-- M004: PIST Geometry Kernel Module
-- Source: pist_shell_state_v1 (2-Search-Space/PIST)
-- Kernel Function: ProcessTopology
--
-- Processes live on PIST torus geometry. Shell state S(n) = (k, a, b, width).
-- Process scheduling follows shell-state classification: A, G, C, T.
-- Truth Seal: [ SSS-ENE-PIST-2026-05-03 ]

module M004_PISTGeometry where

import BaseTypes
import Semantics.Q16_16

structure PISTShell where
  n     : Nat           -- Process priority / quantum number
  k     : Nat           -- Shell index = floor(sqrt(n))
  a     : Nat           -- Forward distance = n - k²
  b     : Nat           -- Backward distance = (k+1)² - n
  width : Nat           -- Shell width = 2k + 1

structure PISTProcess where
  pid       : PID
  shell     : PISTShell
  et        : BaseType    -- A, G, C, T classification
  position  : Vec3        -- On torus surface
  spin      : Q16_16      -- Scheduling priority weight

inductive BaseType where
  | A  -- Adenine  : n = k² (perfect square, stable)
  | G  -- Guanine  : n = k² + k (mid-shell, balanced)
  | C  -- Cytosine : n = k² + k + 1 (near-edge, active)
  | T  -- Thymine  : n = (k+1)² - 1 (shell boundary, volatile)

-- Compute shell state for process priority n
def shellState (n : Nat) : PISTShell :=
  let k := isqrt n
  let a := n - k * k
  let b := (k + 1) * (k + 1) - n
  { n := n, k := k, a := a, b := b, width := 2 * k + 1 }

-- Classify process by its shell position
def classifyProcess (proc : PISTProcess) : BaseType :=
  let s := proc.shell
  if s.n == s.k * s.k then .A
  else if s.n == s.k * s.k + s.k then .G
  else if s.n == s.k * s.k + s.k + 1 then .C
  else if s.n == (s.k + 1) * (s.k + 1) - 1 then .T
  else .A  -- Default stable

-- Torus embedding: position from shell geometry
def torusPosition (s : PISTShell) (θ : Float) (φ : Float) : Vec3 :=
  let R := 1.0  -- Major radius
  let r := 1.0 / (s.k.toFloat + 1.0)  -- Minor radius shrinks with shell
  let x := (R + r * cos φ) * cos θ
  let y := (R + r * cos φ) * sin θ
  let z := r * sin φ
  Vec3.mk (Q16_16.ofFloat x) (Q16_16.ofFloat y) (Q16_16.ofFloat z)

-- Scheduling weight from base type and shell position
def schedulingWeight (proc : PISTProcess) : Q16_16 :=
  let baseWeight := match proc.et with
    | .A => Q16_16.ofFloat 0.25  -- Stable, low priority
    | .G => Q16_16.ofFloat 0.50  -- Balanced
    | .C => Q16_16.ofFloat 0.75  -- Active, higher priority
    | .T => Q16_16.ofFloat 1.00  -- Volatile, urgent
  
  -- Shell position adjustment: edge processes (high a or b) get boost
  let edgeFactor := Q16_16.ofFloat (
    (proc.shell.a.toFloat + proc.shell.b.toFloat) / 
    (2.0 * proc.shell.k.toFloat + 1.0)
  )
  
  baseWeight + edgeFactor * Q16_16.ofFloat 0.25

-- Kernel interface: PIST-aware scheduler
def pistScheduleNext (readyQueue : Array PISTProcess) : IO PISTProcess := do
  let scored := readyQueue.map (\p => { proc := p, weight := schedulingWeight p })
  let next := scored.maxBy (\s => s.weight)
  return next.proc

end M004_PISTGeometry