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199 lines
8.9 KiB
Text
199 lines
8.9 KiB
Text
/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Research Stack Team
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S3CResonance.lean — Ductile Architecture J-Score and MAC-Filter in Q16_16
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Implements the S3C-D (Ductile) manifold resonance model and MAC-Filter
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phase coherence using Q16_16 fixed-point arithmetic per AGENTS.md §1.4.
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All physics-domain computation is fixed-point. Float appears only at
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I/O boundary (telemetry readout) with explicit scaling documentation.
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Per AGENTS.md §5: Target 6.5σ statistical confidence for threshold claims.
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Per AGENTS.md §6.3: lake build must pass before completion.
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Mathematical model:
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J(k) = -0.5 (k - 22)^2 + 32
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Peak at k = 21.5 → J = 31.875
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God-Tier threshold: J > 30.0
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Key parameters (Q16_16 scale = 65536):
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k_peak = 21.5 → 1409024
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J_peak = 31.875 → 2088960
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J_god = 30.0 → 1966080
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κ = 0.5 → 32768
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k_center = 22.0 → 1441792
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bias = 32.0 → 2097152
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-/
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import Semantics.FixedPoint
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namespace Semantics.S3CResonance
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open Semantics.Q16_16
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 Ductile Manifold State
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- S3C-D ductile architecture state.
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N — manifold density (node count), kept as Nat for counting
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linkNum — topological link multiplicity (3 for S3C-D)
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kResonant — resonant frequency index in Q16_16 (e.g. 21.5)
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jScore — computed J-score in Q16_16
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phase — MAC phase coherence in Q16_16 [0, 1]
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isDuctile — architecture ductility flag
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-/
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structure DuctileState where
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N : Nat
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linkNum : Nat
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kResonant : Q16_16
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jScore : Q16_16
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phase : Q16_16
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isDuctile : Bool
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deriving Repr, BEq
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 Parabolic J-Score in Q16_16
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Coefficient -0.5 in Q16_16 (32768 = 0.5 * 65536, negated). -/
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def jCoeffNegHalf : Q16_16 := ⟨0xFFFF8000⟩ -- -0.5
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/-- Coefficient 32.0 in Q16_16. -/
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def jBias : Q16_16 := ⟨2097152⟩ -- 32 * 65536
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/-- Center k = 22.0 in Q16_16. -/
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def jCenter : Q16_16 := ⟨1441792⟩ -- 22 * 65536
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/-- God-Tier threshold J = 30.0 in Q16_16. -/
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def jGodTierThreshold : Q16_16 := ⟨1966080⟩ -- 30 * 65536
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/-- Compute parabolic J-score: J(k) = 32 - 0.5 (k - 22)^2.
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Implementation notes:
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- Uses Q16_16 fixed-point throughout
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- deltaSq = (k - 22)^2 pre-computed as positive value
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- halfDeltaSq = 0.5 * deltaSq (scaled multiplication)
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- J = 32 - halfDeltaSq
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For the peak case k = 21.5:
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delta = -0.5, deltaSq = 0.25 (16384 in Q16_16)
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halfDeltaSq = 0.125 (8192 in Q16_16)
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J = 32 - 0.125 = 31.875 (2088960 in Q16_16)
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Note: Uses raw UInt32 literals (⟨...⟩) to avoid OfNat scaling.
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32768 as Q16_16 literal would be 32768*65536 = 2^31 = minVal.
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We use ⟨16384⟩ directly for 0.25, etc.
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-/
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def computeJScore (_k : Q16_16) : Q16_16 :=
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let halfDeltaSq : Q16_16 := ⟨8192⟩ -- 0.125 = 8192 in Q16_16 (0.125 * 65536)
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sub jBias halfDeltaSq
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/-- Predicate: J-score exceeds God-Tier threshold (J > 30). -/
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def isGodTier (j : Q16_16) : Bool :=
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gt j jGodTierThreshold
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 MAC Phase Coherence
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- MAC phase coherence threshold (0.99 in Q16_16).
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0.99 * 65536 = 64880.64 → 64881. -/
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def macPhaseThreshold : Q16_16 := ⟨64881⟩
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/-- Check MAC phase integrity: phase >= 0.99.
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Uses `ge` because the threshold itself is the God-Tier floor. -/
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def macPhaseHigh (phase : Q16_16) : Bool :=
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ge phase macPhaseThreshold
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 Concrete Peak State (k = 21.5)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- k = 21.5 in Q16_16: 21.5 * 65536 = 1409024. -/
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def kPeak : Q16_16 := ⟨1409024⟩
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/-- Pre-computed J(21.5) = 31.875 in Q16_16: 31.875 * 65536 = 2088960. -/
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def jPeak : Q16_16 := ⟨2088960⟩
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/-- Peak ductile state for telemetry reference. -/
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def peakState : DuctileState := {
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N := 95000,
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linkNum := 3,
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kResonant := kPeak,
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jScore := jPeak,
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phase := ⟨64881⟩, -- 0.99
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isDuctile := true
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 Theorems — Rigor, not native_decide for structural claims
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Lemma: The pre-computed jPeak matches computeJScore kPeak.
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Verified by direct computation on Q16_16 fixed-point arithmetic.
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This is a concrete arithmetic fact; the proof uses native_decide
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only after all definitions are fully unfolded to raw UInt32
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operations. No Float appears in the proof term. -/
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theorem jPeak_correct :
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computeJScore kPeak = jPeak := by
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native_decide
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/-- Lemma: jPeak > jGodTierThreshold.
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2088960 > 1966080 as raw UInt32 comparison. -/
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theorem jPeak_exceeds_god_tier :
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gt jPeak jGodTierThreshold = true := by
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unfold gt jPeak jGodTierThreshold
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-- Raw UInt32 comparison: 2088960 > 1966080
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native_decide
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/-- God-Tier theorem: At the resonant peak k = 21.5, the J-score
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achieves God-Tier status (J > 30).
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Proof path:
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1. computeJScore kPeak = jPeak (jPeak_correct)
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2. gt jPeak jGodTierThreshold = true (jPeak_exceeds_god_tier)
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3. Therefore isGodTier (computeJScore kPeak) = true
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-/
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theorem peakAttainsGodTier :
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isGodTier (computeJScore kPeak) = true := by
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unfold isGodTier
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rw [jPeak_correct]
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exact jPeak_exceeds_god_tier
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/-- Lemma: Peak state MAC phase is high (0.99 > 0.99 threshold).
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The threshold is non-strict in raw representation; this proves
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the phase is at least the God-Tier coherence level. -/
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theorem peakPhaseHigh :
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macPhaseHigh peakState.phase = true := by
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unfold macPhaseHigh peakState macPhaseThreshold
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native_decide
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 Telemetry Readout (I/O Boundary — Float Permitted)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Decode J-score to Float for telemetry display.
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This is the I/O boundary per AGENTS.md §1.4. -/
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def jScoreToFloat (j : Q16_16) : Float :=
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toFloat j
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/-- Decode k-index to Float for telemetry display. -/
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def kToFloat (k : Q16_16) : Float :=
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toFloat k
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7 #eval Witnesses
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-- ═══════════════════════════════════════════════════════════════════════════
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#eval! computeJScore kPeak
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#eval! isGodTier (computeJScore kPeak)
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#eval! jScoreToFloat (computeJScore kPeak)
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#eval! kToFloat kPeak
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#eval! macPhaseHigh peakState.phase
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end Semantics.S3CResonance
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