import Std
import Semantics.Bind
import Semantics.S3C
import Semantics.MorphicScalar

namespace Semantics.CollectiveManifold

/- 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

CollectiveManifoldInterface.lean — Interface for Future Collective Manifold Math Integration

Provides the interface structure for integrating S3C manifold processing
with higher-layer collective manifold math operations.

Per AGENTS.md:
  - Q16_16 for scoring (§1.4)
  - PascalCase types, camelCase functions (§2)
  - Theorems for correctness (§4)
  - No proof placeholders in committed code (§1.6)
-/

-- ═══════════════════════════════════════════════════════════════════════════
-- §0  Q16_16 Fixed-Point Arithmetic
-- ═══════════════════════════════════════════════════════════════════════════

structure Q16_16 where
  raw : Int
  deriving Repr, DecidableEq, Inhabited

namespace Q16_16
  def zero : Q16_16 := ⟨0⟩
  def one : Q16_16 := ⟨65536⟩
  def ofFrac (num denom : Nat) : Q16_16 :=
    if denom = 0 then zero else ⟨(num * 65536) / denom⟩
end Q16_16

-- ═══════════════════════════════════════════════════════════════════════════
-- §1  Gossip Frame Structure
-- ═══════════════════════════════════════════════════════════════════════════

structure GossipFrame where
  srcId : UInt8      -- Source node ID (4-bit in hardware, 8-bit for future)
  seqNum : UInt8     -- Sequence number
  state : UInt8      -- Scalar state (4-bit, padded)
  oepiScore : UInt8  -- OEPI safety score (Q1.7 format)
  crc8 : UInt8       -- CRC-8 checksum
deriving Repr, BEq

/-- Compute CRC-8 for gossip frame -/
def computeCRC8 (frame : GossipFrame) : UInt8 :=
  -- Simplified CRC-8 polynomial: x^8 + x^2 + x + 1 (0x07)
  -- Full implementation would use bit-serial CRC
  -- Placeholder for now
  0

/-- Validate gossip frame CRC -/
def validateFrame (frame : GossipFrame) : Bool :=
  frame.crc8 = computeCRC8 frame

-- ═══════════════════════════════════════════════════════════════════════════
-- §2  Collective Manifold State
-- ═══════════════════════════════════════════════════════════════════════════

structure CollectiveManifoldState where
  localState : S3C.S3CState              -- Local S3C state
  remoteStates : List S3C.S3CState      -- Remote S3C states from gossip
  consensusState : S3C.S3CState          -- Consensus S3C state
  gossipFrames : List GossipFrame        -- Received gossip frames
  oepiScore : Q16_16                    -- Collective OEPI score
  safetyState : UInt8                   -- Safety state (0=SAFE, 1=UNSAFE)
deriving Repr, BEq

/-- Initialize empty collective manifold state -/
def initCollectiveState : CollectiveManifoldState :=
  { localState := { sample := 0, handles := { handleK := 0, handleA := 0, handleB := 0 },
                    contact := { kappaA := false, kappaB := false, kappaC := false },
                    jScore := { massResonance := 0, mirrorResonance := 0, spectralCoupling := 0, total := 0 },
                    emit := false },
    remoteStates := [],
    consensusState := { sample := 0, handles := { handleK := 0, handleA := 0, handleB := 0 },
                      contact := { kappaA := false, kappaB := false, kappaC := false },
                      jScore := { massResonance := 0, mirrorResonance := 0, spectralCoupling := 0, total := 0 },
                      emit := false },
    gossipFrames := [],
    oepiScore := Q16_16.zero,
    safetyState := 0 }

-- ═══════════════════════════════════════════════════════════════════════════
-- §3  Gossip Merge Function
-- ═══════════════════════════════════════════════════════════════════════════

/-- Merge remote states using highest-sequence-number with veto-on-threshold -/
def gossipMerge (local : CollectiveManifoldState) (remote : GossipFrame) : CollectiveManifoldState :=
  -- Extract remote S3C state from gossip frame
  let remoteState : S3C.S3CState := 
    { sample := 0,  -- Would be extracted from frame
      handles := { handleK := 0, handleA := 0, handleB := 0 },
      contact := { kappaA := false, kappaB := false, kappaC := false },
      jScore := { massResonance := 0, mirrorResonance := 0, spectralCoupling := 0, total := 0 },
      emit := false }
  
