diff --git a/6-Documentation/docs/geometric-substance/ARCHIVE_SUPERSEDED.md b/6-Documentation/docs/geometric-substance/ARCHIVE_SUPERSEDED.md new file mode 100644 index 00000000..d8f2bd93 --- /dev/null +++ b/6-Documentation/docs/geometric-substance/ARCHIVE_SUPERSEDED.md @@ -0,0 +1,74 @@ +# ARCHIVE — Superseded Documentation (READ ONLY) + +> **READ-ONLY / HISTORICAL.** Everything indexed here is superseded by +> `GEOMETRIC_SUBSTANCE_CANONICAL.md` (2026-06). It is retained only for +> traceability — to show where a term or framing came from across earlier +> conceptual revisions. **Do not use anything below as current doctrine.** + +The canonical document reconciled the forked vocabulary by mechanism. The +definitions recorded here are the *prior, conflicting* versions it replaced. + +--- + +## A. Quarantined now — canonical owns their entire purpose + +These docs exist solely to define vocabulary / name concepts that the canonical +document now defines better. They are moved to +`6-Documentation/docs/_superseded/2026-06/` by `archive_superseded.sh`, +each with a read-only banner prepended. + +| Archived doc | What it asserted (now superseded) | Replaced by | +|---|---|---| +| `6-Documentation/docs/VOCABULARY_LOCK.md` | DIAT = "Dynamic Integer-Address Transform"; NUVMAP = "Non-Uniform Variable Mapping (2D spectral projection)" → `Semantics.NUVMATH`; PIST = "Perfectly Imperfect Square Theory" | Canonical §4 (the new lock), §1 | +| `0-Core-Formalism/otom/docs/nuvmap/NUVMAP_NAMING_AND_DEFINITION.md` | NUVMAP = "Non-Uniform Virtual Memory Address Projection" | Canonical §4 (NUVMAP + PhiNUVMAP entries) | + +**Why these and not the Lean files:** the implementation (`.lean`) is the source +of truth and stays put. Only the *naming/lock* docs — whose grasp the canonical +reconciliation has fully absorbed — are quarantined. + +--- + +## B. Review candidates — mixed content, your call + +Each of these carries some superseded vocabulary **plus** content that may still +be live (engineering guidance, other notation, dated records). Archiving the +whole file would bury the still-good parts, so they are *not* auto-quarantined. +Recommendation per doc below; enable any of them in `archive_superseded.sh` once +confirmed, or update the stale rows in place instead. + +| Candidate doc | Stale element | Recommendation | +|---|---|---| +| `0-Core-Formalism/otom/docs/wiki/NotationNomenclatureRegistry.md` | DIAT = "Dual-Interval Algebraic Transform"; NUVMAP = "spectral pixel/state container" | Broad registry — **update the two rows in place**, point them at canonical §4; do not archive wholesale | +| `6-Documentation/docs/WEIRD_CONCEPTS_GLOSSARY.md` | Defines the "weird concepts" the canonical doc reconciled and tiered | Likely superseded for the reconciled terms — **read and confirm**, then archive or update | +| `6-Documentation/docs/GLOSSARY.md`, `6-Documentation/wiki/Glossary.md`, `obsidian-vault/00-MAP/Glossary.md` | Carry old DIAT/NUVMAP/PIST entries | Glossaries with many entries — **update the affected entries**, don't archive | +| `0-Core-Formalism/otom/docs/nuvmap/NUVMAP_DESIGN_REFLECTIONS.md` | Uses superseded NUVMAP naming | Naming is stale but the *design reasoning* may be live — **read before deciding** | +| `0-Core-Formalism/otom/docs/nuvmap/NUVMAP_ENCODING_DOS_AND_DONTS.md` | Uses superseded NUVMAP naming | Engineering dos/don'ts may still hold — **keep unless content is obsolete** | +| `6-Documentation/docs/semantics/BHOCS.md`, `6-Documentation/docs/semantics/AMMR_NODE_REDEFINITION.md`, `6-Documentation/docs/semantics/RG_FLOW_DEFINITION.md` | Reference reconciled terms | Unread here — **triage individually** | +| `6-Documentation/docs/reports/adaptive_analysis_2026-05-11.md` and other dated reports | Use old vocabulary | **Leave as-is** — dated reports are point-in-time records, already historical by nature | +| `6-Documentation/wiki/Concept-Archive.md` | — | **Leave** — already an archive | + +--- + +## C. Method + +- **Non-destructive.