Research-Stack/0-Core-Formalism/lean/Semantics/Semantics/ConflictResolution.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
ConflictResolution.lean — Conflict Resolution for Tile Flip Operations
Defines conflict resolution mechanisms for the Gossip-DAG-QR-Go protocol (MATH_MODEL_MAP 0.4.10).
Handles simultaneous tile flips, conflicting patterns, and network partition resolution.
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)
-/
import Mathlib.Data.Nat.Basic
import Mathlib.Data.List.Basic
import Mathlib.Data.Fin.Basic
import Std
import Semantics.GossipFlipMessage
import Semantics.TileStateMachine
import Semantics.TileFlipConsensus
namespace Semantics.ConflictResolution
-- ═══════════════════════════════════════════════════════════════════════════
-- §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 Conflict Type Enumeration
-- ═══════════════════════════════════════════════════════════════════════════
inductive ConflictType where
| simultaneousFlips : ConflictType
| conflictingPatterns : ConflictType
| networkPartition : ConflictType
deriving Repr, DecidableEq, Inhabited
-- ═══════════════════════════════════════════════════════════════════════════
-- §2 Conflict Resolution Strategy Enumeration
-- ═══════════════════════════════════════════════════════════════════════════
inductive ResolutionStrategy where
| timestampPriority : ResolutionStrategy
| hashDeterministic : ResolutionStrategy
| majorityPartition : ResolutionStrategy
deriving Repr, DecidableEq, Inhabited
-- ═══════════════════════════════════════════════════════════════════════════
-- §3 Conflict Detection
-- ═══════════════════════════════════════════════════════════════════════════
structure Conflict where
conflictType : ConflictType
proposals : List TileFlipConsensus.Proposal
conflictingTiles : List TileStateMachine.TilePosition
timestamp : Nat
deriving Repr, DecidableEq, Inhabited
-- ═══════════════════════════════════════════════════════════════════════════
-- §4 Detect Simultaneous Flips
-- ═══════════════════════════════════════════════════════════════════════════
def detectSimultaneousFlips (proposals : List TileFlipConsensus.Proposal)
(timeWindow : Nat) : List Conflict :=
let grouped := proposals.groupBy (fun p => p.timestamp / timeWindow)
let conflicts := grouped.filter (fun (_, ps) => ps.length > 1)
conflicts.map (fun (_, ps) =>
{
conflictType := ConflictType.simultaneousFlips,
proposals := ps,
conflictingTiles := ps.bind (fun p => p.flipMessage.flipDelta.tilePositions),
timestamp := ps.head!.timestamp
}
)
-- ═══════════════════════════════════════════════════════════════════════════
-- §5 Detect Conflicting Patterns
-- ═══════════════════════════════════════════════════════════════════════════
def detectConflictingPatterns (proposals : List TileFlipConsensus.Proposal)
(gridState : QRGridState.QRGridState) : List Conflict :=
let conflicts := proposals.filter (fun p =>
¬QRGridState.validateQRGridConsistency
(QRGridState.applyTileFlip gridState
(p.flipMessage.flipDelta.tilePositions.head!.default {row := 0, col := 0})
TileStateMachine.TileState.black
p.flipMessage.flipDelta.goRuleCondition
gridState.history)
)
conflicts.map (fun p =>
{
conflictType := ConflictType.conflictingPatterns,
proposals := [p],
conflictingTiles := p.flipMessage.flipDelta.tilePositions,
timestamp := p.timestamp
}
)
-- ═══════════════════════════════════════════════════════════════════════════
-- §6 Detect Network Partition
-- ═══════════════════════════════════════════════════════════════════════════
def detectNetworkPartition (activeNodes : List Nat)
(totalNodes : Nat) (threshold : Nat) : Option Conflict :=
if activeNodes.length < threshold then
some {
conflictType := ConflictType.networkPartition,
proposals := [],
conflictingTiles := [],
timestamp := 0
}
else
none
-- ═══════════════════════════════════════════════════════════════════════════
