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117 lines
3.4 KiB
Text
117 lines
3.4 KiB
Text
/-
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BraidStrand.lean - Transport Topology with Bracket Shell
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Braids carry the flow. Each strand accumulates PhaseVec contributions linearly
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and carries a BraidBracket shell for local admissibility.
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Hierarchy: DIAT leaf → AMMR vector → braid strand → bracket shell
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-/
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import Semantics.DynamicCanal
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import Semantics.BraidBracket
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namespace Semantics.BraidStrand
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open DynamicCanal
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open Semantics.BraidBracket
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/-- BraidStrand: a single transport strand in the braid topology
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zᵢ = Σₖ Φᵢₖ (linear AMMR accumulation)
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Bᵢ = C(zᵢ, μᵢ) (bracket from accumulated state)
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-/
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structure BraidStrand where
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phaseAcc : PhaseVec -- zᵢ: accumulated phase vector
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parity : Bool -- strand parity for crossing orientation
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slot : UInt32 -- μᵢ: transport slot / channel assignment
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residue : Fix16 -- residual from prior crossings
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jitter : Fix16 -- timing/phase jitter bound
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bracket : BraidBracket -- C(zᵢ, μᵢ): admissibility shell
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deriving Repr, DecidableEq, BEq
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namespace BraidStrand
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/-- Create a fresh strand from initial phase contribution
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For DIAT leaf encoding: strand starts with single AMMR contribution.
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-/
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def fromLeaf (Φ : PhaseVec) (slot : UInt32) (μ : Fix16) : BraidStrand :=
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let z := Φ
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{ phaseAcc := z
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, parity := true
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, slot := slot
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, residue := Fix16.zero
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, jitter := Fix16.zero
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, bracket := BraidBracket.fromPhaseVec z μ }
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/-- Update bracket after phase accumulation changes
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Recompute C(z, μ) from current phaseAcc and slot.
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This is the correct pattern: merge linearly, then derive bracket.
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-/
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def updateBracket (s : BraidStrand) : BraidStrand :=
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let μ := Fix16.mk s.slot -- slot as Q16.16 fraction
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{ s with bracket := BraidBracket.fromPhaseVec s.phaseAcc μ }
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/-- Add AMMR contribution to strand (linear accumulation)
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Φ is the local vector contribution from a mode/carrier.
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Bracket is NOT updated here — updateBracket must be called explicitly.
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-/
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def addContribution (s : BraidStrand) (Φ : PhaseVec) : BraidStrand :=
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{ s with phaseAcc := PhaseVec.add s.phaseAcc Φ }
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/-- Zero strand (identity element for merge) -/
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def zero (slot : UInt32) : BraidStrand :=
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let z := PhaseVec.zero
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let μ := Fix16.mk slot
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{ phaseAcc := z
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, parity := true
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, slot := slot
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, residue := Fix16.zero
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, jitter := Fix16.zero
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, bracket := BraidBracket.fromPhaseVec z μ }
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/-- Check if strand is admissible (bracket bounds valid) -/
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def isAdmissible (s : BraidStrand) : Bool :=
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s.bracket.admissible && s.bracket.gapConserved
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/-- Strand magnitude ‖zᵢ‖ (norm approximation) -/
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def magnitude (s : BraidStrand) : Fix16 :=
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s.phaseAcc.normApprox
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/-- Strand phase angle (0 if zero vector) -/
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def phaseAngle (s : BraidStrand) : Fix16 :=
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s.bracket.phi
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end BraidStrand
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/-- Strand registry for AVMR append-only storage -/
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structure StrandRegistry where
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entries : List BraidStrand
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nextSlot : UInt32
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deriving Repr, DecidableEq
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namespace StrandRegistry
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def empty : StrandRegistry :=
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{ entries := [], nextSlot := 0 }
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def register (reg : StrandRegistry) (strand : BraidStrand) : StrandRegistry :=
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{ entries := strand :: reg.entries
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, nextSlot := reg.nextSlot + 1 }
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def count (reg : StrandRegistry) : Nat :=
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reg.entries.length
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def allAdmissible (reg : StrandRegistry) : Bool :=
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reg.entries.all BraidStrand.isAdmissible
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end StrandRegistry
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#eval (BraidStrand.zero 0).isAdmissible
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#eval (StrandRegistry.empty.nextSlot)
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end Semantics.BraidStrand
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