Research-Stack/library/codec_receipt.md

Hachimoji Codec — Library Receipt

Generated: 2025-01-15
Library: hachimoji_codec.py + HachimojiCodec.lean
Pipeline: Equation → Hachimoji State → Logogram Receipt → RRC Admission → Emit

---

1. Architecture Overview

Equation string (e.g. "E = mc^2")
  │
  ▼
[Step 1: parse_equation]        ──► EquationShape
  │                                 (n_vars, n_ops, max_depth,
  ▼                                  n_quantifiers, n_relations)
[Step 2: classify_hachimoji]    ──► HachimojiState (one of 8)
  │
  ▼
[Step 3: build_receipt]         ──► LogogramReceipt
  │                                 (regime + 5 witness booleans)
  ▼
[Step 4: admit_receipt]         ──► ADMIT / QUARANTINE / HOLD
  │
  ▼
[Step 5: emit_stamped]          ──► AVMIsa.Emit stamped dict

---

2. Data Structures

EquationShape

Field	Type	Description
n_vars	int	Distinct variables
n_ops	int	Operator count (including structural)
max_depth	int	Maximum nesting depth
n_quantifiers	int	∀ / ∃ count
n_relations	int	= / ∈ / ∉ / → count

HachimojiState (8 Greek States)

State	Name	Condition
Φ	Phi	≤3 vars, no quantifiers, 1 relation, not symmetric
Λ	Lambda	Quantifiers present, max_depth ≤ 2
Ρ	Rho	>5 ops, no quantifiers, ≤10 ops
Κ	Kappa	>5 vars, max_depth ≤ 1
Ω	Omega	Contradiction OR (quantifiers > 0 ∧ relations = 0)
Σ	Sigma	Palindromic / self-dual / sum-of-squares pattern
Π	Pi	>10 ops
Ζ	Zeta	Default (undetermined)

LogogramReceipt

Field	Type	Description
shape	str	Human-readable state label
status	str	State enum name
regime	str	beautifulTopologicalFolding / tornManifoldRegime / horribleManifoldTearing
payloadBound	bool	Topological folding integrity
contradictionWitness	bool	Active contradiction detected
tearBoundary	bool	Manifold boundary torn
detachedMass	bool	Orphaned symbolic mass
residualLane	bool	Unresolved inference lane

---

3. Regime Table

State	Regime	payloadBound	contradictionWitness	tearBoundary	detachedMass	residualLane
Φ	beautifulTopologicalFolding	✅	❌	❌	❌	❌
Λ	beautifulTopologicalFolding	✅	❌	✅	❌	❌
Ρ	tornManifoldRegime	❌	❌	✅	✅	❌
Κ	tornManifoldRegime	❌	❌	✅	❌	✅
Ω	horribleManifoldTearing	❌	✅	✅	✅	✅
Σ	beautifulTopologicalFolding	✅	❌	❌	❌	❌
Π	tornManifoldRegime	❌	❌	✅	✅	❌
Ζ	horribleManifoldTearing	❌	❌	❌	❌	✅

---

4. Admission Gates

Gate	Logic	Rejects
typeAdmissible	regime ∈ {beautiful, torn, horrible}	never (all regimes recognized)
projectionAdmissible	payloadBound ∨ (tearBoundary ∧ ¬detachedMass)	Ρ, Κ, Π, Ω, Ζ
mergeAdmissible	¬residualLane	Κ, Ω, Ζ

Admission Verdict

if ¬typeAdmissible      → HOLD
else if ¬projection     → QUARANTINE
else if ¬merge          → QUARANTINE
else                    → ADMIT

State	type	projection	merge	Verdict
Φ	✅	✅	✅	ADMIT
Λ	✅	✅	✅	ADMIT
Ρ	✅	❌	✅	QUARANTINE
Κ	✅	❌	❌	QUARANTINE
Ω	✅	❌	❌	QUARANTINE
Σ	✅	✅	✅	ADMIT
Π	✅	❌	✅	QUARANTINE
Ζ	✅	❌	❌	QUARANTINE

---

5. Test Results

#	Equation	Parsed Shape	State	Regime	Admission	Result
1	E = mc^2	(3 vars, 1 op, depth 0, 0 quant, 1 rel)	Φ	beautiful	ADMIT	✅ PASS
2	a^2 + b^2 = c^2	(3 vars, 3 ops, depth 0, 0 quant, 1 rel)	Σ	beautiful	ADMIT	✅ PASS
3	∀x. P(x) → Q(x)	(3 vars, 6 ops, depth 1, 1 quant, 1 rel)	Λ	beautiful	ADMIT	✅ PASS
4	0 = 1	(0 vars, 0 ops, depth 0, 1 quant, 0 rel)	Ω	horrible	QUARANTINE	✅ PASS
5	∃x. x ∉ x	(1 var, 3 ops, depth 0, 1 quant, 1 rel)	Λ	beautiful	ADMIT	✅ PASS
6	∫ f(x) dx = F(x) + C	(4 vars, 12 ops, depth 1, 0 quant, 1 rel)	Π	torn	QUARANTINE	✅ PASS

Overall: 6/6 tests passed

---

6. File Inventory

File	Lines	Purpose
hachimoji_codec.py	~512	Python library with full pipeline + self-test
HachimojiCodec.lean	~290	Lean 4 formalization with proofs
codec_receipt.md	—	This documentation receipt

---

7. API Reference (Python)

parse_equation(eq_str: str) -> EquationShape

Tokenizes the equation string and extracts structural metrics.

classify_hachimoji(shape: EquationShape, eq_str: str = "") -> HachimojiState

Maps structural metrics to one of the 8 Hachimoji states.

build_receipt(state: HachimojiState) -> LogogramReceipt

Constructs a fully populated receipt from a state via the regime table.

admit_receipt(receipt: LogogramReceipt) -> str

Runs the three RRC admission gates. Returns "ADMIT", "QUARANTINE", or "HOLD".

emit_stamped(receipt: LogogramReceipt, admission: str) -> dict

Builds the final AVMIsa.Emit stamped output dictionary.

equation_to_emit(eq_str: str) -> dict

Master function. Runs the complete pipeline and returns the stamped output.

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8. Determinism Guarantee

The pipeline is fully deterministic: the same equation string always produces the same HachimojiState, the same LogogramReceipt, and the same admission verdict. No randomness, no machine learning, no external state.

"Same equation → same state → same receipt → same stamp. Every time."