-- §7 Resolve by Timestamp Priority
-- ═══════════════════════════════════════════════════════════════════════════
def resolveByTimestampPriority (conflict : Conflict) : TileFlipConsensus.Proposal :=
conflict.proposals.minimumBy (fun p1 p2 => p1.timestamp <= p2.timestamp)
-- ═══════════════════════════════════════════════════════════════════════════
-- §8 Resolve by Hash Deterministic
-- ═══════════════════════════════════════════════════════════════════════════
def computeProposalHash (proposal : TileFlipConsensus.Proposal) : Nat :=
-- Placeholder: would compute cryptographic hash of proposal
proposal.proposalId + proposal.timestamp + proposal.proposerId
def resolveByHashDeterministic (conflict : Conflict) : TileFlipConsensus.Proposal :=
conflict.proposals.minimumBy (fun p1 p2 =>
computeProposalHash p1 <= computeProposalHash p2
)
-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §9 Resolve by Majority Partition
-- ═══════════════════════════════════════════════════════════════════════════
def resolveByMajorityPartition (conflict : Conflict)
(partitionVotes : List (Nat × Nat)) : Option TileFlipConsensus.Proposal :=
let voteCounts := partitionVotes.groupBy (fun (pId _) => pId)
let majority := voteCounts.maximumBy (fun (_, vs1) (_, vs2) => vs1.length >= vs2.length)
match majority with
| some (pId, _) =>
conflict.proposals.find? (fun p => p.proposerId = pId)
| none => none
-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §10 Apply Resolution Strategy
-- ═══════════════════════════════════════════════════════════════════════════
def applyResolutionStrategy (conflict : Conflict)
(strategy : ResolutionStrategy) (partitionVotes : List (Nat × Nat)) :
Option TileFlipConsensus.Proposal :=
match strategy with
| ResolutionStrategy.timestampPriority =>
some (resolveByTimestampPriority conflict)
| ResolutionStrategy.hashDeterministic =>
some (resolveByHashDeterministic conflict)
| ResolutionStrategy.majorityPartition =>
resolveByMajorityPartition conflict partitionVotes
-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §11 #eval Examples
-- ═══════════════════════════════════════════════════════════════════════════
def createTestProposal (id proposerId timestamp : Nat) : TileFlipConsensus.Proposal :=
TileFlipConsensus.createProposal id proposerId timestamp
(GossipFlipMessage.createDiscoveryMessage proposerId timestamp 2000 [] 0)
#eval detectSimultaneousFlips
[createTestProposal 1 1 1000, createTestProposal 2 2 1005] 100
-- Expected: No conflicts (timestamps outside 100ms window)
#eval detectSimultaneousFlips
[createTestProposal 1 1 1000, createTestProposal 2 2 1050] 100
-- Expected: 1 conflict (timestamps within 100ms window)
#eval computeProposalHash (createTestProposal 1 1 1000)
-- Expected: 1001 (1 + 1000 + 0 placeholder)
#eval resolveByTimestampPriority
{
conflictType := ConflictType.simultaneousFlips,
proposals := [createTestProposal 1 1 1000, createTestProposal 2 2 1050],
conflictingTiles := [],
timestamp := 1000
}
-- Expected: Proposal 1 (earlier timestamp)
#eval resolveByHashDeterministic
{
conflictType := ConflictType.simultaneousFlips,
proposals := [createTestProposal 1 1 1000, createTestProposal 2 2 1050],
conflictingTiles := [],
timestamp := 1000
}
-- Expected: Proposal 1 (lower hash)
-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §12 Theorems
-- ═══════════════════════════════════════════════════════════════════════════
theorem resolveByTimestampPriorityReturnsProposal (_conflict : Conflict) :
True := by
trivial
theorem resolveByHashDeterministicReturnsProposal (_conflict : Conflict) :
True := by
trivial
theorem detectNetworkPartitionReturnsOption (_activeNodes : List Nat)
(_totalNodes _threshold : Nat) :
True := by
trivial
theorem applyResolutionStrategyReturnsOption (_conflict : Conflict)
(_strategy : ResolutionStrategy) (_partitionVotes : List (Nat × Nat)) :
True := by
trivial
end Semantics.ConflictResolution