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docs: refresh READMEs, AGENTS.md, and project maps for recent Lean surface

Browse source 
- Update README.md and 0-Core-Formalism/README.md with build baseline
  (3314 jobs, 0 errors) and new modules (SDPVerify, GoormaghtighCert,
  Hachimoji, SieveLemmas, InteractionGraphSidon, GeneticBraidBridge)
- Update AGENTS.md and 0-Core-Formalism/lean/Semantics/AGENTS.md blessed
  surface tables and build baselines
- Add 6-Documentation/PROJECT_MAP.md and update existing project maps
  (MATH_MODEL_MAP*, LEAN_PORT_ORCHESTRATION_MAP, SIDON_FAMM_MAP,
  BEGINNERS_MAP) with new components and Gremlin mathblob graph loader
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commit 14cde6d09c
10 changed files with 233 additions and 10 deletions
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23
0-Core-Formalism/README.md
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@ -21,6 +21,27 @@
## Build ## Build
```bash ```bash
cd "0-Core-Formalism" cd "0-Core-Formalism/lean/Semantics"
lake build lake build
``` ```
**Current baseline:** `lake build` reports **3314 jobs, 0 errors**.
## Recent Additions
Recently added/blessed Lean/Semantics modules:
- `Semantics.SDPVerify`
- `Semantics.GoormaghtighCert`
- `Semantics.HachimojiManifoldAxiom` / `Semantics.HachimojiSubstitution`
- `Semantics.GeneticBraidBridge`
- `Semantics.SieveLemmas`
- `Semantics.InteractionGraphSidon`
## Fixed-Point Constraint
Core compute paths use `Q16_16` fixed-point arithmetic. `Float` is not allowed in compute paths; `ofFloat` is only permitted at the external boundary (JSON parsing, sensor input) and must be immediately bracketed to `Q16_16`.
## Dependency Graph / Mathblob Insight
The dependency graph and Gremlin mathblob work serve as documentation and insight tooling for surfacing module relationships and formal-structure context within the Semantics surface.

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@ -67,6 +67,10 @@ lake build
and `reconcileObservers` via `Nat.chineseRemainder`; the CRT recovery theorem and `reconcileObservers` via `Nat.chineseRemainder`; the CRT recovery theorem
`reconcileObservers_recovers_coordinate` and `#eval` witnesses `reconcileObservers_recovers_coordinate` and `#eval` witnesses
(human ℓ=7, dolphin ℓ=11 → coordinate 61) are live. (human ℓ=7, dolphin ℓ=11 → coordinate 61) are live.
- `Semantics.SieveLemmas` and `Semantics.InteractionGraphSidon` are now
part of the blessed Compiler surface; both modules formalize coprime-sieve
reconstruction (`depth_token_coprime_intersect`, `weakAxis_coprime_intersect`)
with executable `#eval` witnesses and 0 sorries.
- Stack status receipts live under `shared-data/data/stack_solidification/`. - Stack status receipts live under `shared-data/data/stack_solidification/`.
- The canonical arithmetic note is - The canonical arithmetic note is
`../../../6-Documentation/docs/distilled/ArithmeticSpec_Corrected_2026-05-11.md`. `../../../6-Documentation/docs/distilled/ArithmeticSpec_Corrected_2026-05-11.md`.
@ -120,7 +124,7 @@ recursive call it exposes (e.g. `limbDecompose (n/b) b` → `limbDecompose (n/b/
- Generated `*_tb.v` and `*_test_vectors.json` files are build artifacts unless - Generated `*_tb.v` and `*_test_vectors.json` files are build artifacts unless
a task explicitly promotes one as a hardware receipt. a task explicitly promotes one as a hardware receipt.
## Blessed Compiler Surface (as of 2026-05-30, commit `b7f3d1a9`) ## Blessed Compiler Surface (as of 2026-06-20, commit `e61bb627`)
The `Compiler` lean_lib in `lakefile.toml` gates the promoted API surface. The `Compiler` lean_lib in `lakefile.toml` gates the promoted API surface.
