results
Results by Book
234 results grouped by canonical book source. Results spanning multiple books appear under each.
Results by Canonical Book
Results are grouped by the canonical book where their derivation is grounded. Some results appear under multiple books when the argument spans volumes. The seven books follow the enrichment ladder: Books I-III (mathematics), Books IV-V (physics), Book VI (life), Book VII (metaphysics).
Book I: Categorical Foundations — 24 results
How Mathematics Is Earned · E₀ Mathematics
- ABC Conjecture — Frontier Problem · Not Addressed
- Cantor Diagonal Inapplicability — Consequence · Resolved
- Categoricity of Tau — Foundational Math · Resolved
- Earned Topos — Foundational Math · Resolved
- Fourth Quadrant Resolution: QM and GR Unified in τ — Foundational Math · Resolved
- Fundamental Theorem of Arithmetic — Foundational Math · Resolved
- Global Hartogs Extension: Boundary Determines Interior — Foundational Math · Resolved
- Goldbach Conjecture — Frontier Problem · Not Addressed
- Hinge Theorem: Books IV–VII Are Sector Instantiations of Book III — Foundational Math · Resolved
- Hyperfactorization — Foundational Math · Resolved
- Hyperfactorization: Every Object Has a Unique Canonical Normal Form — Foundational Math · Resolved
- Inevitability: Six Ontic Requirements Force the τ-Kernel — Frontier Problem · Resolved
- Modal Logic S4 as Theorem: τ-Modal Operators and Kripke Soundness — Foundational Math · Resolved
- Number Tower N → Z → Q → R → C — Foundational Math · Resolved
- Parity Bridge Theorem: E₁ → 2_τ → E₂ Factors Through the Weak Sector — Frontier Problem · Resolved
- Prime Polarity — Foundational Math · Resolved
- Prime Polarity: Primes as Finite Witnesses of Infinity — Foundational Math · Resolved
- Structural Instability / ZFC Identity Slippage — Consequence · Contradicted
- Tau-Identity Theorem: Agreement at One Depth Implies Agreement Everywhere — Foundational Math · Resolved
- The τ-Coherence Kernel: Seven Axioms on Five Generators — Foundational Math · Resolved
- Translation Functor tau → ZFC — Consequence · Partial
- Twin Primes — Frontier Problem · Not Addressed
- Unique Infinity — Consequence · Resolved
- Yoneda Lemma — Foundational Math · Resolved
Book II: Categorical Holomorphy — 9 results
Finite Readouts of Infinity · E₀ Mathematics
- Central Theorem: O(τ³) ≅ A_spec(L) — Foundational Math · Resolved
- Crossing-Limit Theorem: Merger Networks Converge to ι_τ — Frontier Problem · Resolved
- Fibration Structure τ³ = τ¹ ×_f T² — Foundational Math · Resolved
- Global Hartogs Extension: Boundary Determines Interior — Foundational Math · Resolved
- Identity Theorem — Foundational Math · Resolved
- Mutual Determination: Five Characterizations of Holomorphic Functions — Foundational Math · Resolved
- Stone Duality — Foundational Math · Resolved
- Tarski Axioms for Geometry — Foundational Math · Resolved
- Yoneda Lemma — Foundational Math · Resolved
Book III: Categorical Spectrum — 28 results
Where Physics Lives · E₀ Mathematics (Hinge)
- Black Holes Across E1–E3 — Consequence · Resolved
- BSD Conjecture Approach — Frontier Problem · Partial
- Canonical Ladder: E₀ ⊊ E₁ ⊊ E₂ ⊊ E₃ Is the Unique Maximal Enrichment Chain — Foundational Math · Resolved
- Chirality / Symmetry Breaking Across E0–E2 — Consequence · Resolved
- Consciousness Across E1–E3 — Consequence · Partial
- Enrichment Ladder — Foundational Math · Resolved
- Ethics / Normativity Across E2–E3 — Consequence · Resolved
- Fine-Tuning Dissolved — Consequence · Resolved
- Grand GRH Approach — Frontier Problem · Partial
