mirror of
https://github.com/allaunthefox/Research-Stack.git
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229 lines
9.3 KiB
Text
229 lines
9.3 KiB
Text
import Semantics.Witness
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import Semantics.Canon
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import Semantics.FixedPoint
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namespace Semantics.ENE
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open Semantics.Q16_16
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-- Evolution
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--
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-- Defines self-modification under constitution.
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-- The system may change, but it must never become alien to its own audit surface.
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §0 Hardware-Native Evolution Structures (from HachimojiPipeline improvements)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Discrete evolution state using Q16_16 for hardware-native computation -/
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structure DiscreteEvolutionState where
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entropy : Q16_16 -- System entropy in Q16.16
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complexity : Q16_16 -- System complexity in Q16.16
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stability : Q16_16 -- System stability in Q16.16
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coherence : Q16_16 -- System coherence in Q16.16
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deriving Repr, Inhabited
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/-- Evolution grid for spatial discretization -/
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structure EvolutionGrid where
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dimension : Nat -- Grid dimension
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spacing : Q16_16 -- Grid spacing Δt
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values : Array DiscreteEvolutionState -- State values at grid points
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deriving Repr
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/-- Evolution manifold for geometric phase -/
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structure EvolutionManifold where
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dimension : Nat -- Manifold dimension
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curvature : Q16_16 -- Scalar curvature (affects evolution rate)
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torsion : Q16_16 -- Torsion (evolution path deviation)
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metric : Array Q16_16 -- Metric tensor diagonal elements
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deriving Repr
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/-- Christoffel symbols for evolution geometric phase -/
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structure EvolutionChristoffel where
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dimension : Nat -- Manifold dimension
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symbols : Array Q16_16 -- Flattened symbol array [i][j][k]
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deriving Repr, Inhabited
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/-- Evolution lock pattern for frustration computation -/
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structure EvolutionLockPattern where
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entropy : Q16_16
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complexity : Q16_16
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stability : Q16_16
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deriving Repr, Inhabited
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/-- Evolution frustration wave parameters -/
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structure EvolutionFrustrationWave where
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waveVector : Array Q16_16 -- k_r wave vector
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weight : Q16_16 -- w_r weight from anisotropy
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deriving Repr, Inhabited
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/-- Compute evolution Christoffel symbols -/
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def computeEvolutionChristoffel (manifold : EvolutionManifold) : EvolutionChristoffel :=
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let n := manifold.dimension
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let symbolCount := n * n * n
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let symbols := Array.replicate symbolCount zero
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let rec computeSymbol (i j k : Nat) (acc : Array Q16_16) : Array Q16_16 :=
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if i >= n then acc
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else if j >= n then computeSymbol (i + 1) 0 0 acc
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else if k >= n then computeSymbol i (j + 1) 0 acc
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else
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let symbol := if i = j ∧ j = k then zero else zero
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let idx := i * n * n + j * n + k
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computeSymbol i j (k + 1) (acc.set! idx symbol)
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let result := computeSymbol 0 0 0 symbols
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{ dimension := n, symbols := result }
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/-- Compute cosine using Taylor series for Q16_16 -/
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def evolutionCos (x : Q16_16) : Q16_16 :=
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let x2 := mul x x
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let term2 := mul x2 (div (ofNat 1) (ofNat 2))
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one - term2
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/-- Compute evolution frustration W(z;A) = Σ_r w_r(A)(1 - cos(k_r·z)) -/
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def computeEvolutionFrustration (z : EvolutionLockPattern) (waves : Array EvolutionFrustrationWave) : Q16_16 :=
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let zArray := #[z.entropy, z.complexity, z.stability, zero]
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let rec sumWaves (i : Nat) (acc : Q16_16) : Q16_16 :=
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if i >= waves.size then acc
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else
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let wave := waves[i]!
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let rec dotProduct (j : Nat) (sum : Q16_16) : Q16_16 :=
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if j >= 4 then sum
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else dotProduct (j + 1) (sum + zArray[j]! * wave.waveVector[j]!)
