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