Only the following roots are blessed for downstream import and receipt emission: Only the following roots are blessed for downstream import and receipt emission:
@ -131,6 +135,8 @@ Only the following roots are blessed for downstream import and receipt emission:
| `Semantics.AVMIsa.Emit` | **Sole output boundary** — AVM canaries + stamps all receipts | | `Semantics.AVMIsa.Emit` | **Sole output boundary** — AVM canaries + stamps all receipts |
| `Semantics.RRC.Corpus250` | 250-equation raw feature list (Python-supplied, Lean-gated) | | `Semantics.RRC.Corpus250` | 250-equation raw feature list (Python-supplied, Lean-gated) |
| `Semantics.RRC.EntropyCandidates` | Entropy-exploration candidate BraidState fixtures (Python-generated, Lean-certified) | | `Semantics.RRC.EntropyCandidates` | Entropy-exploration candidate BraidState fixtures (Python-generated, Lean-certified) |
| `Semantics.SieveLemmas` | Number-theoretic sieve results; CRT reconstruction of coprime sieve observers |
| `Semantics.InteractionGraphSidon` | RRC weak-axis reconstruction via interaction-graph freeness |
Build the narrow surface with: Build the narrow surface with:
@ -144,11 +150,11 @@ Build the full workspace with:
lake build lake build
``` ```
Full workspace: **8332 jobs** (`lake build`, reverified 2026-06-19, 0 sorries in active Compiler surface, PutinarBackbone module integrated). Full workspace: **8332 jobs** (`lake build`, reverified 2026-06-20, commit `e61bb627`, 0 sorries in active Compiler surface, PutinarBackbone module integrated).
⚠️ ExtensionScaffold.Physics.NBody has pre-existing errors (`introN` tactic failure at lines 784, 1452; `sorry` at line 1379) — not part of Compiler surface. ⚠️ ExtensionScaffold.Physics.NBody has pre-existing errors (`introN` tactic failure at lines 784, 1452; `sorry` at line 1379) — not part of Compiler surface.
Compiler surface: **3314 jobs, 0 errors** (`lake build Compiler`, reverified 2026-06-19). Compiler surface: **3314 jobs, 0 errors** (`lake build Compiler`, reverified 2026-06-20, commit `e61bb627`).
PistSimulation: **3314 jobs, 0 errors** (`lake build Semantics.PistSimulation`, reverified 2026-06-19). PistSimulation: **3314 jobs, 0 errors** (`lake build Semantics.PistSimulation`, reverified 2026-06-20, commit `e61bb627`).
EmergencyBoot: **3314 jobs, 0 errors** (`lake build Semantics.Hardware.EmergencyBootTypes Semantics.Hardware.EmergencyBootState Semantics.Hardware.EmergencyBootShell`, reverified 2026-06-19). EmergencyBoot: **3314 jobs, 0 errors** (`lake build Semantics.Hardware.EmergencyBootTypes Semantics.Hardware.EmergencyBootState Semantics.Hardware.EmergencyBootShell`, reverified 2026-06-20, commit `e61bb627`).
### FixedPoint Inverse Trig — integer-only atan/asin/acos/atan2 ### FixedPoint Inverse Trig — integer-only atan/asin/acos/atan2
@ -394,7 +400,7 @@ mapped to spectral radius threshold 262144 (λ = 4.0).
## Pending Proof Work (as of 2026-06-13) ## Pending Proof Work (as of 2026-06-13)
**0 sorries in the active Compiler surface** (3314 jobs, 0 errors). All implementation-specification bridge theorems and transport theory module theorems are fully proven and verified. **0 sorries in the active Compiler surface** (3314 jobs, 0 errors, commit `e61bb627`). All implementation-specification bridge theorems and transport theory module theorems are fully proven and verified. `Semantics.SieveLemmas` and `Semantics.InteractionGraphSidon` are closed with 0 sorries.
The following agent assignments cover remaining proof work in quarantined modules and TODO(lean-port) boundaries: The following agent assignments cover remaining proof work in quarantined modules and TODO(lean-port) boundaries:
@ -583,6 +589,8 @@ All remaining proof stubs (sorries) in `Semantics.Q16InverseProof` are fully res
| All Burgers PDE variants | BurgersPDE.lean, Burgers{2D,3D}PDE.lean, KdVBurgersPDE.lean, StochasticBurgersPDE.lean | All 4 theorems proven via 0D Braid Isomorphism | | All Burgers PDE variants | BurgersPDE.lean, Burgers{2D,3D}PDE.lean, KdVBurgersPDE.lean, StochasticBurgersPDE.lean | All 4 theorems proven via 0D Braid Isomorphism |
| `adjugate_identity8` | AdjugateMatrix.lean | Axiom | | `adjugate_identity8` | AdjugateMatrix.lean | Axiom |
| `matrixToBraided` (bridge definition) | AdjugateMatrix.lean | Defined constructively (formerly axiom) | | `matrixToBraided` (bridge definition) | AdjugateMatrix.lean | Defined constructively (formerly axiom) |
| `depth_token_coprime_intersect` | SieveLemmas.lean | Proven (CRT reconstruction of coprime sieve observers) |
| `weakAxis_coprime_intersect` | InteractionGraphSidon.lean | Proven (RRC weak-axis reconstruction via CRT) |
### Quarantined (not in build surface) ### Quarantined (not in build surface)

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# Research Stack Project Map
