Research-Stack/4-Infrastructure/nano-kernel/gcl-modules/m004-pist-geometry.gcl

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-- 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