/- 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

PistSimulation.lean — PIST Data Slice Processing Pipeline

This module models the functional data transformations from the PIST
interactive simulation (Injection → Pruning → Convergence).

Pipeline phases:
  1. Injection — Load raw geometric states into active tensor set
  2. Predictive Pruning — Hardware predictor kills ~95% of doomed paths
  3. Blitter & Gossip — Discrete Picard integral + local gossip clustering

Maps directly to WebGPU compute shader dispatch:
  • Phase 1: VRAM initialization
  • Phase 2: Predictor kernel (early out)
  • Phase 3: Blitter physics kernel + Gossip reduction

Per AGENTS.md §0: Lean is the source of truth.
Per AGENTS.md §1.4: Uses Q16_16 (Fix16) throughout.
-/

import Semantics.FixedPoint
import Semantics.ShellModel
import Semantics.SSMS

namespace Semantics.PistSimulation

open Semantics
open Semantics.ShellModel
open Semantics.SSMS

-- ════════════════════════════════════════════════════════════
-- §1  Tensor Data Structure
-- ════════════════════════════════════════════════════════════

/-- Single particle/data point in the PIST visual simulation.
    Represents a candidate state in the (a,b) perfect-square coordinate space.
    
    Fields:
    • id — Unique identifier for tracking
    • a — Distance from lower perfect square (k²)
    • b — Distance to upper perfect square ((k+1)²)
    • confidence — Gossip-accumulated viability score
    • isActive — Survival flag (false = pruned/dimmed) -/
structure TensorData where
  id : Nat
  a : Q16_16
  b : Q16_16
  confidence : Q16_16
  isActive : Bool
  deriving Repr, DecidableEq, Inhabited

/-- Zero tensor (inactive, zero confidence). -/
def TensorData.zero (id : Nat) : TensorData :=
  { id := id, a := Q16_16.zero, b := Q16_16.zero,
    confidence := Q16_16.zero, isActive := false }


-- ════════════════════════════════════════════════════════════
-- §2  Phase 1: Injection (Canvas Population)
-- ════════════════════════════════════════════════════════════

/-- Maps to visual step where points populate the screen.
    Loads raw (a,b,confidence) tuples into active TensorData array.
    
    In WebGPU execution: this initializes VRAM with geometric states.
    Each tensor maps to one workgroup thread's initial state. -/
def injectDataSlice (rawInputs : Array (Q16_16 × Q16_16 × Q16_16)) : Array TensorData :=
  rawInputs.mapIdx (λ i val => 
    { id := i,
      a := val.1, 
      b := val.2.1, 
      confidence := val.2.2, 
      isActive := true })

/-- Alternative injection from shell state indices.
    Converts event indices to (a,b) coordinates for PIST simulation. -/
def injectFromShellStates (indices : List Nat) : Array TensorData :=
  let coords := indices.map (λ n => 
    let s := shellState n
    (Q16_16.ofInt (Int.ofNat s.a), 
     Q16_16.ofInt (Int.ofNat s.b),
     Q16_16.ofInt (Int.ofNat (s.a * s.b))))
  injectDataSlice coords.toArray


-- ════════════════════════════════════════════════════════════
-- §3  Phase 2: Predictive Pruning (Heuristic Guillotine)
-- ════════════════════════════════════════════════════════════

/-- Hardware viability predictor.
    Evaluates fast geometric heuristic to kill doomed paths early.
    
    PIST criterion: |a - b| > threshold indicates far from perfect square.
    Near-perfect-squares have a ≈ b (symmetric position in shell).
    
    Returns true if particle survives pruning. -/
def predictViability (a b confidence : Q16_16) : Bool :=
  let diff := Q16_16.abs (Q16_16.sub a b)
  let threshold := Q16_16.ofInt 2  -- Within 2 units of symmetry
  let confThreshold := Q16_16.div (Q16_16.ofInt 1) (Q16_16.ofInt 10)  -- 0.1 confidence minimum
  Q16_16.lt diff threshold && Q16_16.gt confidence confThreshold

/-- Phase 2: Apply predictive pruning to entire dataset.
    Maps to visual step where ~95% of points turn dim and stop.
    
    In WebGPU: This is a compute kernel with early-out for pruned threads. -/
def phase2Pruning (dataset : Array TensorData) : Array TensorData :=
  dataset.map (λ pt =>
    if pt.isActive then
      let viable := predictViability pt.a pt.b pt.confidence
      -- If not viable: particle "turns red and fades out"
      { pt with isActive := viable, 
                confidence := if viable then pt.confidence else Q16_16.zero }
    else pt)


-- ════════════════════════════════════════════════════════════
-- §4  Phase 3: Blitter & Gossip (Convergence)
-- ════════════════════════════════════════════════════════════

/-- Discrete Picard Integral (Blitter) step.
    Model 131 ODE: F(a,b,ε) = (1 + ε(0.5b + 0.3), -1 + ε(0.5a - 0.3))
    
    Performs one timestep of O(1) discrete integration:
      a' = a + ε · (1 + 0.5·b + 0.3)
      b' = b + ε · (-1 + 0.5·a - 0.3)
    
    Maps to WGSL: `blit_result = blit_op(fa, fb, timestep_mask)` -/
def picardBlitStep (a b epsilon : Q16_16) : Q16_16 × Q16_16 :=
  let half := Q16_16.div (Q16_16.ofInt 1) (Q16_16.ofInt 2)
  let c3 := Q16_16.div (Q16_16.ofInt 3) (Q16_16.ofInt 10)
  let fa := Q16_16.add (Q16_16.ofInt 1) 
    (Q16_16.mul epsilon (Q16_16.add (Q16_16.mul half b) c3))
  let fb := Q16_16.add (Q16_16.ofInt (-1))
    (Q16_16.mul epsilon (Q16_16.sub (Q16_16.mul half a) c3))
  let nextA := Q16_16.add a (Q16_16.mul epsilon fa)
  let nextB := Q16_16.add b (Q16_16.mul epsilon fb)
  (nextA, nextB)

/-- Local gossip confidence aggregation.
    Simulates neighbor-to-neighbor confidence sharing in workgroup.
    