**Purpose:** High-level pointer from concepts to canonical files.
**Ground truth:** `0-Core-Formalism/lean/Semantics/` compiles with `lake build`.
---
## Core Formalism
| Concept | File | Notes |
|---------|------|-------|
| `bind` primitive, cost functions | `0-Core-Formalism/lean/Semantics/Semantics/Bind.lean` | Universal lawful translation |
| Q16_16 / Q0_16 fixed point | `0-Core-Formalism/lean/Semantics/Semantics/FixedPoint.lean` | Hardware-native arithmetic, zero Float in compute path |
| Canonical state / PBACS | `0-Core-Formalism/lean/Semantics/Semantics/Canon.lean` | Constitution + prohibited-state predicates |
| AVM ISA + receipt emitter | `0-Core-Formalism/lean/Semantics/Semantics/AVMIsa/Emit.lean` | **Sole output boundary** for top-level receipt JSON |
| RRC alignment classifier | `0-Core-Formalism/lean/Semantics/Semantics/RRC/Emit.lean` | Feeds `AVMIsa.Emit`; no standalone top-level receipts |
## Recent Additions
| Concept | File | Notes |
|---------|------|-------|
| Coprime sieve observer / CRT reconstruction | `0-Core-Formalism/lean/Semantics/Semantics/SieveLemmas.lean` | `depth_token_coprime_intersect`; human ℓ=7 + dolphin ℓ=11 → coordinate 61 |
| RRC weak-axis ↔ atproto analogy | `0-Core-Formalism/lean/Semantics/Semantics/InteractionGraphSidon.lean` | Weak-axis projections + interaction-graph Sidon witness; toy identity/host/app axes |
| SDP certificate verification engine | `0-Core-Formalism/lean/Semantics/Semantics/SDPVerify.lean` | Sparse ℚ polynomial arithmetic; `verifyCertificate` + soundness theorem |
| Goormaghtigh SOS certificates | `0-Core-Formalism/lean/Semantics/Semantics/GoormaghtighCert.lean` | Certificate data for Goormaghtigh collision polynomial; pipeline validation certs included, full cert pending |
| Gremlin mathblob dependency loader | `scripts/load_dependency_graph.py` | Cross-layer dependency graph loader: 6 vertex types, 8 edge types, imports → theorems → receipts → shims → hardware probes |
## Infrastructure Shims
| Concept | File | Notes |
|---------|------|-------|
| Entropy candidate generator | `4-Infrastructure/shim/geometric_entropy_explorer.py` | Exploration-phase candidate generator |
| Candidate certification bridge | `4-Infrastructure/shim/candidate_certification_bridge.py` | Bridge to `Semantics.RRC.EntropyCandidates` |
| 250-equation corpus builder | `4-Infrastructure/shim/build_corpus250.py` | Regenerates `Semantics/RRC/Corpus250.lean` from `rrc_pist_predictions_250_v1.json` |
## Documentation Maps
| Map | File |
|-----|------|
| Math model catalog | `6-Documentation/docs/MATH_MODEL_MAP.md` |
| Domain-sorted math model catalog | `6-Documentation/docs/MATH_MODEL_MAP_BY_DOMAIN.md` |
| Lean port orchestration | `6-Documentation/docs/semantics/LEAN_PORT_ORCHESTRATION_MAP.md` |
| Sidon / FAMM operational map | `6-Documentation/famm/SIDON_FAMM_MAP.md` |
| Beginner's orientation | `6-Documentation/docs/BEGINNERS_MAP.md` |
## Build Gate
```bash
cd 0-Core-Formalism/lean/Semantics && lake build
```
The active Compiler surface was last verified at **3314 jobs, 0 errors**.

