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{"type":"new","contents":"/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.\nReleased under Apache 2.0 license as described in the file LICENSE.\nAuthors: Research Stack Team\n\nPistSimulation.lean — PIST Data Slice Processing Pipeline\n\nThis module models the functional data transformations from the PIST\ninteractive simulation (Injection → Pruning → Convergence).\n\nPipeline phases:\n 1. Injection — Load raw geometric states into active tensor set\n 2. Predictive Pruning — Hardware predictor kills ~95% of doomed paths\n 3. Blitter & Gossip — Discrete Picard integral + local gossip clustering\n\nMaps directly to WebGPU compute shader dispatch:\n • Phase 1: VRAM initialization\n • Phase 2: Predictor kernel (early out)\n • Phase 3: Blitter physics kernel + Gossip reduction\n\nPer AGENTS.md §0: Lean is the source of truth.\nPer AGENTS.md §1.4: Uses Q16_16 (Fix16) throughout.\n-/\n\nimport Semantics.FixedPoint\nimport Semantics.ShellModel\nimport Semantics.SSMS\n\nnamespace Semantics.PistSimulation\n\nopen Semantics\nopen Semantics.ShellModel\nopen Semantics.SSMS\n\n-- ════════════════════════════════════════════════════════════\n-- §1 Tensor Data Structure\n-- ════════════════════════════════════════════════════════════\n\n/-- Single particle/data point in the PIST visual simulation.\n Represents a candidate state in the (a,b) perfect-square coordinate space.\n \n Fields:\n • id — Unique identifier for tracking\n • a — Distance from lower perfect square (k²)\n • b — Distance to upper perfect square ((k+1)²)\n • confidence — Gossip-accumulated viability score\n • isActive — Survival flag (false = pruned/dimmed) -/\nstructure TensorData where\n id : Nat\n a : Q16_16\n b : Q16_16\n confidence : Q16_16\n isActive : Bool\n deriving Repr, DecidableEq, Inhabited\n\n/-- Zero tensor (inactive, zero confidence). -/\ndef TensorData.zero (id : Nat) : TensorData :=\n { id := id, a := Q16_16.zero, b := Q16_16.zero,\n confidence := Q16_16.zero, isActive := false }\n\n\n-- ════════════════════════════════════════════════════════════\n-- §2 Phase 1: Injection (Canvas Population)\n-- ════════════════════════════════════════════════════════════\n\n/-- Maps to visual step where points populate the screen.\n Loads raw (a,b,confidence) tuples into active TensorData array.\n \n In WebGPU execution: this initializes VRAM with geometric states.\n Each tensor maps to one workgroup thread's initial state. -/\ndef injectDataSlice (rawInputs : Array (Q16_16 × Q16_16 × Q16_16)) : Array TensorData :=\n rawInputs.mapIdx (λ i val => \n { id := i,\n a := val.1, \n b := val.2.1, \n confidence := val.2.2, \n isActive := true })\n\n/-- Alternative injection from shell state indices.\n Converts event indices to (a,b) coordinates for PIST simulation. -/\ndef injectFromShellStates (indices : List Nat) : Array TensorData :=\n let coords := indices.map (λ n => \n let s := shellState n\n (Q16_16.ofInt (Int.ofNat s.a), \n Q16_16.ofInt (Int.ofNat s.b),\n Q16_16.ofInt (Int.ofNat (s.a * s.b))))\n injectDataSlice coords.toArray\n\n\n-- ════════════════════════════════════════════════════════════\n-- §3 Phase 2: Predictive Pruning (Heuristic Guillotine)\n-- ════════════════════════════════════════════════════════════\n\n/-- Hardware viability predictor.\n Evaluates fast geometric heuristic to kill doomed paths early.\n \n PIST criterion: |a - b| > threshold indicates far from perfect square.\n Near-perfect-squares have a ≈ b (symmetric position in shell).\n \n Returns true if particle survives pruning. -/\ndef predictViability (a b confidence : Q16_16) : Bool :=\n let diff := Q16_16.abs (Q16_16.sub a b)\n let threshold := Q16_16.ofInt 2 -- Within 2 units of symmetry\n let confThreshold := Q16_16.div (Q16_16.ofInt 1) (Q16_16.ofInt 10) -- 0.1 confidence minimum\n Q16_16.lt diff threshold && Q16_16.gt confidence confThreshold\n\n/-- Phase 2: Apply predictive pruning to entire dataset.\n Maps to visual step where ~95% of points turn dim and stop.\n \n In WebGPU: This is a compute kernel with early-out for pruned threads. -/\ndef phase2Pruning (dataset : Array TensorData) : Array TensorData :=\n dataset.map (λ pt =>\n if pt.isActive then\n let viable := predictViability pt.a pt.b pt.confidence\n -- If not viable: particle \"turns red and fades out\"\n { pt with isActive := viable, \n confidence := if viable then pt.confidence else Q16_16.zero }\n else pt)\n\n\n-- ════════════════════════════════════════════════════════════\n-- §4 Phase 3: Blitter & Gossip (Convergence)\n-- ════════════════════════════════════════════════════════════\n\n/-- Discrete Picard Integral (Blitter) step.