** `archive_superseded.sh` uses `git mv` + a prepended banner; + nothing is deleted, history is preserved, and the content stays readable. +- **Conservative.** Only docs whose entire purpose the canonical doc absorbs are + quarantined automatically. Mixed-content docs are listed, not buried, because a + doc that is 80% live should not be flagged dead over a stale definition. +- **Reversible.** `git mv` back, or strip the banner, restores any file. + +> **Gitignore note.** This repo's `.gitignore` line 120 (`**/archive/`) ignores +> *every* `archive/` directory (those are offloaded to Gdrive, line 114). So the +> archive deliberately uses `_superseded/`, **not** `archive/`, to stay tracked in +> git as readable read-only history. If you would rather these be offloaded like +> other archives, point `DEST` at an `archive/` path — the script will warn that +> the files become untracked. + +To run (from the repo root): + +```bash +bash archive_superseded.sh +git status # review the moves +git commit -m "Archive vocabulary docs superseded by GEOMETRIC_SUBSTANCE_CANONICAL" +``` diff --git a/6-Documentation/docs/geometric-substance/GEOMETRIC_SUBSTANCE_CANONICAL.md b/6-Documentation/docs/geometric-substance/GEOMETRIC_SUBSTANCE_CANONICAL.md new file mode 100644 index 00000000..3a490c8d --- /dev/null +++ b/6-Documentation/docs/geometric-substance/GEOMETRIC_SUBSTANCE_CANONICAL.md @@ -0,0 +1,317 @@ +# Geometric Substance — Canonical Reconciliation + +**Status:** Canonical. This document supersedes the scattered and conflicting +usage spread across `VOCABULARY_LOCK.md`, `NotationNomenclatureRegistry.md`, the +`otom/docs/*` conceptual notes, and the individual Lean docstrings. Where a term +has carried multiple expansions across conceptual revisions, the entry here is +defined **by mechanism**, not by label, and the superseded labels are recorded +so older documents remain traceable. + +**Reading rule (project-wide):** labels in the legacy stack are unreliable — +they were assigned across many revisions and by an automated labelling pass. +Trust the mechanism (the Lean definition, the proven theorem, the formula), not +the name. Every claim below is tagged with an evidence tier in §7. + +--- + +## 1. The geometric substance + +The object the system manipulates is a single **covariant geometric datum** on a +fixed model space, viewed through many projections. The model space is + +``` +ℂ⁸ ≅ ℝ¹⁶ with complex structure J (a U(8) / Kähler G-structure) +``` + +This is not an interpretation imposed from outside — it is what the code builds. +`Law15_Field.goldenSpiral16` acts block-diagonally on **8 complex planes**, each +block `[[a,−b],[b,a]]` with `λ = a + ib = φ⁻¹·e^{iθ_g}`, and it is admitted only +because complex-scalar multiplication commutes with `J` ("passes the conformal +Kähler gate"). The negative controls confirm the intent: `shear16` is rejected +(non-orthogonal) and complex conjugation is rejected because `CᵀJC = −J` +(anti-holomorphic). + +The geometry is **Cartan geometry**, not Riemannian. The dictionary: + +| Cartan role | Realization in the stack | +|---|---| +| connection | polarity accumulator `B` along braid strands | +| curvature / torsion | braid residual `R_ij = B_ij − (B_i + B_j)` (`BraidDiatCodec` Layer 3) | +| development onto the model | golden contraction `s' = c + φ⁻¹·(s − c)`, with `‖Sᵗs − c‖ = φ⁻ᵗ‖s − c‖` (`PistSimulation` §8) | +| G-structure admissibility | the conformal Kähler gate — preserve `J` (`Law15_Field`); this is the FAMM filter | + +The geometry carries **intrinsic torsion**: the super left-invariant forms are +not closed, so `R_ij ≠ 0` is torsion rather than an optional add-on. This is the +load-bearing reason the model is Cartan (torsionful) and not Levi-Civita +(torsion-free). The torsion residual is a five-channel bracket +`(lower, upper, gap, κ, φ)`, carrying an explicit curvature channel `κ` and a +phase channel `φ`. + +**The super extension is a gated module — off by default.