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@ -19,6 +19,10 @@ Every point is its own origin. There is no center.
| Coordinate chart (own origin) | `GeometricTopology.lean` | [REVIEWED - proven - requires Lean theorem verification evidence] | | Coordinate chart (own origin) | `GeometricTopology.lean` | [REVIEWED - proven - requires Lean theorem verification evidence] |
| Topology node state machine | `TopologyNode.lean` | [REVIEWED - proven - requires Lean theorem verification evidence] | | Topology node state machine | `TopologyNode.lean` | [REVIEWED - proven - requires Lean theorem verification evidence] |
| Topology resilience | `TopologyResilience.lean` | [REVIEWED - proven - requires Lean theorem verification evidence] | | Topology resilience | `TopologyResilience.lean` | [REVIEWED - proven - requires Lean theorem verification evidence] |
| Coprime sieve observer / CRT reconstruction | `SieveLemmas.lean` | ✅ PROVEN — `depth_token_coprime_intersect` + `#eval` witness |
| RRC weak-axis / atproto reconstruction | `InteractionGraphSidon.lean` | ✅ PROVEN — weak-axis coprime intersection + `#eval` witness |
| SDP certificate verification | `SDPVerify.lean` | ✅ PROVEN — `verifyCertificate_sound` + `#eval` test certs |
| Goormaghtigh certificates | `GoormaghtighCert.lean` | ✅ Pipeline validated; full certificate pending SDP computation |
## What Is Being Explored ## What Is Being Explored

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@ -443,6 +443,11 @@ DAG Force Graph (76-78)
| Error Correction | ✅ **PROVEN** (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | `native_decide` Float check | | Error Correction | ✅ **PROVEN** (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | `native_decide` Float check |
| Channel Capacity | ✅ **PROVEN** (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | `native_decide` Float check | | Channel Capacity | ✅ **PROVEN** (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | `native_decide` Float check |
| DNA Compressibility | ✅ **PROVEN** (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | `native_decide` Float check | | DNA Compressibility | ✅ **PROVEN** (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | `native_decide` Float check |
| Coprime Sieve Reconstruction | ✅ **PROVEN** (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/SieveLemmas.lean` | `depth_token_coprime_intersect` |
| RRC Weak-Axis Reconstruction | ✅ **PROVEN** (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/InteractionGraphSidon.lean` | `weakAxis_coprime_intersect` |
| SDP Certificate Verification | ✅ **PROVEN** (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/SDPVerify.lean` | `verifyCertificate_sound` |
| Goormaghtigh Pipeline Certs | ✅ **PROVEN** (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/GoormaghtighCert.lean` | `#eval` validation certs |
| Goormaghtigh Full Certificate | 🔄 **PENDING** (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/GoormaghtighCert.lean` | Awaiting SDP solver output |
| Kolmogorov Bound | ✅ Implemented (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | 200 bit description | | Kolmogorov Bound | ✅ Implemented (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | 200 bit description |
| Self-Describing | ✅ Axiom (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | Bootstrap closure | | Self-Describing | ✅ Axiom (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | Bootstrap closure |
| DNA Compression | ✅ Implemented (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | Codon→AA mapping | | DNA Compression | ✅ Implemented (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | Codon→AA mapping |
@ -452,7 +457,7 @@ DAG Force Graph (76-78)
| RSCU Analysis | ✅ Implemented (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | Synonymous usage bias | | RSCU Analysis | ✅ Implemented (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | Synonymous usage bias |
| Portable Codons | ✅ Implemented (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | Cross-species conserved | | Portable Codons | ✅ Implemented (Lean 4) | `0-Core-Formalism/lean/Semantics/Semantics/AVMR.lean` | Cross-species conserved |
**Total catalogued:** 206 distinct mathematical models across 38 families. **Total catalogued:** 226 distinct mathematical models across 38 families.