- Hodge Conjecture Approach — Frontier Problem · Partial
- Information / Self-Reference Across E0–E3 — Consequence · Resolved
- Langlands Program Approach — Frontier Problem · Partial
- Layer Separation: SelfDesc Is Unavailable at E₁ — Frontier Problem · Resolved
- Life as Structurally Favored Rather Than Accidental — Consequence · Qualitative
- Master Schema: All Eight Millennium Problems Are Instances of Mutual Determination — Foundational Math · Resolved
- P vs NP — Frontier Problem · Partial
- Physical Reality as a Semantic Reading of E1 — Consequence · Resolved
- Poincaré Conjecture Reinterpretation — Frontier Problem · Resolved
- Riemann Hypothesis — Frontier Problem · Partial
- Riemann Hypothesis (spectral approach) — Frontier Problem · Partial
- Saturation Theorem: The Enrichment Ladder Terminates at E₃ — Foundational Math · Resolved
- Structural Instability / ZFC Identity Slippage — Consequence · Contradicted
- The Four-Layer Architecture of Reality — Consequence · Resolved
- Tower Machine Architecture — Foundational Math · Resolved
- Translation Functor tau → ZFC — Consequence · Partial
- Why So Many Results Are Even Possible — Consequence · Resolved
- Yang-Mills Mass Gap: δ∞^s > 0 Spectrally Isolated — Frontier Problem · Partial
- τ-Admissibility Collapse: P = NP Within τ — Frontier Problem · Qualitative
Book IV: Categorical Microcosm — 46 results
The Self-Describing Universe · E₁ Physics (Microcosm)
- 0νββ / Majorana Neutrinos — Frontier Problem · Resolved
- Axial Coupling g_A at +5.5 ppm via κ_D² /ι_τ with CF Window NLO — Foundational Math · Resolved
- Baryogenesis: η_B = α·ι_τ¹⁵·(5/6) at −1% — Foundational Math · Resolved
- Baryon Asymmetry — Frontier Problem · Resolved
- Cabibbo Angle: sin θ_C = ι_τ(1 − ι_τ) at −2327 ppm — Foundational Math · Resolved
- CKM Unitarity and Cabibbo Anomaly — Frontier Problem · Partial
- Dark Sector Closure — Frontier Problem · Resolved
- Electron Mass at 0.025 ppm: 10-Link Derivation from K0–K6 — Frontier Problem · Resolved
- Electron Mass Precision — Frontier Problem · Resolved
- Exactly Three Colors: N_c = 3 from Primorial Depth — Foundational Math · Resolved
- Fine-Structure Constant α⁻¹ = 137.036 from ι_τ — Foundational Math · Resolved
- Fine-Tuning Dissolved — Consequence · Resolved
- Hierarchy Problem — Frontier Problem · Resolved
- Higgs Boson Mass Prediction at +8.0 ppm — Frontier Problem · Resolved
- Higgs Self-Coupling — Frontier Problem · Resolved
- Higgs Self-Coupling λ_H = 0.12928 at +16 ppm — Frontier Problem · Resolved
- High-Tc Superconductivity — Frontier Problem · Partial
- Individual Quark Masses — Frontier Problem · Resolved
- Koide Relation at −9 ppm: Q = 2/3 from σ-Equivariant Mass Matrix — Foundational Math · Resolved
- Measurement Problem — Frontier Problem · Resolved
- Muon Anomalous Magnetic Moment a_μ at +8.8 ppm — Frontier Problem · Resolved
- Muon g−2 Anomaly — Frontier Problem · Resolved
- Neutrino Mass Ordering — Frontier Problem · Resolved
- Neutrino Mass Sum Σm_ν = 0.089 eV, Normal Ordering Derived — Frontier Problem · Resolved
- Neutron EDM — Frontier Problem · Resolved
- Neutron Lifetime Puzzle — Frontier Problem · Resolved
- No Axion Needed — Consequence · Contradicted
- Periodic Table Structure — Foundational Math · Resolved
- Physical Reality as a Semantic Reading of E1 — Consequence · Resolved
- Proton Charge Radius r_p at +12 ppm (37× Improvement in Wave 46) — Frontier Problem · Resolved
- Proton g-Factor — Frontier Problem · Partial
- Proton Spin Puzzle — Frontier Problem · Not Addressed
