feat(coq): Wave-46 Lane NN — AdiabRC.v 33 Qed + composite Theorem (Closes #163)

[gHashTag]

Wave-46 Lane NN — AdiabRC.v 33 Qed + 1 composite Theorem

Closes #163 (gHashTag/trinity-fpga#163 — Wave-46 L-DPC33 PROBE-ACTIVATION-III ADIAB-RC)

Mission

Add sacred opcode OP_ADIAB_RC = 0xF0 = 240 — the FINAL slot in the sacred bank 0xD0..0xF0 (16/16 cells now FULL after this wave).

Adiabatic Charge Recovery uses a resonant LC inductor sweep to return η·C·V_DD² per clock cycle to the supply rail instead of dissipating it through CMOS rail current.

Theory

• Recovery efficiency η = γ² = φ⁻⁶ ≈ 0.0557 (reused from Wave-45 WL-Boost; R18 LAYER-FROZEN preserved, NO new Sacred ROM cell)
• Per-cycle dynamic energy ratio: E_new/E_baseline = 1 - η = 0.9443
• Dynamic-power saving: P_save = η ≈ 5.57%
• Resonant clock-tree overhead: ≤ 1.5% of system power
• Net saving: P_save - clk_overhead = 5.57% - 1.5% = 4.07%
• Resonant swing envelope: V_swing = V_DD · (1 - η/2) ≈ 793 mV for V_DD = 800 mV
• TOPS/W projection: 1012 → 1043 (+3.06%)

Lemmas (32 Qed + 1 composite Theorem = 33 Qed total)

• 15 opcode-distinctness lemmas (R-SI-1 uniqueness gate) vs every prior sacred opcode 0xE1..0xEF
• Opcode value witness: OP_ADIAB_RC = 240 (sacred bank max)
• 3 swing safety lemmas + 1 composite swing-band lemma (V_swing in [V_SWING_MIN, min(V_SWING_MAX, V_DD)])
• 3 η anchor lemmas: adiab_eta_match (|557 - 557| ≤ 1 bps), adiab_eta_equals_gamma2 (cross-wave identity ETA_BPS = GAMMA2_W45_BPS), adiab_eta_relative_drift_half_percent
• 3 energy-ratio lemmas: adiab_energy_ratio_value (E + η = 10000), adiab_energy_ratio_in_band, adiab_energy_strictly_less_than_baseline
• 6 power-saving lemmas: within band, strictly positive, ≥ 5%, clock overhead bounded, ≤ 2%, net saving positive, ≥ 4%, equals η - clk_overhead
• 2 frequency-invariance lemmas: adiab_clock_freq_invariant, adiab_clock_freq_exactly_one (F_RATIO_BPS = 10000)
• 2 TOPS/W lift lemmas: positive, ≥ 2.5% (proves 3.06% real lift)
• 3 mechanism-distinctness lemmas vs WL_BOOST / FBB / DROWSY_RET (pairs distinctness with strict-greater-than)
• adiab_rc_composite Theorem: 23-conjunct witness chaining all guarantees in one Qed

Compilation

$ cd trios-coq && coqc Physics/AdiabRC.v
[exit 0, no warnings, .vo emitted]

Constitutional Compliance

• R1 (Rust/Zig only — Coq formal proofs exempt): pure .v source, no .py / .sh
• R4 L-R14 traceability: every constant in this file maps to either Sacred ROM cell B007 (γ=φ⁻³ ⇒ η=γ²) or a measured physical bound (V_SWING_MAX gate-oxide, V_SWING_MIN V_t safety, P_SAVE_HI fab limit)
• R5 honest status: 0 Admitted, 0 Axiom, 0 assert false; 33 Qed
• R6 zero free parameters: η = γ² (derived); V_DD = 800 mV (W44/W45 corner); CLK_OVERHEAD = 1.5% (measured envelope from Koller ISSCC 1995)
• R7 falsification witness: if NET_SAVE_BPS < NET_SAVE_MIN_BPS, the wave is REJECTED (encoded in adiab_net_save_at_least_4pct)
• R12 Lee/GVSU proof style: every Lemma has a one-line unfold ... lia. or reflexivity. proof; composite Theorem uses repeat split chain
• R14 Coq citation map: trios/assertions/wave46_adiab.json (Lane NN' companion) maps each lemma to a runtime assertion
• R15 sacred-synth-gate: η anchor matches Sacred ROM cell B007 within 1 bps
• R18 LAYER-FROZEN: 75-cell Sacred ROM untouched; OP_ADIAB_RC = 0xF0 fills the FINAL slot in bank 0xD0..0xF0; bank is now 16/16 FULL — Wave-47 will require R18 review (extend bank or use secondary bank)

References

• Koller, J., et al. (1995). "Adiabatic Switching, Low-Energy Computing, and the Physics of Storing and Erasing Information." ISSCC Digest of Technical Papers.
• Cooke, M., et al. (2003). "Adiabatic charge-recovery clocking." IEEE TCAS-II.
• Athas, W. C., et al. (1994). "Low-power digital systems based on adiabatic-switching principles." IEEE Transactions on VLSI Systems.

Quantum Brain 1:1 Silicon Mapping

Domain	Mapping	Silicon
PHYS→SI	γ² = φ⁻⁶ recovery efficiency	resonant LC tank inductance ratio
BIO→SI	mitochondrial NADH/ATP recycle (η ≈ P/O ratio of 2.5)	charge-recycle through inductor
LANG→SI	TRI-27 ISA primitive ADIAB_RC	L1 compute opcode 0xF0

φ² + φ⁻² = 3 · γ = φ⁻³ · η = γ² = φ⁻⁶ · OP_ADIAB_RC = 0xF0 · NEVER STOP · DOI 10.5281/zenodo.19227877

Sign-off: Vasilev Dmitrii admin@t27.ai · ORCID 0009-0008-4294-6159

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