)
- paper_index.md — All 25 papers with abstracts
- bibliography.md — References
- preprints.md — Preprint status
markdown/— 64 mirrored paper markdown files (source PDFs inpdf/), plus the interactive Exponential Triangle visualization README
- repo_index.md — All 37 repositories
- test_file_index.md — All test files
- reproducibility.md — How to reproduce results
- ligo_tests_findings.md — ssz-ligo-tests: pipeline findings, H1/L1 delay test, open blockers
- prime_directive.md — Observable → Class → Method → Scope
- method_assignment.md — Which method for which observable
- confusion_prevention.md — Common errors and how to avoid them
- cross_repo_rules.md — Cross-repository consistency rules
- glossary_en.md — English terminology
- glossary_de.md — German terminology
- holonomy_invariants.md — I_ABC=1, LISA connection, topological invariance
- frequency_curvature.md — d²D/dr² = 4× GR, 3-clock measurement
- future_experimental_prospects.md — Timeline 2024–2038: EHT, eXTP, ET, LISA, Athena
- full-segmented-memory.md — Full segmented memory (project brain)
- FULL_PIPELINE_REPORT.md — Latest pipeline report (generated, see below)
- LICENSE.md — Anti-Capitalist Software License v1.4
| Metric | Value |
|---|---|
| Papers | 25 primary + 7 additional |
| LIGO Tests (ssz-ligo-tests) | v0.5.0 — 330+ tests, GW240925 O4b, long-baseline xcorr, NO CLAIM |
| Repositories | 37 total (35 public, 2 private) |
| Tests | 1296/1296 verified in canonical all-tests run |
| Documentation files | 172 MD files (105 core + 67 under 09_PAPERS/: 3 indexes + 64 markdown mirrors) — audited 2026-10-11 |
| Consistency checks | 0 failed in all-tests snapshot; pipeline formula check 11/11 OK (2026-10-11) |
Animated GIF plots of the SSZ core physics, rendered by demos/render_core_physics_animations.py (numpy + matplotlib + pillow, dark theme). All formulas are taken verbatim from the canonical documentation — sources are cited in the module docstring.
| GIF | Frames | Shows |
|---|---|---|
demos/output/ssz_time_dilation_gr_vs_ssz.gif |
76 | D(r) = 1/(1+Ξ(r)) built up dynamically; GR D→0 at r_s vs SSZ D(r_s) = 0.55503 (finite) |
demos/output/ssz_regime_map_animated.gif |
80 | Weak/strong regime map with transition radii fading in (very close / blend / photon sphere / strong / weak, in r/r_s) |
demos/output/ssz_phi_lattice_bracket_theorem.gif |
66 | φ-lattice x_k = φ^k growing + bracket-theorem intervals [F_k, F_k+1] |
Render (self-checks run automatically; exit code 0 on success):
/home/error/physics/venv/bin/python demos/render_core_physics_animations.pySee REPRODUCE.md for how to re-derive every number shown.
tools/run_full_pipeline.py (stdlib only) runs three checks over the repository and writes FULL_PIPELINE_REPORT.md:
- Inventory — MD files per section, core vs paper-mirror counts
- Link check — resolves all relative Markdown links, reports dead targets (policy: report only, never silently fix)
- Formula consistency — recomputes the canonical key numbers (Ξ(r_s) = 0.80171, D(r_s) = 0.55503, r*/r_s = 1.594811 and 1.386562, …) and counts their cross-file presence
Latest run (2026-10-11, after this revision): 172 MD files, formula identities 11/11 OK, 0 dead links (the two historical LIGO dead links in 08_FALSIFICATION were openly re-pointed to their GitHub URLs in this README revision; the pipeline now resolves every link).
/home/error/physics/venv/bin/python tools/run_full_pipeline.pyNumerical research lives in separate repositories; this repo is the canonical documentation.
| Repository | Purpose |
|---|---|
| SSZ_FULL_CLOSURE | Full-closure numerical program: FK coupled model, SRF gates, bridge runs |
| SSZ-Transport-Bridge | Transport-bridge calculations |
| SSZ-Spectroscopy-Bridge | Spectroscopy-bridge calculations (QNM/ε-220 program) |
Re-certification 2026-10-11 (documented in SSZ_FULL_CLOSURE):
- FK coupled model V1: 6/6 gates PASS
- SRF: 5/5 gates PASS
- Bridge Run 6: STAGE1 + STAGE2 PASS
- SW-Diag: verdict PEAKS_NOT_ROBUST
- New to SSZ? → Start with 01_OVERVIEW/ssz_overview.md
- Need formulas? → Go to 03_FORMULAS/formula_compendium.md
- Quick card → See 03_FORMULAS/quick_reference.md
- Method selection → Read 11_GUARDRAILS/prime_directive.md
- Validation data → Check 07_VALIDATION/all_tests_2026-05-07.md and 07_VALIDATION/gr_vs_ssz_tables.md
- Regime vs formula domains? → Read 02_FOUNDATIONS/regime_and_formula_domain_clarification.md
- φ-Lattice → See 02_FOUNDATIONS/phi_lattice_discretization.md
- Experimental timeline → See 13_FREQUENCY_FRAMEWORK/future_experimental_prospects.md
- See the physics animated → Run the animation renderer, watch the GIFs in
demos/output/ - Audit the repo → Run the full pipeline, read FULL_PIPELINE_REPORT.md
- Reproduce / peer-review → Follow REPRODUCE.md; review notes in PEER_REVIEW.md
Observable → Class → Method → Scope → Then calculate.
| Observable Type | Method | Formula |
|---|---|---|
| Timelike (clocks) | Ξ-based | D = 1/(1+Ξ) |
| Null (light) | PPN (1+γ) | α = 2r_s/b |
| Orbit (precession) | PPN (β,γ) | Standard PPN |
This project is licensed under the Anti-Capitalist Software License v1.4.
See LICENSE.md for the full license text.
@misc{wrede2026sszdocs,
title={Segmented Spacetime (SSZ) -- Complete Documentation},
author={Wrede, Carmen N. and Casu, Lino P.},
year={2026},
note={Available at https://github.com/error-wtf/ssz-complete-documentation}
}© 2025–2026 Carmen N. Wrede, Lino P. Casu