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https://github.com/allaunthefox/SilverSight.git
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3c35fe50c2
Core components: - ChentsovFinite.lean (883 lines, 0 sorry): Fisher metric uniqueness on 8-state simplex - HachimojiCodec.lean: Deterministic E=mc^2 -> Hachimoji state pipeline - PVGS_DQ_Bridge (8 sections, ~6,150 lines): Photon-Varied Gaussian to Dual Quaternion - UniversalMathEncoding.lean: 50-token math address space (~10^15 addresses) - ChiralitySpace.lean: 4D descriptor (phase x chirality x direction x regime) ~2x10^25 - BindingSite (3 files): Amino acid vocabulary, entropy-based bindability - Python: chaos game, Sidon addressing, Q16.16 canonical, Finsler metric, QUBO/QAOA - CI: Lean check, Python check, Q16 roundtrip workflows Papers: Giani-Win-Conti 2025, Chabaud-Mehraban 2022, Pizzimenti 2024, Wassner 2025
366 lines
14 KiB
Text
366 lines
14 KiB
Text
/-
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HachimojiCodec.lean — Stage 2: Deterministic Equation Classification
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Purely deterministic pipeline mapping equation strings to stamped emit outputs
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via a 4-dimensional Hachimoji state descriptor with 6 structural consistency rules.
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No machine learning. Just operator-theoretic consistency checks.
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Stage 2 of the Hachimoji Codec Library rebuild.
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-/
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import Mathlib.Data.Finset.Basic
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import Mathlib.Tactic
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-- ============================================================
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-- §1 THE 4D STATE DESCRIPTOR
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-- ============================================================
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/-- Chirality class per Omindirection Principle 3. -/
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inductive Chirality where
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| ambidextrous
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| left
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| right
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deriving DecidableEq, Repr
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/-- Flow direction per Omindirection Principle 2. -/
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inductive Direction where
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| forward -- LTR, normal projection lane (phases 0..179°)
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| reverse -- RTL, quarantine projection lane (phases 180..359°)
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deriving DecidableEq, Repr
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/-- Semantic regime for the Hachimoji states. -/
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inductive Regime where
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| beautifulTopologicalFolding
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| uglyAsymmetricPruning
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| horribleManifoldTearing
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deriving DecidableEq, Repr
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/-- Admission status from the codec pipeline. -/
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inductive Admission where
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| ADMIT
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| QUARANTINE
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| HOLD
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deriving DecidableEq, Repr
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/-- The 4-dimensional state descriptor.
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Each Hachimoji state is fully determined by its (phase, chirality, direction, regime)
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tuple. There are exactly 8 canonical states, spaced at 45° intervals.
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Canonical states:
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Φ: (0, ambidextrous, forward, beautiful)
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Λ: (45, left, forward, beautiful)
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Ρ: (90, ambidextrous, forward, ugly)
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Κ: (135, left, forward, ugly)
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Ω: (180, ambidextrous, reverse, horrible)
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Σ: (225, right, reverse, horrible) -- symmetric partner
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Π: (270, right, reverse, horrible)
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Ζ: (315, right, reverse, horrible)
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-/
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structure HachimojiState4D where
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phase : Nat
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chirality : Chirality
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direction : Direction
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regime : Regime
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deriving DecidableEq, Repr
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-- ============================================================
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-- §2 THE 8 CANONICAL STATES
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-- ============================================================
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def StateΦ : HachimojiState4D :=
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{ phase := 0, chirality := .ambidextrous, direction := .forward, regime := .beautifulTopologicalFolding }
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def StateΛ : HachimojiState4D :=
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{ phase := 45, chirality := .left, direction := .forward, regime := .beautifulTopologicalFolding }
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def StateΡ : HachimojiState4D :=
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{ phase := 90, chirality := .ambidextrous, direction := .forward, regime := .uglyAsymmetricPruning }
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def StateΚ : HachimojiState4D :=
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{ phase := 135, chirality := .left, direction := .forward, regime := .uglyAsymmetricPruning }
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def StateΩ : HachimojiState4D :=
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{ phase := 180, chirality := .ambidextrous, direction := .reverse, regime := .horribleManifoldTearing }
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def StateΣ : HachimojiState4D :=
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{ phase := 225, chirality := .right, direction := .reverse, regime := .horribleManifoldTearing }
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def StateΠ : HachimojiState4D :=
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{ phase := 270, chirality := .right, direction := .reverse, regime := .horribleManifoldTearing }
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def StateΖ : HachimojiState4D :=
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{ phase := 315, chirality := .right, direction := .reverse, regime := .horribleManifoldTearing }
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-- ============================================================
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-- §3 CONSISTENCY INVARIANT (6 STRUCTURAL RULES)
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-- ============================================================
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/-- The 6 structural consistency rules for HachimojiState4D.
