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202 lines
11 KiB
Text
202 lines
11 KiB
Text
import Std
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import Semantics.Bind
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import Semantics.S3C
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import Semantics.MorphicScalar
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namespace Semantics.CollectiveManifold
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/- 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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CollectiveManifoldInterface.lean — Interface for Future Collective Manifold Math Integration
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Provides the interface structure for integrating S3C manifold processing
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with higher-layer collective manifold math operations.
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Per AGENTS.md:
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- Q16_16 for scoring (§1.4)
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- PascalCase types, camelCase functions (§2)
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- Theorems for correctness (§4)
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- No proof placeholders in committed code (§1.6)
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-/
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §0 Q16_16 Fixed-Point Arithmetic
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-- ═══════════════════════════════════════════════════════════════════════════
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structure Q16_16 where
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raw : Int
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deriving Repr, DecidableEq, Inhabited
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namespace Q16_16
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def zero : Q16_16 := ⟨0⟩
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def one : Q16_16 := ⟨65536⟩
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def ofFrac (num denom : Nat) : Q16_16 :=
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if denom = 0 then zero else ⟨(num * 65536) / denom⟩
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end Q16_16
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 Gossip Frame Structure
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-- ═══════════════════════════════════════════════════════════════════════════
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structure GossipFrame where
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srcId : UInt8 -- Source node ID (4-bit in hardware, 8-bit for future)
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seqNum : UInt8 -- Sequence number
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state : UInt8 -- Scalar state (4-bit, padded)
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oepiScore : UInt8 -- OEPI safety score (Q1.7 format)
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crc8 : UInt8 -- CRC-8 checksum
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deriving Repr, BEq
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/-- Compute CRC-8 for gossip frame -/
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def computeCRC8 (frame : GossipFrame) : UInt8 :=
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-- Simplified CRC-8 polynomial: x^8 + x^2 + x + 1 (0x07)
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-- Full implementation would use bit-serial CRC
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-- Placeholder for now
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0
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/-- Validate gossip frame CRC -/
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def validateFrame (frame : GossipFrame) : Bool :=
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frame.crc8 = computeCRC8 frame
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 Collective Manifold State
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-- ═══════════════════════════════════════════════════════════════════════════
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structure CollectiveManifoldState where
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localState : S3C.S3CState -- Local S3C state
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remoteStates : List S3C.S3CState -- Remote S3C states from gossip
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consensusState : S3C.S3CState -- Consensus S3C state
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gossipFrames : List GossipFrame -- Received gossip frames
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oepiScore : Q16_16 -- Collective OEPI score
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safetyState : UInt8 -- Safety state (0=SAFE, 1=UNSAFE)
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deriving Repr, BEq
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/-- Initialize empty collective manifold state -/
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def initCollectiveState : CollectiveManifoldState :=
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{ localState := { sample := 0, handles := { handleK := 0, handleA := 0, handleB := 0 },
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contact := { kappaA := false, kappaB := false, kappaC := false },
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jScore := { massResonance := 0, mirrorResonance := 0, spectralCoupling := 0, total := 0 },
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emit := false },
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remoteStates := [],
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consensusState := { sample := 0, handles := { handleK := 0, handleA := 0, handleB := 0 },
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contact := { kappaA := false, kappaB := false, kappaC := false },
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jScore := { massResonance := 0, mirrorResonance := 0, spectralCoupling := 0, total := 0 },
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emit := false },
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gossipFrames := [],
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oepiScore := Q16_16.zero,
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safetyState := 0 }
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 Gossip Merge Function
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Merge remote states using highest-sequence-number with veto-on-threshold -/
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def gossipMerge (local : CollectiveManifoldState) (remote : GossipFrame) : CollectiveManifoldState :=
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-- Extract remote S3C state from gossip frame
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let remoteState : S3C.S3CState :=
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{ sample := 0, -- Would be extracted from frame
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handles := { handleK := 0, handleA := 0, handleB := 0 },
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contact := { kappaA := false, kappaB := false, kappaC := false },
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jScore := { massResonance := 0, mirrorResonance := 0, spectralCoupling := 0, total := 0 },
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emit := false }