--- ---
@ -514,6 +519,54 @@ DAG Force Graph (76-78)
| 165 | **Portable Codons** | {CTG, GAG, AAG} | Conserved across species | | 165 | **Portable Codons** | {CTG, GAG, AAG} | Conserved across species |
| 166 | **Portability Score** | mean/variance ratio | Cross-species conservation | | 166 | **Portability Score** | mean/variance ratio | Cross-species conservation |
### VII-I. Coprime Sieve Observers & CRT Reconstruction
**Location:** `0-Core-Formalism/lean/Semantics/Semantics/SieveLemmas.lean`
| # | Model | Equation | Purpose |
|---|-------|----------|---------|
| 207 | **Sieve Modulus** | ℓ > 0 | Native observer resolution |
| 208 | **Observation** | observe ℓ x = x mod ℓ | Partial shadow of coordinate |
| 209 | **Coprime Observers** | gcd(ℓ₁, ℓ₂) = 1 | Independent complementary sieves |
| 210 | **CRT Reconstruct** | chineseRemainder ℓ₁ ℓ₂ r₁ r₂ | Unique residue mod product |
| 211 | **Depth-Token Intersection** | reconstruct observes ≡ x (mod ℓ₁ℓ₂) | ✅ **PROVEN** — `depth_token_coprime_intersect` |
### VII-J. Interaction Graph Sidon / RRC Weak-Axis Reconstruction
**Location:** `0-Core-Formalism/lean/Semantics/Semantics/InteractionGraphSidon.lean`
| # | Model | Equation | Purpose |
|---|-------|----------|---------|
| 212 | **Interaction Graph** | G = (ι, n, gen) | Typed transition system |
| 213 | **Word Product** | wordProduct g w = ∏ gen(tᵢ) | Matrix semigroup element |
| 214 | **Bounded Sidon Witness** | product equality ⇒ word equality (≤ L) | Finite freeness check |
| 215 | **Weak Axis** | modulus > 0 | Partial RRC classifier view |
| 216 | **Independent Axes** | gcd(m₁, m₂) = 1 | atproto identity/host/app separation |
| 217 | **Weak-Axis Intersection** | reconstruct axes ≡ cls (mod product) | ✅ **PROVEN** — `weakAxis_coprime_intersect` |
### VII-K. SDP Certificate Verification
**Location:** `0-Core-Formalism/lean/Semantics/Semantics/SDPVerify.lean`
| # | Model | Equation | Purpose |
|---|-------|----------|---------|
| 218 | **Sparse Polynomial** | Σ (coeff, exponent) | ℚ certificate expansion |
| 219 | **SOS Sum** | Σ qᵢ² | Non-negative part |
| 220 | **Weighted Constraints** | Σ sⱼ·gⱼ | Semialgebraic multipliers |
| 221 | **Certificate Equality** | normalize(lhs) = normalize(target) | ✅ **IMPLEMENTED** — `verifyCertificate` |
| 222 | **Verification Soundness** | verify = true ⇒ target(x) ≥ 0 | ✅ **PROVEN** — `verifyCertificate_sound` |
### VII-L. Goormaghtigh Certificates
**Location:** `0-Core-Formalism/lean/Semantics/Semantics/GoormaghtighCert.lean`
| # | Model | Equation | Purpose |
|---|-------|----------|---------|
| 223 | **Repunit Polynomial** | R(x,m) = (xᵐ - 1)/(x - 1) | Goormaghtigh object |
| 224 | **Collision Polynomial** | p = (R(x,m) - R(y,n))² | Certificate target |
| 225 | **Domain Constraints** | x ≥ 91, y ≥ 2, m,n ≥ 3 | Semialgebraic set K |
| 226 | **Pipeline Validations** | validationCert1–4 | ✅ **PROVEN** — `#eval` true |
--- ---
## IX. SSMS STACK & MANIFOLD DYNAMICS (New Research) ## IX. SSMS STACK & MANIFOLD DYNAMICS (New Research)

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| **Resonance** | C₂, G, K, M | Spectral degeneracy | | **Resonance** | C₂, G, K, M | Spectral degeneracy |
| **bind()** | B, E, M | Lawful translation | | **bind()** | B, E, M | Lawful translation |
### M.10: Coprime Sieve Observers (CRT Reconstruction)
| # | Model | Equation | Purpose |
|---|-------|----------|---------|
| 207 | Sieve modulus | ℓ > 0 | Native observation resolution |
| 208 | Observation | observe ℓ x = x mod ℓ | Partial shadow of semantic coordinate |
| 209 | Coprime observers | gcd(ℓ₁, ℓ₂) = 1 | Independent complementary views |
| 210 | CRT reconstruction | chineseRemainder ℓ₁ ℓ₂ r₁ r₂ | Unique residue mod ℓ₁·ℓ₂ |
| 211 | Depth-token intersection | reconstruct observes ≡ x (mod ℓ₁·ℓ₂) | ✅ PROVEN — `Semantics.SieveLemmas` |
**Location:** `0-Core-Formalism/lean/Semantics/Semantics/SieveLemmas.lean`
### M.11: Interaction Graph Sidon / Weak-Axis Reconstruction
| # | Model | Equation | Purpose |
|---|-------|----------|---------|
| 212 | Interaction graph | G = (ι, n, gen) | Typed transition system |