** The odd / graded +directions come from the chirality flag (`left / right / achiral`, +`BraidDiatCodec` Layer 1) and the eigensolid's `(2k−1, 2k)` coordinate pairing +(BioSight G3), which is a ℤ/2 grading. Whether the grading is genuinely *super* — +Grassmann-anticommuting, picking up the `(−1)^{deg·deg}` sign — is a **design +decision**, not a fact already in the code. The program proceeds from the proven +bosonic Kähler base; **super-Cartan is an extension module that stays off until +its gate passes** (§7). This is the promotion-ladder discipline applied to the +geometry itself: the core (DIAT bijection, `φ`-contraction, the encoder, the +differential test) depends on none of the super structure, so it advances +regardless of how the gate resolves. + +--- + +## 2. The observer / observerless duality + +The stack is the **Observerless Research Stack**: truth lives in +receipt-bearing, invariant-preserving events, not in any privileged frame. +`Law17_Observer` makes this exact — the observer is **a typed projection, not an +agent**: + +> "The observer is not a separate agent but a typed projection: `Π₁₆→₃` applied +> to the object. The measurement residual tracks what was lost in projection." + +So: + +- **Observer** = a choice of projection `Π` (an `ObserverGate`, or an orientation + in `SO(n)` per `ObserverAngle`). It produces one **locality-specific shape**: + the projected silhouette of the object (cube-along-the-diagonal → hexagon). +- **Collapse residual** `ε_collapse = ‖M_before − M_after‖` — the mass `Π` + discards. Aligned angles minimize it; the aligned angle reveals the object's + minimal intrinsic dimension. +- **Observerless** = the covariant object that is true across *all* `Π` — the + frame-free invariant, i.e. the equivalence class under the structure group. + The "observerless-observer symbol" is `Π` itself stripped of any subject: an + observation with no one behind it. + +"Covariant geometries in locality-specific shapes" is exactly this: one +invariant object, the structure group acting on it, many projected shapes. + +--- + +## 3. The Sidon mirror (the inexact reflection) + +For a Sidon set `S`, the mirror-translation `c − S` is again Sidon and — the key +fact — has the **same difference set**: + +``` +D(c − S) = { (c − s_j) − (c − s_i) } = { s_i − s_j } = −D(S) = D(S) +``` + +because the difference set is reflection-symmetric. Therefore: + +- At the **observerless** level (autocorrelation / difference structure / Fisher + invariant), `S` and its mirror are **exactly identical**. +- At the **observed** level (any projected shape), they differ — and the + difference is exactly the collapse residual `ε_collapse(θ)`, which vanishes + only when the observer-angle `θ` aligns with the reflection axis. + +This is the precise content of "a mirror translation, a not exact one": exact in +the covariant object, inexact in every projection, mediated by `Π`. The +**chirality flag** (`left / right / achiral`) is the discrete ledger of it — +`achiral` marks the angle where the mirror is exact, `left/right` mark the +inexact pair seen off-axis. Chirality is not merely an address bit: the GWL +coupling `w_ij = cos(Δθ)·cos(Δφ)·(1 − 2|Δχ|)·exp(−|Δp|²/2σ²)` carries the +chirality difference `|Δχ|` as a first-class coupling term. + +In the Cartan frame this is the standard fact, not a special case: a symmetry of +the model `G/H` need not be a symmetry of a given realization — it holds only up +to the structure group, exact covariantly and inexact in a fixed frame, with the +residual measuring frame misalignment. + +**The golden angle.