Canon v27.0: Ontological Resolution Theory The Architecture of Executable Reality — Complete Axiomatic and Theorem Reference

Canon v27.0 is the complete reference document of Ontological Resolution Theory (ORT). It presents the full axiomatic framework, all theorems with status labels (Exact / Explicit / Ansatz / Open), the master status table, the publication index, and the current list of open problems. All artistic and motivational text has been removed. Only structural content remains. Key achievements in Canon v27.0 Open Problem L14 closed (Paper M v5.0): Zgeom = π⁴ + 4π² + (π−3) + 1/144 fully derived from D₄ triality. All four sectors Explicit. Zero free parameters. Open Problem L11 closed (Paper S v2.1): The imaginary unit i is the unique canonical automorphism realizing ℤ₂ monodromy of ℝP³. Derived via Frobenius theorem. Not introduced as convention. Paper Zero v1.2: Three new Exact theorems closing implicit gaps: polynomial class (Occam's Razor), normalization c=1 (executability), linearity from self-application. R(τ) = 9 from three independent geometric paths: FCC geometry (k−d=9), jet tower monotonicity, and Bifurcation Identity (Ngluon+(4−d)=8+1=9). Geo-bit unit system: complete lepton hierarchy in dimensionless units with zero free parameters within ORT. One SI anchor required for translation to GeV. Axiom 0 formalized: The observer cannot contain the observed. Iobs/Isystem = 4/137 ≈ 3% per tick. Structure Foundational Principles (three-level hierarchy, status labels) Axioms (Axiom 0 through Axiom 6) Source Algebra (Theorems Z.1–Z.3, balance equation, jet tower, ℤ₂ symmetry, origin of i, dimensional guards, Euler–Distinction Identity) Carrier Geometry (Perelman → S³ → 600-cell → k=12 → FCC; executability d=3; landscape collapse; Fibonacci Lock; D₄ triality; complete projection tensor; gravity; black holes; special relativity) Master Status Table (all results) Particle Ontology (dictionary, neutrino commit protocol) Lepton Mass Hierarchy (rank bounds, bifurcation identity, Geo-bit system, sieve invariance) Strong Sector (gluon count, αs) Cosmology (dark matter, dark energy, QM reinterpreted, consensus reality) Open Problems (16 open, 2 closed this version) Publication Index (18 papers) Mnemonic Chain (complete derivation in 16 steps) Master Status Summary Category Count Exact results 18 Explicit results 24 Ansatz 4 Open problems 16 Closed this version 2 (L11, L14) Selected Exact Results Result Status g(r) = r(1−r) polynomial class (Occam's Razor) Exact Normalization c=1 from D=5 executability Exact Linearity 1−2r=g(r) from self-application r=x² Exact Balance equation r²−3r+1=0, D=5, φ Exact Jet tower g'''≡0: exactly 3 non-zero levels Exact ℤ₂ symmetry → Möbius monodromy Exact Physical boundary = S³ (Perelman) Exact k(600-cell) = 12 (direct count) Exact d=3 unique (executability criterion) Exact D₄ unique triality (Cartan 1925) Exact No fourth generation (double Exact: jet tower + D₄ triality) Exact × 2 Rmin = 1 (vacuum argument) Exact Branching rules SO(8) ⊃ SU(4) × U(1) (Slansky 1981) Exact Selected Explicit Results Result Status P(8v) = π⁴ (τ sector, ℤ₂ joint measure) Explicit P(8s) = 4π² (μ sector, Law of Pair on S³) Explicit P(8c) = π−3 (e sector, Chiral Residual Gap, L14 closed) Explicit Zgeom = 137.036 (4/4 sectors) Explicit i from ℝP³ + Frobenius theorem (L11 closed) Explicit Spin-½ from ℝP³ monodromy Explicit 600-cell → FCC (D₄ → A₃) Explicit Rmax = k−d = 9 Explicit R(e)=R(μ)=1, R(τ)=9 (three paths) Explicit Bifurcation Identity: R(τ) = Ngluon+(4−d) = 9 Explicit Fibonacci Lock: F₁₂ = k² = 144 Explicit Kcell = 133 bits/node Explicit RS = 2M (Zgeom cancels) Explicit BH entropy 1/4 from 4D projection Explicit E²=p²c²+m²c⁴ from lattice dynamics Explicit Ngluon = k−4 = 8 Explicit αs = 16/Zgeom ≈ 0.1168 (99% accuracy) Explicit Ωreal = {5} (landscape collapse) Explicit VEV = 133 Geo-bit Exact (ORT) mτ = 9/Zgeom Geo-bit Explicit Dark matter ratio = (k−1)/2 = 5.5 (exp: 5.4) Explicit Lorentz invariance from second-order dynamics Explicit Open Problems ID Problem Status M-1 VEV from first principles without lepton masses as input Open M-2 Uniqueness of cascade operators 4φ³ and 12×2πe Open M-3 Source-exact existence tax from g(r*) = φ⁻³ Open M-5 Geometric proof R(e)=R(μ)=1 from Oh orbits Open S-1 Source-exact derivation of ℝP³ topology Open S-2 Source-exact exclusion of quaternions ℍ Open TVR-1 Qcrit from ORT first principles Open L1 Absolute neutrino masses Open L2 PMNS matrix Open L3 Cosmological constant Λ Open L6 Weinberg angle θW Open L7 CKM matrix Open N-1 Exact η in Lorentz violation at Planck scale Open L11 Origin of imaginary unit i CLOSED (Paper S v2.1) L14 Chiral Residual Gap P(8c)=π−3 CLOSED (Paper M v5.0) Publication Index Paper Title Paper Zero v1.2 The Minimal Distinction Problem Paper A v9.1 The Golden Impedance Paper B v2.0 Charged Lepton Ratio Cascade Paper ED v1.0 The Euler–Distinction Identity Paper G v1.2 The Information Bottleneck Paper H v2.0 The Holographic Sieve Paper I v1.0 The Inverse Cascade / VEV Paper J v1.0 Theory of Finite Resolution Observer Paper M v5.0 Mass from Closure Paper N v1.0 The Emergent Interval Paper Phase v2.0 The Phase Transition Theorem Paper Q v2.1 Executability, FCC Geometry, Strong Coupling Paper S v2.1 ℤ₂ Symmetry, Spin, Origin of i Paper T v1.0 The Hawking Fluctuation Paper U v1.0 Global Executable Uniqueness Research Note RN-01 Particle Ontology and TVR Bridge TVR v10.2 Topological Vortex Reactor Canon v27.0 Complete Reference (this document) External Theorems Used Perelman (2002–2003): Poincaré conjecture Hales (2005): Kepler conjecture Cartan (1925): D₄ triality Slansky (1981): Branching rules SO(8) ⊃ SU(4) × U(1) Frobenius (1877): Division algebras over ℝ Cohn (1964): Square Fibonacci numbers Schütte & van der Waerden (1953): Kissing number in 3D Lindemann (1882): Transcendence of π Hermite (1873): Transcendence of e