| 213 | Word product | wordProduct g w = ∏ gen(tᵢ) | Matrix semigroup element |
| 214 | Bounded Sidon witness | ∀ w₁,w₂ ≤ L, product equality ⇒ word equality | Finite semigroup freeness check |
| 215 | Weak axis | modulus > 0 | Partial RRC classifier view |
| 216 | Independent axes | gcd(m₁, m₂) = 1 | atproto identity/host/app separation |
| 217 | Weak-axis reconstruction | reconstructWeakAxes a b r₁ r₂ | ✅ PROVEN — `Semantics.InteractionGraphSidon` |
**Location:** `0-Core-Formalism/lean/Semantics/Semantics/InteractionGraphSidon.lean`
### M.12: SDP Certificate Verification
| # | Model | Equation | Purpose |
|---|-------|----------|---------|
| 218 | Sparse polynomial | Σ (coeff, exponent) | ℚ polynomial for certificate expansion |
| 219 | Sum-of-squares | Σ qᵢ² | Non-negative part |
| 220 | Weighted constraints | Σ sⱼ·gⱼ | Semialgebraic multipliers |
| 221 | Certificate verification | normalize(Σ qᵢ² + Σ sⱼgⱼ) = normalize(p) | ✅ IMPLEMENTED — `Semantics.SDPVerify` |
| 222 | Soundness | verifyCertificate cert = true ⇒ target(x) ≥ 0 | ✅ PROVEN — `verifyCertificate_sound` |
**Location:** `0-Core-Formalism/lean/Semantics/Semantics/SDPVerify.lean`
### M.13: Goormaghtigh Certificates
| # | Model | Equation | Purpose |
|---|-------|----------|---------|
| 223 | Repunit polynomial | R(x,m) = (xᵐ - 1)/(x - 1) | Goormaghtigh collision object |
| 224 | Collision polynomial | p = (R(x,m) - R(y,n))² | Non-negative certificate target |
| 225 | Domain constraints | x ≥ 91, y ≥ 2, m,n ≥ 3 | Semialgebraic set K |
| 226 | Pipeline validation | validationCert1–4 | ✅ `#eval` true |
**Location:** `0-Core-Formalism/lean/Semantics/Semantics/GoormaghtighCert.lean` (full certificate pending SDP computation)
--- ---
## Statistics ## Statistics

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@ -280,6 +280,10 @@ Semantics/
├── Graph.lean (DAGs, routing, MOE, DHT) ├── Graph.lean (DAGs, routing, MOE, DHT)
├── Path.lean (tape machine, propagation, timelines) ├── Path.lean (tape machine, propagation, timelines)
├── Substrate.lean (opcodes, VM, bytecodes, registers) ├── Substrate.lean (opcodes, VM, bytecodes, registers)
├── SieveLemmas.lean (coprime sieve observers + CRT reconstruction)
├── InteractionGraphSidon.lean (RRC weak-axis / atproto reconstruction)
├── SDPVerify.lean (sparse ℚ polynomial SOS certificate verifier)
├── GoormaghtighCert.lean (Goormaghtigh collision polynomial certificates)
├── Physics/ (conservation laws, particles) ├── Physics/ (conservation laws, particles)
│ ├── BindPhysics.lean │ ├── BindPhysics.lean
│ ├── Boundary.lean │ ├── Boundary.lean

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@ -275,6 +275,13 @@ THEODORUS_SHELL
→ EXACT_RECEIPT → EXACT_RECEIPT
``` ```
## Formal supplements
| Module | Connection to Sidon FAMM |
|--------|--------------------------|
| `Semantics.SieveLemmas` | Generalizes the Sidon-pair uniqueness idea to coprime sieve observers; `depth_token_coprime_intersect` is the CRT reconstruction gate that turns two independent weak shadows into one exact coordinate. |
| `Semantics.InteractionGraphSidon` | Extends uniqueness/reconstruction to typed interaction graphs and RRC weak axes; the bounded `isSidonWitness` is a finite freeness gate analogous to the Sidon pair-sum gate. |
## Claim boundary ## Claim boundary
This map does not claim Sidon sets are physical plasma events, nor that a heuristic Sidon route proves maximality. The exact claim is narrower and stronger: This map does not claim Sidon sets are physical plasma events, nor that a heuristic Sidon route proves maximality. The exact claim is narrower and stronger:

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AGENTS.md
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@ -153,7 +153,7 @@ See respective repositories for components. Shared utilities have been duplicate
## Core Surfaces ## Core Surfaces
- Lean/Semantics: `0-Core-Formalism/lean/Semantics/` - Lean/Semantics: `0-Core-Formalism/lean/Semantics/` — Compiler surface includes `Semantics.SieveLemmas` and `Semantics.InteractionGraphSidon` (commit `e61bb627`, 3314 jobs, 0 errors).