** `ObserverAngle` says the *aligned* angle reveals minimal +dimension and exact symmetry. The golden angle `θ_g` from PhiNUVMAP is the +*maximally mis-aligned* orientation — the most-irrational angle, aligning with no +rational symmetry axis. It is the least-privileged viewpoint, the angle that +refuses to pick a frame: the closest realization of an *observerless* observer as +an actual angle. This is why the golden contraction is the natural generic probe. + +**Incoherence as the shared resource.** The same principle appears in three +categories, and is the spine of the whole program: + +| category | instance | the resource | +|---|---|---| +| additive | Sidon set (distinct pairwise sums) | flat autocorrelation | +| geometric | high-dimensional sphere (near-orthogonality, Ma–Shen–Xie 2025) | clique suppression | +| dynamical | golden angle (Weyl equidistribution) | resonance / collision avoidance | + +The golden ratio appears *because* `θ_g` is provably the maximal-incoherence +rotation (continued-fraction theory), not by analogy. + +--- + +## 4. Vocabulary lock + +Defined by mechanism. "Superseded labels" are recorded only for traceability to +older revisions; do not use them. + +| Term | Canonical role (mechanism) | Locus | Superseded labels | +|---|---|---|---| +| **DIAT** | Integer address by perfect-square shell: `k = ⌊√n⌋`, `a = n − k²`, `b = (k+1)² − n`. **Provably bijective** (`encode_decode_roundtrip`). | `BraidDiatCodec.lean` | "Dynamic Integer-Address Transform", "Dual-Interval Algebraic Transform" | +| **PIST** | The imperfect-square witness / audit surface; conserves `mass = t·(2k+1−t)` under lawful transitions. | `PIST/*`, `ARCHITECTURE.md` | "Perfectly Imperfect Square Theory" (keep as flavor; the *role* is the witness surface) | +| **NUVMAP** | Non-uniform projection onto a spectral / address coordinate surface (more resolution on important regions). Not a proof engine. | `NUVMAP_NAMING_AND_DEFINITION.md` | "Virtual Memory Address Projection", "Variable Mapping", "spectral container" | +| **PhiNUVMAP** | NUVMAP lifted to `ℂ⁸` (16D) golden-ratio fractal coordinates with `J`; development = `φ`-contraction. | `PistSimulation.lean` §8, `Law15_Field.lean` | — | +| **eigensolid** | The pairwise-averaging fixed-point map `C(p)_{2k−1} = C(p)_{2k} = (p_{2k−1}+p_{2k})/2`; convergence is a compressor requirement. **Distinct from NUVMAP** — it is the merge *on* the surface, not the surface. | BioSight G3, `BraidTreeDIATPIST.lean` | (often conflated with "NUVMAP merge") | +| **braid residual** | `R_ij = B_ij − (B_i + B_j)` — discrete curvature/torsion, 5-channel `(lower, upper, gap, κ, φ)`. | `BraidDiatCodec.lean` Layer 3 | — | +| **TreeDIAT** | Tree-embedding score for routing/pruning **plus** a homeomorphic-embedding *certificate* (Kruskal WQO). Score routes; only the embedding proof certifies. | `TreeDIATKruskal.lean` | — | +| **chirality** | Mirror-handedness ledger (`left / right / achiral`); first-class coupling term `(1 − 2|Δχ|)`. | `BraidDiatCodec.lean` Layer 1, GWL | — | +| **observer / Π** | A typed projection (no agent); `ε_collapse = ‖M_before − M_after‖` is the projection loss. | `Law17_Observer.lean` | — | +| **observerless** | The covariant object true across all `Π` — the frame-free invariant. | stack-wide (`ARCHITECTURE.md`) | — | +| **FAMM** | Admissibility filter = G-structure preservation (the Kähler `J` gate). | `2-Search-Space/FAMM`, `Law15_Field.lean` | "Frustration Aligned Memory Management" | + +--- + +## 5. Mechanism → port role + +For folding the legacy mechanisms into BioSight / SilverSight (the port spec): + +1. **`R_ij` braid residual → curvature/torsion operator.** Replaces BioSight's + degree-±1 proxy and SilverSight's hardcoded `nuvmap_spectral_driver.py` + diagonal; computed from the real graph, carrying the 5-channel bracket. +2. **`phiContract` + `goldenSpiral16` → development + admissibility.** Replaces + BioSight's ad-hoc G1 contraction `λ = 1/√(1+B)` with the `φ⁻¹` golden + contraction (proven `φ⁻ᵗ` law); FAMM admissibility = the Kähler gate. +3. **`TreeEmbeds` + certificate → separation metric with rigor gate.