Research-Stack/0-Core-Formalism/lean/Semantics/Semantics/Timing.lean
2026-05-25 16:24:21 -05:00

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/-
Semantics/Timing.lean - Frustration-Aware Manifold Memory (FAMM) Protocol
This module derives dynamic RAM timing parameters from the manifold physics
state (Torsion, Interlocking Energy, Laplacian).
Parameters calculated:
- tTCL (Torsional CAS Latency)
- tMRE (Manifold Refresh Epoch)
- tDLL (Damping Laplacian Latency)
Lean is the source of truth.
-/
import Semantics.DynamicCanal
import Semantics.ManifoldFlow
namespace Semantics.Timing
open DynamicCanal
open Semantics.ManifoldFlow
-- =============================================================================
-- 1. FAMM TIMING CALCULUS (Q16.16)
-- =============================================================================
/-- Base JEDEC-adjacent constants for a 3200MT/s baseline -/
def tBaseCAS : Q16_16 := Q16_16.ofRawInt 0x00160000 -- 22 cycles
def tBaseREF : Q16_16 := Q16_16.ofRawInt 0x1E000000 -- 7.8μs (approx scaled)
def tBaseHammer : Q16_16 := Q16_16.ofRawInt 0x00080000 -- 8 cycles damping
def tMinFactor : Q16_16 := Q16_16.ofRawInt 0x00008000 -- 0.5
/-- Clamp a scaling factor into a positive timing-safe interval. -/
def clampFactor (value floor ceil : Q16_16) : Q16_16 :=
if value.isNeg then floor
else if value.val < floor.val then floor
else if value.val > ceil.val then ceil
else value
/-- Largest multiplicative factor that keeps tBaseREF inside Q16_16 range. -/
def maxRefreshFactor : Q16_16 :=
Q16_16.div Q16_16.maxVal tBaseREF
/--
Calculate Torsional CAS Latency (tTCL).
Higher torsional stress (Σ^2) indicates a "snagged" state that is easier to sense.
tTCL = tBase * (1 - λ * stress)
-/
def calculateTCL (stress : Q16_16) : Q16_16 :=
-- λ = 0.2 frustration sensitivity
let lambda : Q16_16 := Q16_16.ofRawInt 0x00003333
let reduction := Q16_16.mul lambda stress
let factor := Q16_16.sub Q16_16.one reduction
-- Clamp factor between [0.5, 1.0] to prevent physical instability
let clampedFactor := clampFactor factor tMinFactor Q16_16.one
Q16_16.mul tBaseCAS clampedFactor
/--
Calculate Manifold Refresh Epoch (tMRE).
Low interlocking energy (I_lock) implies the manifold is "slipping" from
its lock and needs refresh.
tMRE = tBase * (1 + β * lockingEnergy)
-/
def calculateMRE (energy : Q16_16) : Q16_16 :=
-- β = 1.5 stability gain
let beta : Q16_16 := Q16_16.ofRawInt 0x00018000
let safeEnergy := if energy.isNeg then Q16_16.zero else energy
let gain := Q16_16.mul beta safeEnergy
let factor := Q16_16.add Q16_16.one gain
let clampedFactor := clampFactor factor Q16_16.one maxRefreshFactor
Q16_16.mul tBaseREF clampedFactor
/--
Calculate Damping Laplacian Latency (tDLL) for RowHammer protection.
Based on neighbor-row "vibration" energy (Hodge-Laplacian Δϕ).
-/
def calculateDLL (laplacian : Q16_16) : Q16_16 :=
-- If Laplacian energy > threshold, increase damping delay
let threshold : Q16_16 := Q16_16.ofRawInt 0x00004000 -- 0.25
let lapEnergy := if laplacian.isNeg then Q16_16.abs laplacian else laplacian
if lapEnergy.val > threshold.val then
Q16_16.add tBaseHammer (Q16_16.ofRawInt 0x00040000) -- Add 4 cycles
else
tBaseHammer
-- =============================================================================
-- 2. TIMING STATE
-- =============================================================================
structure ManifoldTiming where
tcl : Q16_16
mre : Q16_16
dll : Q16_16
deriving Repr, DecidableEq, BEq
/-- Derive all FAMM parameters from a single manifold point state -/
def deriveTiming (p : ManifoldPoint) (laplacian : Q16_16) : ManifoldTiming :=
let stress := torsionalStress p.t
let lock := interlockingEnergy p.x_pos p.x0_pos p.a -- energy relative to preferred
{ tcl := calculateTCL stress
, mre := calculateMRE lock
, dll := calculateDLL laplacian
}
-- =============================================================================
-- 3. VERIFICATION WITNESSES
-- =============================================================================
-- #eval example: Baseline timing
#eval (calculateTCL (Q16_16.ofRawInt 0x00020000)).val -- expect slightly reduced CAS
#eval (calculateMRE (Q16_16.ofRawInt 0x00010000)).val -- expect increased refresh epoch
end Semantics.Timing