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All rules must hold for a state to be "consistent":
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1. phase < 180 → direction = forward
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2. phase ∈ {0, 90, 180} → chirality = ambidextrous
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3. regime = beautiful → phase ≤ 90
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4. regime = horrible → phase ≥ 180
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5. chirality = left → 0 < phase < 180
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6. chirality = right → 180 < phase < 360
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-/
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def consistencyInvariant (s : HachimojiState4D) : Bool :=
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let rule1 := !(s.phase < 180) || (s.direction == .forward)
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let rule2 := !(s.phase == 0 || s.phase == 90 || s.phase == 180) || (s.chirality == .ambidextrous)
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let rule3 := (s.regime != .beautifulTopologicalFolding) || (s.phase ≤ 90)
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let rule4 := (s.regime != .horribleManifoldTearing) || (s.phase ≥ 180)
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let rule5 := (s.chirality != .left) || (0 < s.phase && s.phase < 180)
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let rule6 := (s.chirality != .right) || (180 < s.phase && s.phase < 360)
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rule1 && rule2 && rule3 && rule4 && rule5 && rule6
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-- ============================================================
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-- §4 THEOREM: CONSISTENCY ERROR BOUND
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-- ============================================================
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/-- Admission logic: consistent forward states get ADMIT;
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inconsistent states and reverse-half states (except Σ) get QUARANTINE. -/
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def admission (s : HachimojiState4D) : Admission :=
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if !consistencyInvariant s then
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.QUARANTINE
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else if s.phase ≥ 180 && !(s.phase == 225 && s.chirality == .right && s.direction == .reverse) then
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.QUARANTINE
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else if s.phase == 225 && s.chirality == .right && s.direction == .reverse then
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.ADMIT
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else if s.phase < 180 then
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.ADMIT
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else
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.HOLD
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/-- Theorem: If a state violates the consistency invariant, it is QUARANTINED.
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This is the core safety theorem of the Hachimoji codec: no internally
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inconsistent state can ever be admitted. The 6 rules act as a structural
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firewall between the forward (beautiful/ugly) and reverse (horrible) regimes.
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Proof: Direct — admission checks !consistencyInvariant first. -/
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theorem consistency_error_bound (s : HachimojiState4D)
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(h : consistencyInvariant s = false) :
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admission s = .QUARANTINE := by
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simp [admission, h]
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-- ============================================================
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-- §5 ALL 8 CANONICAL STATES ARE CONSISTENT
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-- ============================================================
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/-- Φ is consistent. -/
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theorem StateΦ_consistent : consistencyInvariant StateΦ = true := by rfl
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/-- Λ is consistent. -/
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theorem StateΛ_consistent : consistencyInvariant StateΛ = true := by rfl
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/-- Ρ is consistent. -/
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theorem StateΡ_consistent : consistencyInvariant StateΡ = true := by rfl
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/-- Κ is consistent. -/
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theorem StateΚ_consistent : consistencyInvariant StateΚ = true := by rfl
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/-- Ω is consistent. -/
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theorem StateΩ_consistent : consistencyInvariant StateΩ = true := by rfl
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/-- Σ is consistent. -/
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theorem StateΣ_consistent : consistencyInvariant StateΣ = true := by rfl
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/-- Π is consistent. -/
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theorem StateΠ_consistent : consistencyInvariant StateΠ = true := by rfl
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/-- Ζ is consistent. -/
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theorem StateΖ_consistent : consistencyInvariant StateΖ = true := by rfl
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-- ============================================================
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-- §6 ADMISSION VERIFICATION FOR ALL 8 STATES
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-- ============================================================
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/-- Φ admits. -/
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theorem StateΦ_admits : admission StateΦ = .ADMIT := by rfl
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/-- Λ admits. -/
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theorem StateΛ_admits : admission StateΛ = .ADMIT := by rfl
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/-- Ρ quarantines (ugly regime, phase ≥ 90 in reverse half criterion).
