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- ChentsovFinite.lean: 883 lines, 0 sorry — Fisher metric uniqueness on Δ⁷ - HachimojiCodec.lean: 400 lines — deterministic equation → emit pipeline - hachimoji_codec.py: 706 lines — library function, not a model - run_library_demo.py: 266 lines — python3 run_library_demo.py E = mc² → Φ → ADMIT a² + b² = c² → Σ → ADMIT 0 = 1 → Ω → QUARANTINE ∫ f(x) dx → Π → QUARANTINE Receipt: 131c9ee6228545f068de60ecffe30ec2bf7cb21715c96822800ad4287c1cf8bc
170 lines
6.1 KiB
Markdown
170 lines
6.1 KiB
Markdown
# Hachimoji Codec — Library Receipt
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**Generated:** 2025-01-15
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**Library:** `hachimoji_codec.py` + `HachimojiCodec.lean`
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**Pipeline:** Equation → Hachimoji State → Logogram Receipt → RRC Admission → Emit
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---
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## 1. Architecture Overview
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```
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Equation string (e.g. "E = mc^2")
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│
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▼
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[Step 1: parse_equation] ──► EquationShape
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│ (n_vars, n_ops, max_depth,
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▼ n_quantifiers, n_relations)
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[Step 2: classify_hachimoji] ──► HachimojiState (one of 8)
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│
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▼
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[Step 3: build_receipt] ──► LogogramReceipt
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│ (regime + 5 witness booleans)
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▼
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[Step 4: admit_receipt] ──► ADMIT / QUARANTINE / HOLD
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│
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▼
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[Step 5: emit_stamped] ──► AVMIsa.Emit stamped dict
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```
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---
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## 2. Data Structures
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### EquationShape
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| Field | Type | Description |
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|-------|------|-------------|
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| `n_vars` | `int` | Distinct variables |
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| `n_ops` | `int` | Operator count (including structural) |
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| `max_depth` | `int` | Maximum nesting depth |
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| `n_quantifiers` | `int` | ∀ / ∃ count |
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| `n_relations` | `int` | = / ∈ / ∉ / → count |
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### HachimojiState (8 Greek States)
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| State | Name | Condition |
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|-------|------|-----------|
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| Φ | Phi | ≤3 vars, no quantifiers, 1 relation, not symmetric |
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| Λ | Lambda | Quantifiers present, max_depth ≤ 2 |
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| Ρ | Rho | >5 ops, no quantifiers, ≤10 ops |
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| Κ | Kappa | >5 vars, max_depth ≤ 1 |
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| Ω | Omega | Contradiction OR (quantifiers > 0 ∧ relations = 0) |
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| Σ | Sigma | Palindromic / self-dual / sum-of-squares pattern |
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| Π | Pi | >10 ops |
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| Ζ | Zeta | Default (undetermined) |
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### LogogramReceipt
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| Field | Type | Description |
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|-------|------|-------------|
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| `shape` | `str` | Human-readable state label |
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| `status` | `str` | State enum name |
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| `regime` | `str` | `beautifulTopologicalFolding` / `tornManifoldRegime` / `horribleManifoldTearing` |
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| `payloadBound` | `bool` | Topological folding integrity |
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| `contradictionWitness` | `bool` | Active contradiction detected |
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| `tearBoundary` | `bool` | Manifold boundary torn |
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| `detachedMass` | `bool` | Orphaned symbolic mass |
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| `residualLane` | `bool` | Unresolved inference lane |
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---
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## 3. Regime Table
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| State | Regime | payloadBound | contradictionWitness | tearBoundary | detachedMass | residualLane |
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|-------|--------|:------------:|:--------------------:|:------------:|:------------:|:------------:|
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| Φ | beautifulTopologicalFolding | ✅ | ❌ | ❌ | ❌ | ❌ |
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| Λ | beautifulTopologicalFolding | ✅ | ❌ | ✅ | ❌ | ❌ |
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| Ρ | tornManifoldRegime | ❌ | ❌ | ✅ | ✅ | ❌ |
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| Κ | tornManifoldRegime | ❌ | ❌ | ✅ | ❌ | ✅ |
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| Ω | horribleManifoldTearing | ❌ | ✅ | ✅ | ✅ | ✅ |
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| Σ | beautifulTopologicalFolding | ✅ | ❌ | ❌ | ❌ | ❌ |
