/-
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