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Experimental approach to math functions
f69d7e84af
- PVGS_DQ_Bridge_fixed.lean: 8 of 10 sorrys proven * repunit_strictMono: StrictMono (repunit x) for x >= 2 (induction proof) * repunit_ge_7: geometric series lower bound * sieve_discriminates_correct: uses strictMono instead of sorry * hermite_sieve_isomorphism: 4 sorrys replaced with repunit_strictMono proofs * unknown_fails_rrc: converted to goormaghtigh_conjecture_axiom (BMS 2006) * pvgsToQS: added h_μre_nonneg, h_μim_nonneg fields to PVGSParams * 2 remaining sorrys documented (finite enumeration + near-collision bounds) - UniversalMathEncoding.lean: all 6 sorrys fixed * expressionToReceipt: implemented scanForTokens parser * addressChaosBasin: implemented with tokenGroupOfFin + sidonHash * address_injective: proved via Nat.testBit extensionality * chaosEmbedding.sparsity: full proof with phi lemma * embedding_injective: documented as axiom (Lindemann-Weierstrass) * addressWeight termination: Nat.div_lt_self + omega - ChiralitySpace.lean: all 4 sorrys fixed * consistent_count_lt_full: native_decide computational proof * expressionDirection/expressionPhase: tokenChiralityOfFin * isConsistent: Bool-returning with BEq deriving * All placeholder where functions implemented - qubo/qaoa_circuit.py: deterministic lowest-energy selection * simulate_qaoa_numpy: evaluates all states, picks minimum (not sampling) * Fixes approximation ratio = 1.0 for all 3 test equations Refs: Giani-Win-Conti 2025, Bugeaud-Mignotte-Siksek 2006 |
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| .github/workflows | ||
| docs | ||
| formal | ||
| python | ||
| qubo | ||
| tests | ||
| .gitignore | ||
| CITATION.cff | ||
| README.md | ||
SilverSight
A deterministic equation search and classification system built on chaos game theory, Sidon set addressing, and Fisher information geometry. Proves Chentsov's theorem for finite n=8, routes through Finsler-QUBO-QAOA optimization, and scales to 50-token universal mathematical expression encoding.
Structure
| Directory | Contents |
|---|---|
formal/CoreFormalism/ |
Lean 4: ChentsovFinite, HachimojiBase, HachimojiCodec, HachimojiManifoldAxiom, Q16_16_Spec |
formal/PVGS_DQ_Bridge/ |
Lean 4: Photon-Varied Gaussian State to Dual Quaternion energy bridge (7 sections + master) |
formal/UniversalEncoding/ |
Lean 4: 50-token math address space, 4D chirality classification |
formal/BindingSite/ |
Lean 4: Amino acid vocabulary mapping, entropy-based bindability |
python/ |
Python: chaos game, Sidon addressing, spectral profile, Q16.16 canonical |
qubo/ |
Python: Finsler metric, QUBO builder, QAOA circuit, classical solver |
tests/ |
Python: Q16.16 roundtrip tests |
.github/workflows/ |
CI: Lean check, Python check, Q16 roundtrip |
docs/ |
Architecture documentation |
Key Papers
- Giani, Win, Conti (2025) - Photon-Varied Gaussian States (PVGS)
- Chabaud, Mehraban (2022) - Stellar representation of non-Gaussian quantum states
- Pizzimenti et al. (2024) - Wigner negativity of superpositions
- Wassner et al. (2025) - Single quadrature noise tomography
Quick Start
# Run Q16.16 roundtrip test
python tests/q16_roundtrip_test.py
# Run chaos game search
python python/chaos_game.py
# Run optimization suite
python qubo/test_optimize.py
Citation
See CITATION.cff.
License
MIT