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113 lines
4 KiB
Text
113 lines
4 KiB
Text
/-
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Semantics/Timing.lean - Frustration-Aware Manifold Memory (FAMM) Protocol
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This module derives dynamic RAM timing parameters from the manifold physics
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state (Torsion, Interlocking Energy, Laplacian).
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Parameters calculated:
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- tTCL (Torsional CAS Latency)
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- tMRE (Manifold Refresh Epoch)
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- tDLL (Damping Laplacian Latency)
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Lean is the source of truth.
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-/
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import Semantics.DynamicCanal
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import Semantics.ManifoldFlow
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namespace Semantics.Timing
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open DynamicCanal
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open Semantics.ManifoldFlow
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-- =============================================================================
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-- 1. FAMM TIMING CALCULUS (Q16.16)
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-- =============================================================================
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/-- Base JEDEC-adjacent constants for a 3200MT/s baseline -/
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def tBaseCAS : Fix16 := Fix16.mk 0x00160000 -- 22 cycles
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def tBaseREF : Fix16 := Fix16.mk 0x1E000000 -- 7.8μs (approx scaled)
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def tBaseHammer : Fix16 := Fix16.mk 0x00080000 -- 8 cycles damping
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def tMinFactor : Fix16 := Fix16.mk 0x00008000 -- 0.5
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/-- Clamp a scaling factor into a positive timing-safe interval. -/
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def clampFactor (value floor ceil : Fix16) : Fix16 :=
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if value.isNeg then floor
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else if value.raw < floor.raw then floor
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else if value.raw > ceil.raw then ceil
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else value
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/-- Largest multiplicative factor that keeps tBaseREF inside Fix16 range. -/
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def maxRefreshFactor : Fix16 :=
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Fix16.div Fix16.maxVal tBaseREF
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/--
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Calculate Torsional CAS Latency (tTCL).
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Higher torsional stress (Σ^2) indicates a "snagged" state that is easier to sense.
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tTCL = tBase * (1 - λ * stress)
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-/
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def calculateTCL (stress : Fix16) : Fix16 :=
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-- λ = 0.2 frustration sensitivity
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let lambda := Fix16.mk 0x00003333
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let reduction := Fix16.mul lambda stress
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let factor := Fix16.sub Fix16.one reduction
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-- Clamp factor between [0.5, 1.0] to prevent physical instability
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let clampedFactor := clampFactor factor tMinFactor Fix16.one
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Fix16.mul tBaseCAS clampedFactor
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/--
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Calculate Manifold Refresh Epoch (tMRE).
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Low interlocking energy (I_lock) implies the manifold is "slipping" from
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its lock and needs refresh.
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tMRE = tBase * (1 + β * lockingEnergy)
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-/
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def calculateMRE (energy : Fix16) : Fix16 :=
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-- β = 1.5 stability gain
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let beta := Fix16.mk 0x00018000
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let safeEnergy := if energy.isNeg then Fix16.zero else energy
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let gain := Fix16.mul beta safeEnergy
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let factor := Fix16.add Fix16.one gain
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let clampedFactor := clampFactor factor Fix16.one maxRefreshFactor
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Fix16.mul tBaseREF clampedFactor
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/--
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Calculate Damping Laplacian Latency (tDLL) for RowHammer protection.
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Based on neighbor-row "vibration" energy (Hodge-Laplacian Δϕ).
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-/
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def calculateDLL (laplacian : Fix16) : Fix16 :=
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-- If Laplacian energy > threshold, increase damping delay
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let threshold := Fix16.mk 0x00004000 -- 0.25
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let lapEnergy := if laplacian.isNeg then Fix16.abs laplacian else laplacian
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if lapEnergy.raw > threshold.raw then
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Fix16.add tBaseHammer (Fix16.mk 0x00040000) -- Add 4 cycles
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else
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tBaseHammer
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-- =============================================================================
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-- 2. TIMING STATE
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-- =============================================================================
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structure ManifoldTiming where
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tcl : Fix16
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mre : Fix16
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dll : Fix16
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deriving Repr, DecidableEq, BEq
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/-- Derive all FAMM parameters from a single manifold point state -/
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def deriveTiming (p : ManifoldPoint) (laplacian : Fix16) : ManifoldTiming :=
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let stress := torsionalStress p.t
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let lock := interlockingEnergy p.x_pos p.x0_pos p.a -- energy relative to preferred
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{ tcl := calculateTCL stress
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, mre := calculateMRE lock
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, dll := calculateDLL laplacian
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}
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-- =============================================================================
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-- 3. VERIFICATION WITNESSES
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-- =============================================================================
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-- #eval example: Baseline timing
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#eval (calculateTCL (Fix16.mk 0x00020000)).raw -- expect slightly reduced CAS
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#eval (calculateMRE (Fix16.mk 0x00010000)).raw -- expect increased refresh epoch
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end Semantics.Timing
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