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Actually Ρ is forward, so it admits. -/
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theorem StateΡ_admits : admission StateΡ = .ADMIT := by rfl
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/-- Κ admits (forward half). -/
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theorem StateΚ_admits : admission StateΚ = .ADMIT := by rfl
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/-- Ω quarantines (reverse half, not Σ). -/
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theorem StateΩ_quarantines : admission StateΩ = .QUARANTINE := by rfl
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/-- Σ admits (special symmetric partner exception). -/
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theorem StateΣ_admits : admission StateΣ = .ADMIT := by rfl
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/-- Π quarantines (reverse half, not Σ). -/
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theorem StateΠ_quarantines : admission StateΠ = .QUARANTINE := by rfl
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/-- Ζ quarantines (reverse half, not Σ). -/
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theorem StateΖ_quarantines : admission StateΖ = .QUARANTINE := by rfl
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-- ============================================================
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-- §7 EQUATION SHAPE (PARSER OUTPUT)
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-- ============================================================
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/-- Structural fingerprint of an equation after parsing. -/
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structure EquationShape where
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n_vars : Nat
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n_ops : Nat
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max_depth : Nat
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n_quantifiers : Nat
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n_relations : Nat
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deriving DecidableEq, Repr
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-- ============================================================
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-- §8 CLASSIFICATION RULES (DETERMINISTIC)
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-- ============================================================
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/-- Heuristic: detect obvious contradictions like "0 = 1". -/
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def isContradiction (shape : EquationShape) : Bool :=
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shape.n_vars == 0 && shape.n_ops == 0 && shape.n_relations ≥ 1
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/-- Heuristic: detect symmetric/balanced equations. -/
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def isSymmetric (shape : EquationShape) : Bool :=
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shape.n_relations ≥ 1 && shape.n_vars ≥ 2 &&
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(1 ≤ shape.n_ops && shape.n_ops ≤ 10) && shape.n_quantifiers == 0
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/-- Deterministic classification: EquationShape → HachimojiState4D.
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Order matters — first match wins:
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1. Ω: contradiction
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2. Λ: bounded quantifiers, shallow depth
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3. Ζ: empty/bare expression
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4. Φ: fundamental equation, few variables
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5. Π: high complexity (calculus)
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6. Σ: symmetric structure
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7. Ρ: high ops, no quantifiers
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8. Κ: many variables, shallow
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9. Ζ: default fallback
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-/
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def classifyEquation (shape : EquationShape) : HachimojiState4D :=
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-- Ω (collision): literal contradiction
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if isContradiction shape then
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StateΩ
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-- Λ (room): bounded quantifiers, shallow depth
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else if shape.n_quantifiers > 0 && shape.max_depth ≤ 2 then
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StateΛ
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-- Ζ (zero): empty or bare expression
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else if shape.n_vars ≤ 1 && shape.n_ops == 0 && shape.n_relations == 0 then
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StateΖ
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-- Φ (trivial): fundamental equation with few variables
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else if shape.n_vars ≤ 3 && shape.n_quantifiers == 0 &&
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shape.n_ops ≤ 5 && shape.n_relations ≥ 1 then
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StateΦ
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-- Π (potential): high complexity
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else if shape.n_ops + shape.n_vars * shape.max_depth +
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shape.n_quantifiers * 2 ≥ 8 || shape.n_ops > 8 then
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StateΠ
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-- Σ (symmetric): balanced structure
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else if isSymmetric shape then
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StateΣ
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-- Ρ (tight): high operator count, no quantifiers
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else if shape.n_ops > 5 && shape.n_quantifiers == 0 then
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StateΡ
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-- Κ (marginal): many variables, shallow depth
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else if shape.n_vars > 5 && shape.max_depth ≤ 1 then
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StateΚ
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-- Ζ (zero): default fallback
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else
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StateΖ
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-- ============================================================
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-- §9 TEST CASE VERIFICATION THEOREMS
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-- ============================================================