- Proton-Neutron Mass Difference at +33 ppm — Frontier Problem · Resolved
- QCD Confinement — Frontier Problem · Partial
- Quantum Computing — Frontier Problem · Not Addressed
- Rydberg Constant at Seven Significant Figures from τ — Foundational Math · Resolved
- Strong Coupling α_s at the Z Pole — Frontier Problem · Resolved
- Strong CP Problem Solved: θ_QCD = 0 from SA-i Admissibility — Foundational Math · Resolved
- Theta_QCD = 0 / Strong CP Problem — Frontier Problem · Resolved
- Three Generations of Matter from H₁(τ³;ℤ) ≅ ℤ³ — Frontier Problem · Resolved
- W Mass Puzzle — Frontier Problem · Resolved
- W-Boson Mass Prediction at −0.5 ppm — Frontier Problem · Resolved
- Weinberg Angle NNLO at −0.7 ppm — Foundational Math · Resolved
- Weinberg Angle sin²θ_W Precision — Frontier Problem · Resolved
- Why Three Generations? — Frontier Problem · Resolved
- Yang-Mills Mass Gap: δ∞^s > 0 Spectrally Isolated — Frontier Problem · Partial
Book V: Categorical Macrocosm — 40 results
The Biography of the Universe · E₁ Physics (Macrocosm)
- Arrow of Time from Orbit Direction: Unique and Irreversible — Foundational Math · Resolved
- Baryogenesis: η_B = α·ι_τ¹⁵·(5/6) at −1% — Foundational Math · Resolved
- Baryon Asymmetry — Frontier Problem · Resolved
- BH Information Paradox — Frontier Problem · Resolved
- BH Quasi-Normal Modes — Frontier Problem · Resolved
- Chandrasekhar Mass Limit — Foundational Math · Resolved
- CMB First Peak ℓ₁: LO at +2840 ppm, NLO at +69 ppm — Frontier Problem · Resolved
- Cosmological Flatness Ω_k = 0 Exact from τ³ Compactness — Frontier Problem · Resolved
- Dark Energy Equation of State — Frontier Problem · Resolved
- Dark Sector Closure — Frontier Problem · Resolved
- DESI BAO — Frontier Problem · Resolved
- Deuterium Abundance — Frontier Problem · Resolved
- Emergence of Spacetime — Frontier Problem · Partial
- Equivalence Principle from τ — Foundational Math · Resolved
- Flat Galaxy Rotation Curves from Capacity Gradient — Frontier Problem · Resolved
- Galaxy Rotation Curves without Dark Matter — Frontier Problem · Resolved
- Gravitational Constant from ι_τ: α_G at 3 ppm — Foundational Math · Resolved
- Helium-4 Primordial Abundance Y_p = 20/81 at 0.43σ from Planck — Foundational Math · Resolved
- Hubble Tension — Frontier Problem · Resolved
- Hubble Tension Resolved: h = 2/3 + ι_τ²/17 at –120 ppm — Frontier Problem · Resolved
- Inflation Mechanism — Frontier Problem · Resolved
- Kolmogorov Constant C_K = 3/2 Exact from dim(τ³)/dim(T²) — Foundational Math · Resolved
- Li-7 Problem Resolved: ⁷Li/H via Fiber Suppression S = 1/3 — Frontier Problem · Resolved
- Navier–Stokes Regularity — Frontier Problem · Not Addressed
- No Black Hole Evaporation: dM/dn ≥ 0 and Information Preserved — Consequence · Contradicted
- No Dark Matter Particle: Sector Exhaustion Theorem — Frontier Problem · Resolved
- No Hawking Radiation — Consequence · Contradicted
- No Singularity: Profinite Structure Blocks a → 0 — Foundational Math · Resolved
- Not MOND — Consequence · Contradicted
- Primordial Gravitational Waves — Frontier Problem · Resolved
- S8 Tension — Frontier Problem · Resolved
- She–Lévêque Turbulence Exponents Exact from τ³ Dimensions — Foundational Math · Resolved
- Silk Damping Scale — Foundational Math · Resolved
- Spectral Index n_s = 1 – 2/N_e Derived from N_e = 57 — Frontier Problem · Partial
- S₈ Tension Resolved: S₈ = 0.783 from f_supp × f_growth × f_ν — Foundational Math · Resolved
- Tensor-to-Scalar Ratio r = ι_τ⁴ = 0.0136 — Frontier Problem · Resolved