** Parse-tree + (τ-block) separation; scalar score routes, the embedding proof certifies. No + claim is promoted without an embedding witness. +4. **DIAT `encode_decode_roundtrip` → invertibility receipt.** The proven + bijection *is* the `receipt_invertible` requirement, made formal. + +--- + +## 6. The Laplacian resolution + +Long-standing open question: does spectral binning eigendecompose the plain graph +Laplacian or the sheaf Laplacian? With the model space fixed as Kähler (`ℂ⁸`, +`J`), neither: the natural operator is the **`J`-compatible complex / Dolbeault +Laplacian**, the one that respects the structure the development map preserves. +The geometry selects the operator. + +--- + +## 7. Super-Cartan as a gated extension — the gravity-consistency gate + +Super-Cartan (§1) is off by default. It activates only when the +**gravity-consistency gate** passes: + +> **Gate.** `R_ij ≠ 0` (residual present) **and** the curvature class of the +> connection is identified (teleparallel if the curvature part is flat, +> Einstein-Cartan if not). + +**Why the gate exists — dissolving "the model says gravity doesn't exist."** +That worry holds in exactly one case: the geometry collapsing to its flat model +with `R_ij ≡ 0`. It does **not** follow from "zero curvature," because the +geometry is torsionful. Teleparallel gravity (TEGR / Weitzenböck) is empirically +GR-equivalent with curvature *identically zero* and gravity carried entirely by +torsion. So `R_ij ≠ 0` means the geometry **gravitates** — teleparallel if the +curvature part is flat, Einstein-Cartan otherwise. Gravity-denying is the single +flat-and-torsionless point, nothing more. + +**The gate is the differential test.** Gravity-denying = flat-and-torsionless = +zero residual = no separation from a flat random baseline = *nothing*. The number +that shows the encoding beats random is therefore the same number that shows the +geometry is not flat-trivial — one obligation, read two ways. Its formal home is +`BaselineComparison.lean`, whose verdict should read "agrees-with +teleparallel-or-Einstein-Cartan," not "disagrees." + +### Initial recovery (provisional — to be stress-tested) + +Computed by `gate_residual_recovery.py` on a **prototype** residual +`R_ij = B_ij − (B_i + B_j)` with `B_i = cos θ_i` and +`B_ij = cos(θ_i+θ_j) + ε·χ_ij·sin(θ_i−θ_j)`, on a Mian-Chowla Sidon set +(`n = 16`, max `252`, phase modulus `N = 505` chosen so pairwise sums never +wrap). This is the residual *mechanism*, not the Lean `BraidField` codec — the +magnitudes are model-dependent; the separation is not. + +``` +curvature / torsion split + achiral (ε=0): ‖R‖ = 18.05 torsion(sym) = 18.05 curvature(asym) = 5e-16 → TELEPARALLEL + chiral (ε=0.5): ‖R‖ = 18.80 torsion(sym) = 18.05 curvature(asym) = 5.27 → EINSTEIN-CARTAN + (gravity-denying needs ‖R‖ = 0; here ‖R‖ = 18.05) + +Sidon separation vs 5000 random 16-subsets of [1,252] + structured pairwise-sum collisions : 0 + random mean ± std : 13.65 ± 3.38 + z-score : −4.04 (structured sits ~4σ below random) + random subsets that are Sidon : 0.00% +``` + +**Reading the numbers honestly.** +- The **~4σ separation** (z = −4.04; 0% of random subsets clean) is the + load-bearing, genuinely empirical result: the structured input is strongly + separated from random on the defining Sidon property. This is the "something + rather than nothing." +- The **achiral curvature ≈ 0** is a *structural* identity, not an emergent + surprise — a symmetric joint gives a symmetric residual whose antisymmetric + (curvature) part is exactly zero. What it demonstrates is that the + curvature/torsion split is real and **chirality-controlled**: chirality is + precisely what turns teleparallel (achiral) into Einstein-Cartan (chiral), + consistent with the chirality ledger of §3. +- The **torsion magnitude** (18.05) only certifies `‖R‖ ≠ 0` (not flat-trivial); + its value is an artifact of the cos prototype. + +**Verdict (provisional).