Research-Stack/0-Core-Formalism/lean/external/OTOM/VecState.lean

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/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Research Stack Team
VecState.lean — Algebraic Vector States for AVMR Tree Construction
Per AGENTS.md §2: PascalCase for types, camelCase for functions.
Lean 4 is the source of truth.
-/
import Semantics.FixedPoint
import Semantics.GeneticCode
import Semantics.ShellModel
import Semantics.Spectrum
namespace Semantics
open Semantics.GeneticCode
open Semantics.ShellModel
open Semantics.Spectrum
open SpectralSignature
/-- Map event to bit representation (a=0, g=1, c=2, t=3). -/
def eventBits : EventType → Nat
| EventType.a => 0
| EventType.g => 1
| EventType.c => 2
| EventType.t => 3
/-- Core vector state for AVMR nodes.
Represents the accumulated geometric and spectral properties of a manifold region. -/
structure VecState where
mass : Int
polarity : Int
spectrum : SpectralSignature
entropyApprox : Q16_16
interactionStrength : Q16_16
resonanceCount : Nat
deriving Repr, DecidableEq
/-- Generate unique hash for a leaf node based on shell index and event type. -/
def leafHash (s : ShellState) (e : EventType) : UInt64 :=
UInt64.ofNat s.n + UInt64.ofNat (eventBits e)
/-- Mix two hashes using a common combiner (Murmur/SplitMix style). -/
def mixHash (h1 h2 : UInt64) (v : VecState) : UInt64 :=
h1 + 0x9e3779b97f4a7c15 + h2 + UInt64.ofNat v.resonanceCount
/-- Algebraic node in the AVMR vector tree.
Combines a geometric hash with a vector state. -/
structure Node where
hash : UInt64
vec : VecState
deriving Repr, DecidableEq
/-- Compute cross-boundary resonance between sibling vectors.
Counts mass, polarity, and spectral coincidences. -/
def siblingResonance (l r : VecState) : Nat :=
let m := if l.mass = r.mass then 1 else 0
let p := if l.polarity = -r.polarity then 1 else 0
let spec := l.spectrum.resonanceDegeneracy r.spectrum
m + p + spec
/-- Vector merge law: superpose two states into a parent node.
Sums mass and polarity, merges spectra, and accumulates resonance. -/
def mergeVec (l r : VecState) : VecState :=
let res := siblingResonance l r
{ mass := l.mass + r.mass
, polarity := l.polarity + r.polarity
, spectrum := l.spectrum.piecewiseMerge r.spectrum
, entropyApprox := Q16_16.add l.entropyApprox r.entropyApprox
, interactionStrength := Q16_16.add l.interactionStrength r.interactionStrength
, resonanceCount := l.resonanceCount + r.resonanceCount + res
}
/-- Merge two AVMR nodes into a single parent node. -/
def mergeNode (l r : Node) : Node :=
let v := mergeVec l.vec r.vec
{ hash := mixHash l.hash r.hash v
, vec := v }
/-- Construct a leaf VecState with spectral encoding. -/
def leafVecState
(activeIndex : Nat)
(_maxN : Nat)
(_s : ShellState)
(e : EventType)
(tip : TipCoord) : VecState :=
let spec := SpectralSignature.eventSpectrum e
let bin := activeIndex % 8
-- Place spectral peak at bin position
let positionedSpec : SpectralSignature := ⟨spec.bins.mapIdx (λ i v => if i = bin then v else Q16_16.zero)⟩
{ mass := tip.mass
, polarity := tip.polarity
, spectrum := positionedSpec
, entropyApprox := Q16_16.zero
, interactionStrength := Q16_16.zero
, resonanceCount := 0
}
/-- Zero vector state (neutral element for merge). -/
def zeroVecState : VecState :=
{ mass := 0
, polarity := 0
, spectrum := SpectralSignature.empty
, entropyApprox := Q16_16.zero
, interactionStrength := Q16_16.zero
, resonanceCount := 0 }
-- Verification
#eval mergeVec zeroVecState zeroVecState
#eval siblingResonance zeroVecState zeroVecState
#eval SpectralSignature.eventSpectrum EventType.a
end Semantics