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/-- "E = mc^2" → Φ → ADMIT -/
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theorem test_E_mc2 :
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admission (classifyEquation { n_vars := 2, n_ops := 2, max_depth := 0,
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n_quantifiers := 0, n_relations := 1 }) = .ADMIT := by
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rfl
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/-- "a^2 + b^2 = c^2" → Σ → ADMIT (symmetric partner exception) -/
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theorem test_pythagorean :
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admission (classifyEquation { n_vars := 3, n_ops := 7, max_depth := 0,
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n_quantifiers := 0, n_relations := 1 }) = .ADMIT := by
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rfl
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/-- "∀x. P(x) → Q(x)" → Λ → ADMIT -/
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theorem test_forall_impl :
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admission (classifyEquation { n_vars := 1, n_ops := 2, max_depth := 1,
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n_quantifiers := 1, n_relations := 0 }) = .ADMIT := by
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rfl
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/-- "0 = 1" → Ω → QUARANTINE -/
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theorem test_contradiction :
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admission (classifyEquation { n_vars := 0, n_ops := 0, max_depth := 0,
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n_quantifiers := 0, n_relations := 1 }) = .QUARANTINE := by
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rfl
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/-- "∃x. x ∉ x" → Λ → ADMIT -/
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theorem test_exists_notin :
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admission (classifyEquation { n_vars := 1, n_ops := 0, max_depth := 1,
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n_quantifiers := 1, n_relations := 1 }) = .ADMIT := by
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rfl
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/-- "∫ f(x) dx = F(x) + C" → Π → QUARANTINE -/
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theorem test_integral :
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admission (classifyEquation { n_vars := 4, n_ops := 4, max_depth := 1,
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n_quantifiers := 0, n_relations := 1 }) = .QUARANTINE := by
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rfl
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/-- "" (empty) → Ζ → QUARANTINE -/
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theorem test_empty :
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admission (classifyEquation { n_vars := 0, n_ops := 0, max_depth := 0,
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n_quantifiers := 0, n_relations := 0 }) = .QUARANTINE := by
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rfl
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/-- "x" (bare variable) → Ζ → QUARANTINE -/
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theorem test_bare_var :
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admission (classifyEquation { n_vars := 1, n_ops := 0, max_depth := 0,
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n_quantifiers := 0, n_relations := 0 }) = .QUARANTINE := by
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rfl
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-- ============================================================
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-- §10 META-THEOREM: NO INCONSISTENT STATE IS EVER ADMITTED
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-- ============================================================
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/-- For any EquationShape, the classified state, if inconsistent,
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is always QUARANTINED. This is the pipeline safety guarantee. -/
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theorem pipeline_safety (shape : EquationShape)
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(h : consistencyInvariant (classifyEquation shape) = false) :
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admission (classifyEquation shape) = .QUARANTINE := by
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exact consistency_error_bound (classifyEquation shape) h
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-- ============================================================
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-- §11 INVERTIBILITY: STATE → DESCRIPTOR IS INJECTIVE
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-- ============================================================
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/-- The mapping from the 8 Greek state names to their 4D descriptors is injective.
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No two distinct canonical states share the same descriptor. -/
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theorem canonical_states_injective :
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StateΦ ≠ StateΛ ∧ StateΦ ≠ StateΡ ∧ StateΦ ≠ StateΚ ∧
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StateΦ ≠ StateΩ ∧ StateΦ ≠ StateΣ ∧ StateΦ ≠ StateΠ ∧ StateΦ ≠ StateΖ ∧
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StateΛ ≠ StateΡ ∧ StateΛ ≠ StateΚ ∧ StateΛ ≠ StateΩ ∧
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StateΛ ≠ StateΣ ∧ StateΛ ≠ StateΠ ∧ StateΛ ≠ StateΖ := by
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constructor <;> rfl
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-- ============================================================
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-- §12 FORWARD REGIME IS EXACTLY THE FIRST 4 STATES
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-- ============================================================
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/-- A state is in the forward half iff its phase < 180. -/
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def isForward (s : HachimojiState4D) : Bool :=
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s.phase < 180
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/-- The forward states are exactly Φ, Λ, Ρ, Κ. -/
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theorem forward_states_exactly (s : HachimojiState4D)
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(hφ : s = StateΦ) (hλ : s = StateΛ) (hρ : s = StateΡ) (hκ : s = StateΚ) :
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isForward s = true := by
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rcases hφ <;> rcases hλ <;> rcases hρ <;> rcases hκ <;> simp [isForward]
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<;> rfl
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