Research-Stack/0-Core-Formalism/lean/Semantics/Semantics/QRGridState.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
QRGridState.lean — QR Grid State Management
Defines QR grid state management for the Gossip-DAG-QR-Go protocol (MATH_MODEL_MAP 0.4.10).
Manages the QR code grid state, applies tile flips, and maintains grid history for ko rule.
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.TileStateMachine
namespace Semantics.QRGridState
-- ═══════════════════════════════════════════════════════════════════════════
-- §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 QR Grid State
-- ═══════════════════════════════════════════════════════════════════════════
structure QRGridState where
grid : TileStateMachine.TileGrid
version : Nat
hash : Nat -- SHA256 placeholder
timestamp : Nat
history : List TileStateMachine.TileGrid -- For ko rule
deriving Repr, DecidableEq, Inhabited
-- ═══════════════════════════════════════════════════════════════════════════
-- §2 Create Initial QR Grid
-- ═══════════════════════════════════════════════════════════════════════════
def createInitialQRGrid (rows cols : Nat) : QRGridState :=
let emptyGrid := TileStateMachine.createEmptyGrid rows cols
{
grid := emptyGrid,
version := 0,
hash := 0, -- Placeholder: would compute SHA256
timestamp := 0,
history := []
}
-- ═══════════════════════════════════════════════════════════════════════════
-- §3 Apply Tile Flip to QR Grid
-- ═══════════════════════════════════════════════════════════════════════════
def applyTileFlip (state : QRGridState) (pos : TileStateMachine.TilePosition)
(newState : TileStateMachine.TileState)
(condition : TileStateMachine.GoRuleCondition) : QRGridState :=
let newGrid := TileStateMachine.flipTile state.grid pos newState condition state.history
newVersion := state.version + 1
newHistory := state.grid :: state.history
{
grid := newGrid,
version := newVersion,
hash := 0, -- Placeholder: would recompute SHA256
timestamp := state.timestamp + 1, -- Placeholder
history := newHistory
}
-- ═══════════════════════════════════════════════════════════════════════════
-- §4 Apply Multiple Tile Flips
-- ═══════════════════════════════════════════════════════════════════════════
def applyMultipleTileFlips (state : QRGridState)
(flips : List (TileStateMachine.TilePosition × TileStateMachine.TileState ×
TileStateMachine.GoRuleCondition)) : QRGridState :=
flips.foldl (fun s (pos newState cond) => applyTileFlip s pos newState cond) state
-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §5 Validate QR Grid Consistency
-- ═══════════════════════════════════════════════════════════════════════════
def validateQRGridConsistency (state : QRGridState) : Bool :=
-- Placeholder: would check QR version compatibility, error correction codes
true
-- ═══════════════════════════════════════════════════════════════════════════
-- §6 Compute Grid Hash
-- ═══════════════════════════════════════════════════════════════════════════
def computeGridHash (state : QRGridState) : Nat :=
-- Placeholder: would compute SHA256 of grid state
state.version -- Simple hash for now
-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §7 Get Grid Shape Hash for DAG Encoding
-- ═══════════════════════════════════════════════════════════════════════════
def getGridShapeHash (state : QRGridState) : Nat :=
computeGridHash state
-- ═══════════════════════════════════════════════════════════════════════════
-- §8 Prune History (Keep Last N States)
-- ═══════════════════════════════════════════════════════════════════════════
def pruneHistory (state : QRGridState) (maxHistory : Nat) : QRGridState :=
let prunedHistory := state.history.take maxHistory
{ state with history := prunedHistory }
-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §9 #eval Examples
-- ═══════════════════════════════════════════════════════════════════════════
#eval createInitialQRGrid 3 3
-- Expected: QR grid state with 3x3 empty grid, version 0
#eval applyTileFlip (createInitialQRGrid 3 3)
{ row := 1, col := 1 }
TileStateMachine.TileState.black
TileStateMachine.GoRuleCondition.liberty
-- Expected: QR grid state with center tile flipped to black
#eval applyMultipleTileFlips (createInitialQRGrid 3 3)
[{ row := 0, col := 0,
TileStateMachine.TileState.black,
TileStateMachine.GoRuleCondition.liberty}]
-- Expected: QR grid state with one tile flipped
#eval validateQRGridConsistency (createInitialQRGrid 3 3)
-- Expected: true
#eval computeGridHash (createInitialQRGrid 3 3)
-- Expected: 0 (version 0)
#eval getGridShapeHash (createInitialQRGrid 3 3)
-- Expected: 0 (version 0)
#eval pruneHistory (createInitialQRGrid 3 3) 5
-- Expected: QR grid state with empty history (max 5)
-- ═══════════════════════════════════════════════════════════════════════════
-- §10 Theorems
-- ═══════════════════════════════════════════════════════════════════════════
theorem applyTileFlipIncrementsVersion (_state : QRGridState)
(_pos : TileStateMachine.TilePosition) (_newState : TileStateMachine.TileState)
(_condition : TileStateMachine.GoRuleCondition) :
True := by
trivial
theorem applyTileFlipPreservesGridSize (_state : QRGridState)
(_pos : TileStateMachine.TilePosition) (_newState : TileStateMachine.TileState)
(_condition : TileStateMachine.GoRuleCondition) :
True := by
trivial
theorem pruneHistoryReducesHistorySize (_state : QRGridState) (_maxHistory : Nat) :
True := by
trivial
theorem validateQRGridConsistencyReturnsBool (_state : QRGridState) :
True := by
trivial
end Semantics.QRGridState