\n Model 131 ODE: F(a,b,ε) = (1 + ε(0.5b + 0.3), -1 + ε(0.5a - 0.3))\n \n Performs one timestep of O(1) discrete integration:\n a' = a + ε · (1 + 0.5·b + 0.3)\n b' = b + ε · (-1 + 0.5·a - 0.3)\n \n Maps to WGSL: `blit_result = blit_op(fa, fb, timestep_mask)` -/\ndef picardBlitStep (a b epsilon : Q16_16) : Q16_16 × Q16_16 :=\n let half := Q16_16.div (Q16_16.ofInt 1) (Q16_16.ofInt 2)\n let c3 := Q16_16.div (Q16_16.ofInt 3) (Q16_16.ofInt 10)\n let fa := Q16_16.add (Q16_16.ofInt 1) \n (Q16_16.mul epsilon (Q16_16.add (Q16_16.mul half b) c3))\n let fb := Q16_16.add (Q16_16.ofInt (-1))\n (Q16_16.mul epsilon (Q16_16.sub (Q16_16.mul half a) c3))\n let nextA := Q16_16.add a (Q16_16.mul epsilon fa)\n let nextB := Q16_16.add b (Q16_16.mul epsilon fb)\n (nextA, nextB)\n\n/-- Local gossip confidence aggregation.\n Simulates neighbor-to-neighbor confidence sharing in workgroup.\n \n In WebGPU: This uses shared memory / LDS for neighbor access.\n Returns updated confidence from local neighborhood average. -/\ndef localGossip (neighbors : Array Q16_16) (selfConfidence : Q16_16) : Q16_16 :=\n if neighbors.size = 0 then selfConfidence\n else\n let sum := neighbors.foldl (λ acc c => Q16_16.add acc c) Q16_16.zero\n let avg := Q16_16.div sum (Q16_16.ofInt (Int.ofNat neighbors.size))\n -- Weighted mix: 70% self + 30% neighbor average\n let mixed := Q16_16.add (Q16_16.mul (Q16_16.div (Q16_16.ofInt 7) (Q16_16.ofInt 10)) selfConfidence)\n (Q16_16.mul (Q16_16.div (Q16_16.ofInt 3) (Q16_16.ofInt 10)) avg)\n mixed\n\n/-- Phase 3: Single simulation tick.\n Maps to visual step where surviving points cluster together.\n \n One \"frame\" of physics simulation:\n 1. Blitter update (move toward perfect square)\n 2. Local gossip (pull toward neighbor confidence)\n \n In WebGPU: Dispatch compute shader with barrier between steps. -/\ndef phase3Tick (dataset : Array TensorData) : Array TensorData :=\n dataset.map (λ pt =>\n if pt.isActive then\n -- Step 1: Discrete Picard Integral (particle moves toward resonance)\n let epsilon := Q16_16.div (Q16_16.ofInt 1) (Q16_16.ofInt 10) -- ε = 0.1\n let (nextA, nextB) := picardBlitStep pt.a pt.b epsilon\n \n -- Step 2: Local Gossip (pull toward neighbor confidence)\n -- Neighbors are mod 8 in workgroup for L1 cache efficiency\n let neighborIds := List.range 8 |>.map (λ i => (pt.id + i) % dataset.size)\n let neighbors := neighborIds.filterMap (λ i => \n if i < dataset.size then some (dataset[i]!.confidence) else none)\n let gossipConf := localGossip neighbors.toArray pt.confidence\n \n { pt with a := nextA, b := nextB, confidence := gossipConf }\n else pt)\n\n\n-- ════════════════════════════════════════════════════════════\n-- §5 Full Pipeline Execution\n-- ════════════════════════════════════════════════════════════\n\n/-- Execute complete PIST simulation pipeline.\n \n Steps:\n 1. Inject raw (a,b,confidence) states\n 2. Apply predictive pruning (kill doomed paths)\n 3. Run Blitter+Gossip for N frames\n \n Returns final clustered states (the Perfect Square solutions).\n \n Maps to WebGPU sequence:\n • vkCmdDispatch(Phase1_Init)\n • vkCmdDispatch(Phase2_Prune)\n • for i in 0..frames: vkCmdDispatch(Phase3_BlitGossip) -/\ndef executePipeline (rawInputs : Array (Q16_16 × Q16_16 × Q16_16)) (frames : Nat) : Array TensorData :=\n -- Step 1: Populate canvas\n let injected := injectDataSlice rawInputs\n \n -- Step 2: Apply heuristic (kill doomed paths instantly)\n let pruned := phase2Pruning injected\n \n -- Step 3: Run physics for 'frames' iterations\n let rec loop (data : Array TensorData) (f : Nat) : Array TensorData :=\n match f with\n | 0 => data\n | f' + 1 => loop (phase3Tick data) f'\n loop pruned frames\n\n/-- Execute pipeline from shell event indices.\n Convenience wrapper for AVMR/SSMS integration. -/\ndef executeFromShellIndices (indices : List Nat) (frames : Nat) : Array TensorData :=\n let rawInputs := indices.map (λ n => \n let s := shellState n\n (Q16_16.ofInt (Int.ofNat s.a),\n Q16_16.ofInt (Int.ofNat s.b),\n Q16_16.ofInt (Int.ofNat (s.a * s.b))))\n executePipeline rawInputs.toArray frames\n\n\n-- ════════════════════════════════════════════════════════════\n-- §6 Verification Examples\n-- ════════════════════════════════════════════════════════════\n\n#eval predictViability (Q16_16.ofInt 4) (Q16_16.ofInt 5) (Q16_16.ofInt 10) -- Near symmetric, high conf\n#eval predictViability (Q16_16.ofInt 1) (Q16_16.ofInt 20) (Q16_16.ofInt 10) -- Far from symmetric\n#eval picardBlitStep (Q16_16.ofInt 4) (Q16_16.ofInt 5) (Q16_16.div (Q16_16.ofInt 1) (Q16_16.ofInt 10))\n#eval executePipeline #[(Q16_16.ofInt 4, Q16_16.ofInt 5, Q16_16.ofInt 20)] 5\n\nend Semantics.PistSimulation\n","mtime":1777674400571} |