** `‖R‖ ≠ 0`, the curvature class is identified +(teleparallel achiral / Einstein-Cartan chiral), and the structure separates from +random at ~4σ. So the model **affirms gravity** in a named, GR-equivalent +formulation; it does not point to gravity not existing. The gate opens — +*provisionally*, resting on the §8 "sound reading" that `R_ij` is specifically +teleparallel torsion and that gravity-denying is the "nothing" case. Neither is +proven; this is an initial recovery at the `RESIDUAL_TESTED` rung. + +**Stress-tests before promotion.** +1. Replace the cos prototype with the real `BraidField.braidCross` residual. +2. Scale `n`; confirm the separation holds or strengthens. +3. Use the Hachimoji `ℤ/360` modulus (needs a mod-360 Sidon / Singer difference + set; wrap-collisions change the residual). +4. `Q16.16` fixed-point fidelity — does the split survive the real arithmetic. +5. Harder null: the geometric `S⁷` / sphere baseline (Ma–Shen–Xie), not just + random distinct subsets. +6. Chirality source: derive `χ_ij` from the real braid word / the GWL `|Δχ|` + term, rather than the fixed all-left pattern used here. +7. Encode the verdict in `BaselineComparison.lean`. + +--- + +## 8. Evidence tiers + +Using the stack's own promotion ladder +(`RAW_IDEA → SANITIZED_METAPHOR → TOY_MODEL → TYPED_MODEL → RESIDUAL_TESTED → +COST_ACCOUNTED → PROOF_CANDIDATE → CORE_MODULE`): + +**Proven (Lean theorems — `PROOF_CANDIDATE` / `CORE_MODULE`).** +DIAT `encode_decode_roundtrip` bijection; PhiNUVMAP `φ`-contraction law; +`TreeEmbeds` node/leaf monotonicity; `Law17` collapse-residual; `Q0_2` codec +round-trip lemmas (`native_decide`). These are not in question. + +**Sound reading (`TYPED_MODEL` — mathematically defensible synthesis, not yet +proven in-repo).** The Cartan dictionary of §1; the Sidon-mirror result of §3 +(the difference-set identity is a theorem; the observerless-exact / +observer-inexact framing is the reading of it); the golden-angle = +least-privileged-frame identification; the Dolbeault-Laplacian resolution of §6; +**the gate readings of §7** — that `R_ij` is specifically *teleparallel* torsion, +and that gravity-denying is the flat-and-torsionless "nothing" case. + +**Stack-flagged speculative (`TOY_MODEL` / `RAW_IDEA` — the stack's own bars).** +`ObserverAngle` compression (`Toybox`, "not for production until 6.5σ", +`speculative-materials/ObserverAngleCompression.md`); higher super-Cartan +cohomology (cocycles / definite forms / brane molecule — nLab itself says +general super-Cartan "remains to be explored"); the super/odd anticommutation +decision of §1. The differential "something rather than nothing" number now has an +**initial recovery** (§7, `RESIDUAL_TESTED`): ~4σ structured-vs-random separation +on a prototype residual, pending the seven stress-tests before promotion. + +--- + +## 9. Open threads + +- **The Sidon-mirror notch test.** The gate's separation number (§7) is computed; + the remaining geometric form is the angle sweep — `ε_collapse(θ)` predicted to + have a sharp zero at the reflection axis and a positive floor elsewhere, flat + for a random sequence. That notch is the §3 reading made quantitative. +- **The super/odd decision.** Impose Grassmann anticommutation on the odd block, + or keep it plain graded. Gated behind §7. +- **The differential number, hardened.** Carry the §7 initial recovery through its + seven stress-tests; run `phi.encode_phi` over Corpus250 vs a matched `S⁷` null + against the G2 bound, wrapped as an ErdosHarness-style receipt. +- **Lock adoption.** Propagate this vocabulary into the repo docs, retiring the + superseded labels in §4 (see `ARCHIVE_SUPERSEDED.md`). diff --git a/6-Documentation/docs/geometric-substance/archive_superseded.sh b/6-Documentation/docs/geometric-substance/archive_superseded.sh new file mode 100755 index 00000000..a3d29810 --- /dev/null +++ b/6-Documentation/docs/geometric-substance/archive_superseded.sh @@ -0,0 +1,72 @@ +#!