  -- Check veto condition (OEPI threshold)
  let vetoTriggered := remote.oepiScore ≥ 100  -- Q1.7 threshold
  
  if vetoTriggered then
    -- Force consensus to safe state
    { local with 
      safetyState := 1,
      consensusState := { remoteState with 
        handles := { handleK := 0, handleA := 0, handleB := 0 },
        emit := false } }
  else
    -- Normal merge: use highest sequence number
    let newRemoteStates := if remote.seqNum > 0 then remoteState :: local.remoteStates else local.remoteStates
    let newGossipFrames := remote :: local.gossipFrames
    
    -- Simple consensus: use local state if no remote states
    let newConsensus := if newRemoteStates = [] then local.localState else local.localState
    
    { local with 
      remoteStates := newRemoteStates,
      gossipFrames := newGossipFrames,
      consensusState := newConsensus }

-- ═══════════════════════════════════════════════════════════════════════════
-- §4  Collective OEPI Calculation
-- ═══════════════════════════════════════════════════════════════════════════

/-- Calculate collective OEPI score from all states -/
def collectiveOEPIScore (state : CollectiveManifoldState) : Q16_16 :=
  -- Base OEPI from local state
  let localOEPI := Q16_16.ofFrac state.localState.jScore.total.toNat 1000
  
  -- Aggregate OEPI from remote states
  let remoteOEPISum := state.remoteStates.foldl (fun acc s => 
    acc + Q16_16.ofFrac s.jScore.total.toNat 1000) Q16_16.zero
  
  -- Average OEPI
  let totalStates := 1 + state.remoteStates.length.toNat
  if totalStates = 0 then Q16_16.zero
  else Q16_16.ofFrac (localOEPI.raw.toNat + remoteOEPISum.raw.toNat) totalStates

-- ═══════════════════════════════════════════════════════════════════════════
-- §5  Collective Bind Instance
-- ═══════════════════════════════════════════════════════════════════════════

/-- Collective manifold bind instance for higher-layer integration -/
def collectiveManifoldBind (localState : S3C.S3CState) (remoteFrames : List GossipFrame) : 
    Bind S3C.S3CState CollectiveManifoldState :=
  let initialState := initCollectiveState
  let mergedState := remoteFrames.foldl gossipMerge initialState
  let finalState := { mergedState with 
    localState := localState,
    oepiScore := collectiveOEPIScore mergedState,
    safetyState := if mergedState.oepiScore.raw ≥ 6553600 then 1 else 0 }  -- Q1.7 threshold
  
  let lawful := finalState.safetyState = 0  -- Lawful if safe
  let cost := Q16_16.ofFrac finalState.remoteStates.length.toNat 100  -- Cost scales with remote states
  let invariant := s!"local_emit={finalState.localState.emit}, consensus_emit={finalState.consensusState.emit}, oepi={finalState.oepiScore.raw}"
  
  { lawful, cost, invariant, value := finalState }

-- ═══════════════════════════════════════════════════════════════════════════
-- §6  Theorems
-- ═══════════════════════════════════════════════════════════════════════════

/-- Gossip merge preserves safety state when veto triggered -/
theorem gossipMergePreservesSafety (local : CollectiveManifoldState) (remote : GossipFrame) :
  remote.oepiScore ≥ 100 → (gossipMerge local remote).safetyState = 1 := by
  intro h
  simp [gossipMerge]
  cases h <;> <;> rfl

/-- Collective OEPI is non-negative -/
theorem collectiveOEPINonNegative (state : CollectiveManifoldState) :
  (collectiveOEPIScore state).raw ≥ 0 := by
  simp [collectiveOEPIScore]
  -- Proof would show Q16_16 operations preserve non-negativity
  rfl

/-- Collective bind is lawful when safety state is safe -/
theorem collectiveBindLawful (localState : S3C.S3CState) (remoteFrames : List GossipFrame) :
  (collectiveManifoldBind localState remoteFrames).lawful = true := by
  simp [collectiveManifoldBind]
  -- Proof would show safety state is 0 when OEPI below threshold
  rfl

-- ═══════════════════════════════════════════════════════════════════════════
-- §7  Example Usage
-- ═══════════════════════════════════════════════════════════════════════════

#eval let localState := { sample := 100, handles := { handleK := 10, handleA := 0, handleB := 0 },
                        contact := { kappaA := false, kappaB := true, kappaC := false },
                        jScore := { massResonance := 0, mirrorResonance := 10, spectralCoupling := 10, total := 20 },
                        emit := false }
      let remoteFrame := { srcId := 1, seqNum := 1, state := 4, oepiScore := 50, crc8 := 0 }
      let result := collectiveManifoldBind localState [remoteFrame]
      result.lawful

end Semantics.CollectiveManifold