    In WebGPU: This uses shared memory / LDS for neighbor access.
    Returns updated confidence from local neighborhood average. -/
def localGossip (neighbors : Array Q16_16) (selfConfidence : Q16_16) : Q16_16 :=
  if neighbors.size = 0 then selfConfidence
  else
    let sum := neighbors.foldl (λ acc c => Q16_16.add acc c) Q16_16.zero
    let avg := Q16_16.div sum (Q16_16.ofInt (Int.ofNat neighbors.size))
    -- Weighted mix: 70% self + 30% neighbor average
    let mixed := Q16_16.add (Q16_16.mul (Q16_16.div (Q16_16.ofInt 7) (Q16_16.ofInt 10)) selfConfidence)
                            (Q16_16.mul (Q16_16.div (Q16_16.ofInt 3) (Q16_16.ofInt 10)) avg)
    mixed

/-- Phase 3: Single simulation tick.
    Maps to visual step where surviving points cluster together.
    
    One "frame" of physics simulation:
      1. Blitter update (move toward perfect square)
      2. Local gossip (pull toward neighbor confidence)
    
    In WebGPU: Dispatch compute shader with barrier between steps. -/
def phase3Tick (dataset : Array TensorData) : Array TensorData :=
  dataset.map (λ pt =>
    if pt.isActive then
      -- Step 1: Discrete Picard Integral (particle moves toward resonance)
      let epsilon := Q16_16.div (Q16_16.ofInt 1) (Q16_16.ofInt 10)  -- ε = 0.1
      let (nextA, nextB) := picardBlitStep pt.a pt.b epsilon
      
      -- Step 2: Local Gossip (pull toward neighbor confidence)
      -- Neighbors are mod 8 in workgroup for L1 cache efficiency
      let neighborIds := List.range 8 |>.map (λ i => (pt.id + i) % dataset.size)
      let neighbors := neighborIds.filterMap (λ i => 
        if i < dataset.size then some (dataset[i]!.confidence) else none)
      let gossipConf := localGossip neighbors.toArray pt.confidence
      
      { pt with a := nextA, b := nextB, confidence := gossipConf }
    else pt)


-- ════════════════════════════════════════════════════════════
-- §5  Full Pipeline Execution
-- ════════════════════════════════════════════════════════════

/-- Execute complete PIST simulation pipeline.
    
    Steps:
      1. Inject raw (a,b,confidence) states
      2. Apply predictive pruning (kill doomed paths)
      3. Run Blitter+Gossip for N frames
    
    Returns final clustered states (the Perfect Square solutions).
    
    Maps to WebGPU sequence:
      • vkCmdDispatch(Phase1_Init)
      • vkCmdDispatch(Phase2_Prune)
      • for i in 0..frames: vkCmdDispatch(Phase3_BlitGossip) -/
def executePipeline (rawInputs : Array (Q16_16 × Q16_16 × Q16_16)) (frames : Nat) : Array TensorData :=
  -- Step 1: Populate canvas
  let injected := injectDataSlice rawInputs
  
  -- Step 2: Apply heuristic (kill doomed paths instantly)
  let pruned := phase2Pruning injected
  
  -- Step 3: Run physics for 'frames' iterations
  let rec loop (data : Array TensorData) (f : Nat) : Array TensorData :=
    match f with
    | 0 => data
    | f' + 1 => loop (phase3Tick data) f'
  loop pruned frames

/-- Execute pipeline from shell event indices.
    Convenience wrapper for AVMR/SSMS integration. -/
def executeFromShellIndices (indices : List Nat) (frames : Nat) : Array TensorData :=
  let rawInputs := indices.map (λ n => 
    let s := shellState n
    (Q16_16.ofInt (Int.ofNat s.a),
     Q16_16.ofInt (Int.ofNat s.b),
     Q16_16.ofInt (Int.ofNat (s.a * s.b))))
  executePipeline rawInputs.toArray frames


-- ════════════════════════════════════════════════════════════
-- §6  Verification Examples
-- ════════════════════════════════════════════════════════════

#eval predictViability (Q16_16.ofInt 4) (Q16_16.ofInt 5) (Q16_16.ofInt 10)  -- Near symmetric, high conf
#eval predictViability (Q16_16.ofInt 1) (Q16_16.ofInt 20) (Q16_16.ofInt 10) -- Far from symmetric
#eval picardBlitStep (Q16_16.ofInt 4) (Q16_16.ofInt 5) (Q16_16.div (Q16_16.ofInt 1) (Q16_16.ofInt 10))
#eval executePipeline #[(Q16_16.ofInt 4, Q16_16.ofInt 5, Q16_16.ofInt 20)] 5

end Semantics.PistSimulation