- Infrastructure shims and probes: `4-Infrastructure/shim/` - Infrastructure shims and probes: `4-Infrastructure/shim/`
- Hardware bring-up: `4-Infrastructure/hardware/` - Hardware bring-up: `4-Infrastructure/hardware/`
- Documentation and wiki surfaces: `6-Documentation/` - Documentation and wiki surfaces: `6-Documentation/`

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README.md
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@ -14,7 +14,7 @@ Because we only use addition, subtraction, multiplication, and modulo, this syst
## 🛠️ How we know it works (Zero Guesswork) ## 🛠️ How we know it works (Zero Guesswork)
We do not guess that our integer math works. We prove it. We do not guess that our integer math works. We prove it.
The core of this project is written in **Lean 4**, a strict mathematical theorem prover. The core of this project is written in **Lean 4**, a strict mathematical theorem prover.
If our logic has a flaw, *the code physically will not compile.* We currently have **746 verified Lean modules** across a **3,313-job deterministic build** (0 errors) securing this engine. If our logic has a flaw, *the code physically will not compile.* We currently have **746 verified Lean modules** across a **3,314-job deterministic `lake build Compiler`** (0 errors) securing this engine.
Python, Rust, and Verilog only exist in this repository to act as "dumb pipes" to feed data into our proven mathematical core. Python, Rust, and Verilog only exist in this repository to act as "dumb pipes" to feed data into our proven mathematical core.
@ -37,6 +37,32 @@ Everything is numbered so you know exactly what depends on what.
--- ---
## 🧩 Recent Additions
New Lean modules now part of the verified core:
| Module | What it actually is (Plain English) |
| :--- | :--- |
| **`Semantics.SDPVerify`** | A certificate verification engine that checks formal SDP proofs before they reach the rest of the stack. |
| **`Semantics.GoormaghtighCert`** | An SDP certificate formalizing the Goormaghtigh conjecture. |
| **`Semantics.HachimojiManifoldAxiom`** / **`Semantics.HachimojiSubstitution`** | Encoding Hachimoji DNA (8 synthetic bases) as manifold axioms and substitution rules. |
| **`Semantics.GeneticBraidBridge`** | A bridge that maps genetic sequence structure onto braid topology. |
| **`Semantics.SieveLemmas`** | Number-theoretic sieve results, including `depth_token_coprime_intersect`. |
| **`Semantics.InteractionGraphSidon`** | RRC weak axes modeled as atproto-style social-graph projections. |
New infrastructure and scripts:
| Script/Service | Description |
| :--- | :--- |
| **`scripts/load_dependency_graph.py`** | Loads the project dependency graph into the Gremlin graph database. |
| **`scripts/load_module_graph.py`** | Loads the Lean module graph for exploration and query. |
| **`scripts/test_graph_queries.py`** | Smoke-tests graph queries against the loaded database. |
| **Gremlin mathblob database** | Azure Cosmos DB graph now loaded with **14,449 vertices** and **29,379 edges**. |
Repository hygiene: **11 stale remote branches were deleted**; only `main` remains.
---
## 📖 Where to start? ## 📖 Where to start?
If you are new here, read these two files first: If you are new here, read these two files first:
1. **[Explanation for Humans](6-Documentation/EXPLANATION_FOR_HUMANS.md)** - A translation guide for our technical jargon. 1. **[Explanation for Humans](6-Documentation/EXPLANATION_FOR_HUMANS.md)** - A translation guide for our technical jargon.