Research-Stack/0-Core-Formalism/lean/Semantics/Semantics/Evolution.lean

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