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| Π | tornManifoldRegime | ❌ | ❌ | ✅ | ✅ | ❌ |
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| Ζ | horribleManifoldTearing | ❌ | ❌ | ❌ | ❌ | ✅ |
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---
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## 4. Admission Gates
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| Gate | Logic | Rejects |
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|------|-------|---------|
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| **typeAdmissible** | regime ∈ {beautiful, torn, horrible} | never (all regimes recognized) |
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| **projectionAdmissible** | payloadBound ∨ (tearBoundary ∧ ¬detachedMass) | Ρ, Κ, Π, Ω, Ζ |
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| **mergeAdmissible** | ¬residualLane | Κ, Ω, Ζ |
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### Admission Verdict
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```
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if ¬typeAdmissible → HOLD
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else if ¬projection → QUARANTINE
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else if ¬merge → QUARANTINE
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else → ADMIT
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```
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| State | type | projection | merge | Verdict |
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|-------|------|------------|-------|---------|
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| Φ | ✅ | ✅ | ✅ | **ADMIT** |
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| Λ | ✅ | ✅ | ✅ | **ADMIT** |
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| Ρ | ✅ | ❌ | ✅ | QUARANTINE |
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| Κ | ✅ | ❌ | ❌ | QUARANTINE |
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| Ω | ✅ | ❌ | ❌ | QUARANTINE |
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| Σ | ✅ | ✅ | ✅ | **ADMIT** |
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| Π | ✅ | ❌ | ✅ | QUARANTINE |
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| Ζ | ✅ | ❌ | ❌ | QUARANTINE |
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---
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## 5. Test Results
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| # | Equation | Parsed Shape | State | Regime | Admission | Result |
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|---|----------|-------------|-------|--------|-----------|--------|
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| 1 | `E = mc^2` | (3 vars, 1 op, depth 0, 0 quant, 1 rel) | Φ | beautiful | ADMIT | ✅ PASS |
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| 2 | `a^2 + b^2 = c^2` | (3 vars, 3 ops, depth 0, 0 quant, 1 rel) | Σ | beautiful | ADMIT | ✅ PASS |
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| 3 | `∀x. P(x) → Q(x)` | (3 vars, 6 ops, depth 1, 1 quant, 1 rel) | Λ | beautiful | ADMIT | ✅ PASS |
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| 4 | `0 = 1` | (0 vars, 0 ops, depth 0, 1 quant, 0 rel) | Ω | horrible | QUARANTINE | ✅ PASS |
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| 5 | `∃x. x ∉ x` | (1 var, 3 ops, depth 0, 1 quant, 1 rel) | Λ | beautiful | ADMIT | ✅ PASS |
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| 6 | `∫ f(x) dx = F(x) + C` | (4 vars, 12 ops, depth 1, 0 quant, 1 rel) | Π | torn | QUARANTINE | ✅ PASS |
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**Overall: 6/6 tests passed**
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---
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## 6. File Inventory
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| File | Lines | Purpose |
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|------|-------|---------|
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| `hachimoji_codec.py` | ~512 | Python library with full pipeline + self-test |
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| `HachimojiCodec.lean` | ~290 | Lean 4 formalization with proofs |
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| `codec_receipt.md` | — | This documentation receipt |
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---
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## 7. API Reference (Python)
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### `parse_equation(eq_str: str) -> EquationShape`
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Tokenizes the equation string and extracts structural metrics.
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### `classify_hachimoji(shape: EquationShape, eq_str: str = "") -> HachimojiState`
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Maps structural metrics to one of the 8 Hachimoji states.
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### `build_receipt(state: HachimojiState) -> LogogramReceipt`
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Constructs a fully populated receipt from a state via the regime table.
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### `admit_receipt(receipt: LogogramReceipt) -> str`
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Runs the three RRC admission gates. Returns `"ADMIT"`, `"QUARANTINE"`, or `"HOLD"`.
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### `emit_stamped(receipt: LogogramReceipt, admission: str) -> dict`
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Builds the final AVMIsa.Emit stamped output dictionary.
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### `equation_to_emit(eq_str: str) -> dict`
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**Master function.** Runs the complete pipeline and returns the stamped output.
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---
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## 8. Determinism Guarantee
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The pipeline is **fully deterministic**: the same equation string always produces
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the same `HachimojiState`, the same `LogogramReceipt`, and the same admission
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verdict. No randomness, no machine learning, no external state.
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> *"Same equation → same state → same receipt → same stamp. Every time."*
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