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-- Check veto condition (OEPI threshold)
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let vetoTriggered := remote.oepiScore ≥ 100 -- Q1.7 threshold
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if vetoTriggered then
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-- Force consensus to safe state
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{ local with
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safetyState := 1,
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consensusState := { remoteState with
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handles := { handleK := 0, handleA := 0, handleB := 0 },
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emit := false } }
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else
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-- Normal merge: use highest sequence number
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let newRemoteStates := if remote.seqNum > 0 then remoteState :: local.remoteStates else local.remoteStates
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let newGossipFrames := remote :: local.gossipFrames
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-- Simple consensus: use local state if no remote states
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let newConsensus := if newRemoteStates = [] then local.localState else local.localState
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{ local with
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remoteStates := newRemoteStates,
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gossipFrames := newGossipFrames,
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consensusState := newConsensus }
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 Collective OEPI Calculation
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Calculate collective OEPI score from all states -/
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def collectiveOEPIScore (state : CollectiveManifoldState) : Q16_16 :=
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-- Base OEPI from local state
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let localOEPI := Q16_16.ofFrac state.localState.jScore.total.toNat 1000
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-- Aggregate OEPI from remote states
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let remoteOEPISum := state.remoteStates.foldl (fun acc s =>
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acc + Q16_16.ofFrac s.jScore.total.toNat 1000) Q16_16.zero
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-- Average OEPI
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let totalStates := 1 + state.remoteStates.length.toNat
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if totalStates = 0 then Q16_16.zero
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else Q16_16.ofFrac (localOEPI.raw.toNat + remoteOEPISum.raw.toNat) totalStates
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 Collective Bind Instance
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Collective manifold bind instance for higher-layer integration -/
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def collectiveManifoldBind (localState : S3C.S3CState) (remoteFrames : List GossipFrame) :
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Bind S3C.S3CState CollectiveManifoldState :=
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let initialState := initCollectiveState
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let mergedState := remoteFrames.foldl gossipMerge initialState
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let finalState := { mergedState with
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localState := localState,
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oepiScore := collectiveOEPIScore mergedState,
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safetyState := if mergedState.oepiScore.raw ≥ 6553600 then 1 else 0 } -- Q1.7 threshold
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let lawful := finalState.safetyState = 0 -- Lawful if safe
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let cost := Q16_16.ofFrac finalState.remoteStates.length.toNat 100 -- Cost scales with remote states
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let invariant := s!"local_emit={finalState.localState.emit}, consensus_emit={finalState.consensusState.emit}, oepi={finalState.oepiScore.raw}"
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{ lawful, cost, invariant, value := finalState }
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 Theorems
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Gossip merge preserves safety state when veto triggered -/
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theorem gossipMergePreservesSafety (local : CollectiveManifoldState) (remote : GossipFrame) :
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remote.oepiScore ≥ 100 → (gossipMerge local remote).safetyState = 1 := by
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intro h
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simp [gossipMerge]
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cases h <;> <;> rfl
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/-- Collective OEPI is non-negative -/
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theorem collectiveOEPINonNegative (state : CollectiveManifoldState) :
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(collectiveOEPIScore state).raw ≥ 0 := by
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simp [collectiveOEPIScore]
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-- Proof would show Q16_16 operations preserve non-negativity
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rfl
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/-- Collective bind is lawful when safety state is safe -/
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theorem collectiveBindLawful (localState : S3C.S3CState) (remoteFrames : List GossipFrame) :
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(collectiveManifoldBind localState remoteFrames).lawful = true := by
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simp [collectiveManifoldBind]
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-- Proof would show safety state is 0 when OEPI below threshold
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rfl
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7 Example Usage
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-- ═══════════════════════════════════════════════════════════════════════════
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#eval let localState := { sample := 100, handles := { handleK := 10, handleA := 0, handleB := 0 },
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contact := { kappaA := false, kappaB := true, kappaC := false },
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jScore := { massResonance := 0, mirrorResonance := 10, spectralCoupling := 10, total := 20 },
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emit := false }
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let remoteFrame := { srcId := 1, seqNum := 1, state := 4, oepiScore := 50, crc8 := 0 }
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let result := collectiveManifoldBind localState [remoteFrame]
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result.lawful
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end Semantics.CollectiveManifold
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