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