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let dot := dotProduct 0 zero
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let cosine := evolutionCos dot
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let contribution := mul wave.weight (one - cosine)
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sumWaves (i + 1) (acc + contribution)
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sumWaves 0 zero
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/-- Compute evolution locking energy -/
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def computeEvolutionLockingEnergy (currentPattern previousPattern : EvolutionLockPattern) (waves : Array EvolutionFrustrationWave) : Q16_16 :=
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let z := {
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entropy := currentPattern.entropy - previousPattern.entropy,
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complexity := currentPattern.complexity - previousPattern.complexity,
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stability := currentPattern.stability - previousPattern.stability
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}
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computeEvolutionFrustration z waves
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/-- Update discrete evolution state from geometry -/
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def updateEvolutionStateFromGeometry (state : DiscreteEvolutionState) (manifold : EvolutionManifold) : DiscreteEvolutionState :=
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let newEntropy := state.entropy + manifold.curvature
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let newComplexity := state.complexity + manifold.torsion
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{
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entropy := newEntropy,
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complexity := newComplexity,
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stability := state.stability,
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coherence := state.coherence
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}
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/-- Update discrete evolution state from Christoffel symbols -/
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def updateEvolutionStateFromChristoffel (state : DiscreteEvolutionState) (symbols : EvolutionChristoffel) (i j k : Nat) : DiscreteEvolutionState :=
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let symbol := symbols.symbols[i * symbols.dimension * symbols.dimension + j * symbols.dimension + k]!
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let stabilityIncrement := if symbol > ofNat 100 then one else zero
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{
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entropy := state.entropy,
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complexity := state.complexity,
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stability := state.stability + stabilityIncrement,
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coherence := state.coherence
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 Original Evolution Structures (updated with Q16_16)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- A record of a single self-modification event. -/
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structure SelfModification where
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id : Nat
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description : String
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priorState : Graph
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postState : Graph
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witness : Witness
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timestamp : Q16_16 -- Changed from Float to Q16_16 for hardware-native computation
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discreteState : DiscreteEvolutionState -- Added discrete state tracking
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deriving Repr
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/-- An audit surface is the set of nodes and edges that must remain inspectable
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after any evolution step. -/
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structure AuditSurface where
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requiredNodes : List Node
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requiredEdges : List Edge
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transparency : Q16_16 -- Changed from Float to Q16_16 for hardware-native computation
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deriving Repr, BEq
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/-- An evolution contract governs how the graph may change. -/
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structure EvolutionContract where
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contractId : Nat
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preservesAuditSurface : SelfModification → AuditSurface → Bool
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replayable : SelfModification → Bool
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preservesConstitution : SelfModification → UniverseConstitution → Bool
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/-- An evolution step is admissible if it satisfies the contract. -/
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def EvolutionAdmissible
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(mod : SelfModification)
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(contract : EvolutionContract)
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(surface : AuditSurface)
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(constitution : UniverseConstitution) : Prop :=
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contract.preservesAuditSurface mod surface = true ∧
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contract.replayable mod = true ∧
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contract.preservesConstitution mod constitution = true
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-- Evolution theorems (anti-insect / anti-epistemic-erasure laws)
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/-- No evolution without auditability. -/
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theorem no_evolution_without_auditability
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(mod : SelfModification)
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(contract : EvolutionContract)
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(surface : AuditSurface)
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(constitution : UniverseConstitution)
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(h : EvolutionAdmissible mod contract surface constitution) :
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contract.preservesAuditSurface mod surface = true := by
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unfold EvolutionAdmissible at h
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exact h.1
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/-- No evolution without replayability. -/
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theorem no_evolution_without_replayability
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(mod : SelfModification)
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(contract : EvolutionContract)
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(surface : AuditSurface)
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(constitution : UniverseConstitution)
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(h : EvolutionAdmissible mod contract surface constitution) :
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contract.replayable mod = true := by
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unfold EvolutionAdmissible at h
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exact h.2.1
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/-- No epistemic self-erasure: the constitution must survive evolution. -/
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theorem no_epistemic_self_erasure
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(mod : SelfModification)
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(contract : EvolutionContract)
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(surface : AuditSurface)
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(constitution : UniverseConstitution)
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(h : EvolutionAdmissible mod contract surface constitution) :
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contract.preservesConstitution mod constitution = true := by
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unfold EvolutionAdmissible at h
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exact h.2.2
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/-- Capability legibility is coupled to evolution:
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a valid modification must be replayable, ensuring its capability impact
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remains inspectable. -/
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theorem capability_legibility_coupled
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(mod : SelfModification)
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(contract : EvolutionContract)
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(surface : AuditSurface)
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(constitution : UniverseConstitution)
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(h : EvolutionAdmissible mod contract surface constitution) :
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contract.replayable mod = true := by
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unfold EvolutionAdmissible at h
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exact h.2.1
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/-- Atomic grounding is preserved under evolution if the post-state graph
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contains all atoms referenced by the modification witness. -/
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def preservesAtomicGrounding (mod : SelfModification) : Prop :=
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∀ a ∈ mod.witness.preservedAtoms,
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∃ n ∈ mod.postState.nodes,
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n.type = NodeType.atom ∧ n.label = atomLabel a
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/-- Projection faithfulness is preserved if the post-state graph
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contains no active quarantined edges. -/
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def preservesProjectionContract (mod : SelfModification) : Prop :=
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mod.postState.noActiveQuarantine
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end Semantics.ENE
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