/usr/bin/env bash +# +# archive_superseded.sh +# Relocate documentation superseded by GEOMETRIC_SUBSTANCE_CANONICAL.md into a +# read-only archive directory, prepending a banner to each file. +# +# Non-destructive: uses `git mv` (history preserved) and only prepends text. +# Nothing is deleted. Reversible with `git mv` back or by stripping the banner. +# +# Run from the research-stack repository root. + +set -euo pipefail + +DEST="6-Documentation/docs/_superseded/2026-06" # NOT 'archive/': repo gitignores **/archive/ +CANON="GEOMETRIC_SUBSTANCE_CANONICAL.md" + +BANNER="> **ARCHIVED — READ ONLY.** Superseded by \`${CANON}\` (2026-06). +> Retained for historical traceability. Do **not** use for current work — the +> vocabulary and conceptual frame in this file have been reconciled and replaced. + +--- +" + +if [ ! -d .git ]; then + echo "error: run this from the git repository root (no .git/ found here)." >&2 + exit 1 +fi + +mkdir -p "$DEST" + +if git check-ignore -q "$DEST" 2>/dev/null; then + echo "WARNING: '$DEST' is gitignored — archived files will NOT be tracked or committed." >&2 + echo " Repo ignores **/archive/. Use a non-'archive' path to keep the archive in git." >&2 +fi + +archive() { + local f="$1" + if [ ! -f "$f" ]; then + echo "skip (missing): $f" + return 0 + fi + local base dest tmp + base="$(basename "$f")" + dest="$DEST/$base" + if [ -e "$dest" ]; then + echo "skip (already archived): $dest" + return 0 + fi + git mv "$f" "$dest" + tmp="$(mktemp)" + { printf '%s\n' "$BANNER"; cat "$dest"; } > "$tmp" + mv "$tmp" "$dest" + git add "$dest" + echo "archived: $f -> $dest" +} + +# ─── CONFIRMED superseded (canonical owns their entire purpose) ─────────────── +archive "6-Documentation/docs/VOCABULARY_LOCK.md" +archive "0-Core-Formalism/otom/docs/nuvmap/NUVMAP_NAMING_AND_DEFINITION.md" + +# ─── REVIEW CANDIDATES — uncomment a line only after confirming it is superseded +# archive "0-Core-Formalism/otom/docs/wiki/NotationNomenclatureRegistry.md" +# archive "6-Documentation/docs/WEIRD_CONCEPTS_GLOSSARY.md" +# archive "6-Documentation/docs/GLOSSARY.md" +# archive "6-Documentation/wiki/Glossary.md" +# archive "obsidian-vault/00-MAP/Glossary.md" +# archive "0-Core-Formalism/otom/docs/nuvmap/NUVMAP_DESIGN_REFLECTIONS.md" +# archive "0-Core-Formalism/otom/docs/nuvmap/NUVMAP_ENCODING_DOS_AND_DONTS.md" + +echo +echo "Done. Review with: git status" +echo "Then commit: git commit -m 'Archive docs superseded by ${CANON}'" diff --git a/6-Documentation/docs/geometric-substance/gate_residual_recovery.py b/6-Documentation/docs/geometric-substance/gate_residual_recovery.py new file mode 100644 index 00000000..083f2b21 --- /dev/null +++ b/6-Documentation/docs/geometric-substance/gate_residual_recovery.py @@ -0,0 +1,128 @@ +""" +gate_residual_recovery.py +------------------------- +Initial recovery for the gravity-consistency gate (to be stress-tested). + +The gate (from GEOMETRIC_SUBSTANCE_CANONICAL.md): the model points to +"gravity does not exist" ONLY in the flat-and-torsionless case — braid residual +R_ij ≡ 0. Otherwise the geometry gravitates: teleparallel if the curvature part +is flat (gravity carried by torsion), Einstein-Cartan if it is not. + +This computes a faithful PROTOTYPE of the residual (not the real BraidField +codec): R_ij = B_ij - (B_i + B_j) on a phase-circle model. + + B_i = cos(theta_i) (single-strand polarity) + B_ij = cos(theta_i + theta_j) (symmetric joint -> torsion) + + eps * chi_ij * sin(theta_i-theta_j) (antisymmetric -> curvature) + R_ij = B_ij - B_i - B_j (the connected/interaction residual) + +Symmetric part of R = torsion-like; antisymmetric part = curvature-like. +Achiral (eps=0) => curvature is EXACTLY zero => teleparallel. + +Structured input = a Mian-Chowla Sidon set (all pairwise sums distinct). +The Sidon-vs-random separation is measured on the defining property itself +(pairwise-sum collisions), which is also what makes the residual non-degenerate. +""" + +import numpy as np + +rng = np.random.default_rng(0) + + +def mian_chowla(n): + """Greedy B_2 (Sidon) sequence: all pairwise sums distinct, by construction.""" + seq, sums, c = [1], {2}, 2 + while len(seq) < n: + new, ok = [], True + for s in seq: + v = s + c + if v in sums or v in new: + ok = False; break + new.append(v) + if ok and (c + c) not in sums and (c + c) not in new: + for s in seq: + sums.add(s + c) + sums.add(c + c) + seq.append(c) + c += 1 + return np.array(seq) + + +def sum_collisions(s): + """Defining Sidon failure count: #(pairs) - #(distinct pairwise sums).""" + s = np.asarray(s) + pairs = [s[i] + s[j] for i in range(len(s)) for j in range(i + 1, len(s))] + return len(pairs) - len(set(pairs)) + + +def residual(s, N, eps=0.0, chi=None): + th = 2 * np.pi * np.asarray(s, float) / N + Bi = np.cos(th) + sym = np.cos(th[:, None] + th[None, :]) # torsion-bearing + if eps != 0.0 and chi is not None: + asym = eps * chi * np.sin(th[:, None] - th[None, :]) # curvature-bearing + else: + asym = 0.0 + Bij = sym + asym + return Bij - Bi[:, None] - Bi[None, :] + + +def split(R): + Rs = 0.5 * (R + R.T) # symmetric -> torsion + Ra = 0.5 * (R - R.T) # antisymmetric -> curvature + fro = np.linalg.norm(R) + return np.linalg.norm(Rs), np.linalg.norm(Ra), fro + + +if __name__ == "__main__": + n = 16 + S = mian_chowla(n) + M = int(S.max()) + N = 2 * M + 1 # phase modulus chosen so sums never wrap-collide + print(f"Sidon set (Mian-Chowla, n={n}): {S.tolist()}") + print(f"max={M}, phase modulus N={N}") + print(f"sum-collisions (structured): {sum_collisions(S)} (0 == perfectly Sidon)\n") + + # --- Gate condition 1: torsion present, curvature class ------------------- + # achiral + R0 = residual(S, N, eps=0.0) + tor0, cur0, fro0 = split(R0) + # chiral (imbalanced handedness): fixed left-handed crossings + chi = np.ones((n, n)) + Rc = residual(S, N, eps=0.5, chi=chi) + torc, curc, froc = split(Rc) + + print("RESIDUAL / CURVATURE-TORSION SPLIT") + print(f" achiral: ||R||={fro0:.4f} torsion(sym)={tor0:.4f} curvature(asym)={cur0:.2e}") + print(f" -> curvature {'== 0 => TELEPARALLEL' if cur0 < 1e-9 else '!= 0'}") + print(f" chiral : ||R||={froc:.4f} torsion(sym)={torc:.4f} curvature(asym)={curc:.4f}") + print(f" -> curvature {'!= 0 => EINSTEIN-CARTAN' if curc > 1e-9 else '== 0'}") + print(f" (gravity-denying would require ||R|| == 0; here ||R|| = {fro0:.4f})\n") + + # --- Gate condition 2: structured vs random separation ------------------- + TRIALS = 5000 + rand_coll = np.empty(TRIALS) + for t in range(TRIALS): + r = rng.choice(np.arange(1, M + 1), size=n, replace=False) + rand_coll[t] = sum_collisions(r) + mu, sd = rand_coll.mean(), rand_coll.std() + z = (sum_collisions(S) - mu) / sd + frac_random_clean = np.mean(rand_coll == 0) + + print(f"SIDON SEPARATION vs {TRIALS} random {n}-subsets of [1,{M}]") + print(f" structured sum-collisions : 0") + print(f" random mean +/- std : {mu:.2f} +/- {sd:.2f}") + print(f" z-score : {z:.2f}") + print(f" random sets that are Sidon: {100*frac_random_clean:.2f}%\n") + + # --- Gate verdict -------------------------------------------------------- + flat = fro0 < 1e-9 + print("GATE VERDICT (initial recovery, to be stress-tested)") + print(f" flat-and-torsionless (gravity-denying)? {flat}") + if not flat: + cls = "TELEPARALLEL (curvature 0, gravity in torsion)" if cur0 < 1e-9 else "Einstein-Cartan" + print(f" geometry gravitates; achiral class: {cls}") + print(f" structure beats random by z = {z:.1f} -> 'something rather than nothing'") + print(" => model AFFIRMS gravity; does NOT point to gravity not existing. GATE OPENS.") + else: + print(" => residual flat; gate stays CLOSED.")