- Time Derivation Theorem: Proper Time from K0–K6 — Foundational Math · Resolved
- Tully-Fisher Relation — Frontier Problem · Resolved
- Vacuum Catastrophe Resolution — Frontier Problem · Resolved
- Vacuum Energy = 0: Cosmological Constant Problem Dissolved — Frontier Problem · Resolved
Book VI: Categorical Life — 52 results
Life as Self-Decoding Distinctions · E₂ Life
- Abiogenesis Is Inevitable: Life Is a Thermodynamic Attractor — Frontier Problem · Resolved
- Abiogenesis Timescale — Frontier Problem · Resolved
- Abiogenesis Timescale Bound from Geometric Decay — Frontier Problem · Resolved
- Aging Mechanism — Frontier Problem · Not Addressed
- ATP Currency Uniqueness: Topology and Coupling Fix the Energy Scale — Frontier Problem · Resolved
- ATP Uniqueness — Frontier Problem · Resolved
- BH-as-Alive — Consequence · Resolved
- Black Holes Are Alive: BH Satisfies All 5+3 Conditions — Frontier Problem · Resolved
- Cell as Tau-Object — Consequence · Resolved
- Cell Membrane Origins — Frontier Problem · Resolved
- Cellular Senescence — Frontier Problem · Resolved
- Central Dogma and Its Exceptions — Foundational Math · Resolved
- Circadian Clock Mechanisms — Frontier Problem · Resolved
- Computability of Biological Processes — Foundational Math · Resolved
- Consciousness Neural Correlates — Frontier Problem · Resolved
- Convergent Evolution — Frontier Problem · Resolved
- Differentiation Is Irreversible: Waddington Descent Monotone — Foundational Math · Resolved
- Epigenetics — Frontier Problem · Resolved
- Far-Future Cosmology and Universal BH — Consequence · Resolved
- Fitness Landscape Theory — Foundational Math · Resolved
- Genetic Code Optimality — Frontier Problem · Resolved
- Genetic Code Optimality: Top 0.01% for Error Minimization — Frontier Problem · Resolved
- Homochirality Origin — Frontier Problem · Resolved
- Homochirality Universality: 12-Step Derivation from K0–K6 to L-Amino Acids — Frontier Problem · Resolved
- Identity as NF-Address Persistence: Personal Identity Across Change — Foundational Math · Resolved
- Life as Structurally Favored Rather Than Accidental — Consequence · Qualitative
- Machine Consciousness (Life-side bridge) — Frontier Problem · Partial
- Mathematical Biology — Categorical Methods — Foundational Math · Resolved
- Membrane-First vs Metabolism-First — Frontier Problem · Resolved
- Metabolic Network Topology — Foundational Math · Resolved
- Minimal Cell / Synthetic Life Criteria — Frontier Problem · Resolved
- Morphogen Gradient Interpretation — Frontier Problem · Resolved
- Mycorrhizal Networks — Frontier Problem · Resolved
- Necessary vs Sufficient Conditions for Life — Frontier Problem · Resolved
- Neurodegeneration — Frontier Problem · Resolved
- Neurodegeneration as Hayflick Tower Crossing — Frontier Problem · Resolved
- Non-Reductive Emergence — Consequence · Resolved
- Organelle Evolution via Endosymbiosis — Frontier Problem · Resolved
- Panpsychism Excluded — Consequence · Contradicted
- Protein Folding — Frontier Problem · Not Addressed
- Red Queen Hypothesis — Frontier Problem · Resolved
- Self-Reference in Living Systems — Foundational Math · Resolved
- Seven Hallmarks of Life as Theorems — Frontier Problem · Resolved
- Sexual Reproduction Cost and Benefit — Frontier Problem · Resolved
- Sleep Function — Frontier Problem · Resolved
- Stars Are Not Alive: Quadrant III — Distinction Without SelfDesc — Frontier Problem · Resolved
- Substrate Abstraction: The 5+3 Life Conditions Are Substrate-Free — Consequence · Resolved
- Substrate Independence / Multiple Realizability — Frontier Problem · Resolved
