Results · Topic
Mathematics Results
76 results engaging the mathematics problem-space.
Mathematics
76 results across foundations, number theory, analysis, topology, and category theory. The mathematical results form the layer of the framework – the coherence kernel, the Central Theorem, and the enrichment ladder from which all downstream physics, biology, and metaphysics are derived. Highlights include the Hyperfactorization Theorem (first hinge), the Prime Polarity Theorem (geometry earned from arithmetic), and approaches to several Millennium Problems.
Status: 60 Resolved, 10 Partial, 1 Qualitative, 2 Contradicted, 3 Not Addressed.
Results
- ABC Conjecture — Not Addressed
- Arrow of Time from Orbit Direction: Unique and Irreversible — Resolved
- Axial Coupling g_A at +5.5 ppm via κ_D² /ι_τ with CF Window NLO — Resolved
- Baryogenesis: η_B = α·ι_τ¹⁵·(5/6) at −1% — Resolved
- Black Holes Across E1–E3 — Resolved
- BSD Conjecture Approach — Partial
- Cabibbo Angle: sin θ_C = ι_τ(1 − ι_τ) at −2327 ppm — Resolved
- Canonical Ladder: E₀ ⊊ E₁ ⊊ E₂ ⊊ E₃ Is the Unique Maximal Enrichment Chain — Resolved
- Cantor Diagonal Inapplicability — Resolved
- Categoricity of Tau — Resolved
- Central Theorem: O(τ³) ≅ A_spec(L) — Resolved
- Chirality / Symmetry Breaking Across E0–E2 — Resolved
- Consciousness Across E1–E3 — Partial
- Differentiation Is Irreversible: Waddington Descent Monotone — Resolved
- Earned Topos — Resolved
- Enrichment Ladder — Resolved
- Ethics / Normativity Across E2–E3 — Resolved
- Exactly Three Colors: N_c = 3 from Primorial Depth — Resolved
- Fibration Structure τ³ = τ¹ ×_f T² — Resolved
- Fine-Structure Constant α⁻¹ = 137.036 from ι_τ — Resolved
- Fourth Quadrant Resolution: QM and GR Unified in τ — Resolved
- Fundamental Theorem of Arithmetic — Resolved
- Global Hartogs Extension: Boundary Determines Interior — Resolved
- Goldbach Conjecture — Not Addressed
- Grand GRH Approach — Partial
- Gravitational Constant from ι_τ: α_G at 3 ppm — Resolved
- Gödel Avoidance: Five Mechanisms Prevent Diagonal Self-Negation in τ — Resolved
- Helium-4 Primordial Abundance Y_p = 20/81 at 0.43σ from Planck — Resolved
- Hinge Theorem: Books IV–VII Are Sector Instantiations of Book III — Resolved
- Hodge Conjecture Approach — Partial
- Hubble Tension Resolved: h = 2/3 + ι_τ²/17 at –120 ppm — Resolved
- Hyperfactorization — Resolved
- Hyperfactorization: Every Object Has a Unique Canonical Normal Form — Resolved
- Identity as NF-Address Persistence: Personal Identity Across Change — Resolved
- Identity Theorem — Resolved
- Information / Self-Reference Across E0–E3 — Resolved
- Koide Relation at −9 ppm: Q = 2/3 from σ-Equivariant Mass Matrix — Resolved
- Kolmogorov Constant C_K = 3/2 Exact from dim(τ³)/dim(T²) — Resolved
- Langlands Program Approach — Partial
- Master Schema: All Eight Millennium Problems Are Instances of Mutual Determination — Resolved
- Modal Logic S4 as Theorem: τ-Modal Operators and Kripke Soundness — Resolved
- Muon Anomalous Magnetic Moment a_μ at +8.8 ppm — Resolved
- Mutual Determination: Five Characterizations of Holomorphic Functions — Resolved
- Neutrino Mass Sum Σm_ν = 0.089 eV, Normal Ordering Derived — Resolved
- No Black Hole Evaporation: dM/dn ≥ 0 and Information Preserved — Contradicted
- No Singularity: Profinite Structure Blocks a → 0 — Resolved
- Number Tower N → Z → Q → R → C — Resolved
- P vs NP — Partial
- Poincaré Conjecture Reinterpretation — Resolved
- Prime Polarity — Resolved
- Prime Polarity: Primes as Finite Witnesses of Infinity — Resolved
- Proton Charge Radius r_p at +12 ppm (37× Improvement in Wave 46) — Resolved
- Riemann Hypothesis — Partial
- Riemann Hypothesis (spectral approach) — Partial
- Rydberg Constant at Seven Significant Figures from τ — Resolved
- Saturation Theorem: The Enrichment Ladder Terminates at E₃ — Resolved
- She–Lévêque Turbulence Exponents Exact from τ³ Dimensions — Resolved
- Stone Duality — Resolved
- Strong CP Problem Solved: θ_QCD = 0 from SA-i Admissibility — Resolved
- Structural Instability / ZFC Identity Slippage — Contradicted
- S₈ Tension Resolved: S₈ = 0.783 from f_supp × f_growth × f_ν — Resolved
- Tarski Axioms for Geometry — Resolved
- Tau-Identity Theorem: Agreement at One Depth Implies Agreement Everywhere — Resolved
- The τ-Coherence Kernel: Seven Axioms on Five Generators — Resolved
- Three Generations of Matter from H₁(τ³;ℤ) ≅ ℤ³ — Resolved
- Time Derivation Theorem: Proper Time from K0–K6 — Resolved
- Tower Machine Architecture — Resolved
- Translation Functor tau → ZFC — Partial
- Twin Primes — Not Addressed
- Unique Infinity — Resolved
- W-Boson Mass Prediction at −0.5 ppm — Resolved
- Weinberg Angle NNLO at −0.7 ppm — Resolved
- Why So Many Results Are Even Possible — Resolved
- Yang-Mills Mass Gap: δ∞^s > 0 Spectrally Isolated — Partial
- Yoneda Lemma — Resolved
- τ-Admissibility Collapse: P = NP Within τ — Qualitative