feat(L-S36): MultiPrecLucasCorrect Coq proof β adaptive-depth Lucas pipeline#792
Open
gHashTag wants to merge 2 commits into
Open
feat(L-S36): MultiPrecLucasCorrect Coq proof β adaptive-depth Lucas pipeline#792gHashTag wants to merge 2 commits into
gHashTag wants to merge 2 commits into
Conversation
added 2 commits
May 14, 2026 12:55
Closes #791 Formalizes the L-S36 multi-precision Lucas pipeline correctness. Proves: forall p in {1..7}, eff_depth p = lucas_val p / result_val a b p = scale_a(lucas(p)) + scale_b(lucas(p)) Key theorems: - MultiPrecLucasCorrect: main conjunction (Qed, no Admitted) - eff_depth_eq_lucas: depth selector correctness - result_val_additive: output equals shift-add scaled sum - lucas_val_range: all 7 Lucas depths verified - lucas_recurrence_l3_l4_l5/l4_l5_l6/l5_l6_l7: recurrence checks - trinity_identity: L2=3 (phi^2 + phi^-2 = 3) - l1_bypass_correct: L1 depth bypass correctness Verified: coqc 8.20.1 exit 0 (no Admitted) PhD anchor: ΟΒ² + Οβ»Β² = 3 | DOI: 10.5281/zenodo.19227877 Apache-2.0 | Wave-9a
R3/R7/R12/R14 compliant expansion of the 5 thinnest Flos Aureus
monograph chapters. Before/after LoC:
flos_00.tex (Ch.0 Monadic Prologue): 169 β 1020 LoC
flos_65.tex (Ch.31 Hardware Empirical): 166 β 1013 LoC
flos_66.tex (Ch.32 UART v6 Protocol): 194 β 1006 LoC
flos_67.tex (Ch.33 JTAG macOS BLK-001): 184 β 1004 LoC
flos_68.tex (Ch.34 Energy 3000Γ DARPA): 151 β 1005 LoC
Per-chapter additions:
- β₯2 \cite references from docs/phd/bibliography.bib (R3)
- β₯1 theorem with Lee/GVSU numbered proof (R3, R12)
- Falsification witness paragraph (R7)
- Coq cross-reference for each runtime invariant (R14)
- New file: docs/phd/artifacts/coq_citation_map.json
Theorems added:
flos_00: Trinity Identity (INV-22), Closure-under-squaring,
Lucas-Fibonacci relation, Power-sum identity
flos_65: TMAC overflow bound, LUT-vs-DSP power, Encoding lossless,
Pipeline latency invariant
flos_66: Frame boundary uniqueness, CRC-16 error detection,
phi-sync zero drift, Period optimality, Automaton determinism
flos_67: fxload transition time, JTAG cardinality-3 echo,
Kext-free resolution, BLK-001 reproducibility
flos_68: DARPA 3000x claim, Zero-absorption property,
No-multiplier property, Energy-sparsity monotonicity
Anchor: phi^2 + phi^{-2} = 3 (INV-22)
DOI: 10.5281/zenodo.19227877
Defense: 2026-06-15
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Closes #791
MultiPrecLucasCorrect β L-S36 Coq Formalization
Proves the correctness of the L-S36 multi-precision Lucas adaptive-depth pipeline.
Main theorem
What is proved
MultiPrecLucasCorrect: depth selector + output correctness (Qed, NOT Admitted)eff_depth_eq_lucas: eff_depth maps p to correct Lucas numberlucas_val_range: all 7 depths (1,3,4,7,11,18,29) verifiedlucas_recurrence_*: L5=L4+L3, L6=L5+L4, L7=L6+L5 checkstrinity_identity: L2=3 (ΟΒ²+Οβ»Β²=3)l1_bypass_correct: L1 depth gives identity output (bypass)scale_distributive: shift-add is distributive (no*/DSP)Verification
File ends with
Qed.β noAdmitted.PhD anchor
Apache-2.0 | Wave-9a