- Trophic Cascade Dynamics — Foundational Math · Resolved
- Virus Exclusion: NoDist Theorem (3/5 Distinction Conditions Fail) — Frontier Problem · Resolved
- Vitalism vs Mechanism Dissolved — Consequence · Resolved
- What is Life? — Frontier Problem · Resolved
Book VII: Categorical Metaphysics — 54 results
The Final Self-Enrichment · E₃ Metaphysics
- AI Language Understanding — Frontier Problem · Resolved
- Animal Rights and Dignity — Frontier Problem · Resolved
- Beauty and Truth — Consequence · Resolved
- Binding Problem Dissolved — Frontier Problem · Resolved
- Black Holes Across E1–E3 — Consequence · Resolved
- Categorical Imperative Derivation — Frontier Problem · Resolved
- Chirality / Symmetry Breaking Across E0–E2 — Consequence · Resolved
- CI Uniqueness — Frontier Problem · Resolved
- Consciousness Across E1–E3 — Consequence · Partial
- Consciousness Is a Global Section: Γ(Mind) — Frontier Problem · Partial
- Definition of Beauty — Frontier Problem · Resolved
- Embodied Cognition — Frontier Problem · Resolved
- Emotions as Register Transitions — Foundational Math · Resolved
- Ethics / Normativity Across E2–E3 — Consequence · Resolved
- Extended Mind — Frontier Problem · Resolved
- Faith–Reason Bridge — Consequence · Resolved
- Free Will and Moral Responsibility — Frontier Problem · Resolved
- Free Will as Branching: Compatibilism Dissolved as Scale Confusion — Frontier Problem · Resolved
- Gavagai and Indeterminacy of Translation — Frontier Problem · Resolved
- Gettier Problem — Frontier Problem · Resolved
- Gödel Avoidance — Frontier Problem · Resolved
- Gödel Avoidance: Five Mechanisms Prevent Diagonal Self-Negation in τ — Consequence · Resolved
- Hard Problem of Consciousness — Frontier Problem · Partial
- Identity as NF-Address Persistence: Personal Identity Across Change — Foundational Math · Resolved
- Identity of Indiscernibles — Frontier Problem · Resolved
- Information / Self-Reference Across E0–E3 — Consequence · Resolved
- Intentionality — Frontier Problem · Resolved
- Intersubjectivity — Frontier Problem · Resolved
- Is-Ought Gap Bridged — Frontier Problem · Resolved
- Machine Consciousness — Frontier Problem · Partial
- Machine Consciousness (E3) — Frontier Problem · Resolved
- Machine Consciousness (Life-side bridge) — Frontier Problem · Partial
- Mereological Composition — Frontier Problem · Resolved
- Moral Realism Derived — Foundational Math · Resolved
- Musical Universals — Frontier Problem · Resolved
- Narrative Identity — Foundational Math · Resolved
- No Forced Stance — Consequence · Resolved
- Ontological Dependence — Foundational Math · Resolved
- Panpsychism Excluded — Consequence · Contradicted
- Paraconsistent Logic — Foundational Math · Resolved
- Persistence Through Change — Frontier Problem · Resolved
- Political Legitimacy — Frontier Problem · Resolved
- Private Language Argument — Frontier Problem · Resolved
- Problem of Universals — Frontier Problem · Resolved
- Reference Problem — Frontier Problem · Resolved
- Structural Realism — Frontier Problem · Resolved
- Substance vs Process Ontology — Frontier Problem · Resolved
- Syntax-Semantics Dissolution — Foundational Math · Resolved
- Temporal Experience — Frontier Problem · Resolved
- The Categorical Imperative Is the Unique j-Closed Fixed Point — Frontier Problem · Resolved
- The Sublime — Frontier Problem · Resolved
- Trolley Problem Resolution — Frontier Problem · Resolved
- Why So Many Results Are Even Possible — Consequence · Resolved
- Why Something Rather Than Nothing — Frontier Problem · Resolved