Distinction Algebra: From Distinction to Quantum Mechanics, Gravity, and the Standard Model — v11.0

**Distinction Algebra v11. 0** An algebraic framework deriving the Standard Model and General Relativity from two axioms — Distinction (D) and Norm (N) — plus the Hurwitz / Cayley–Dickson chain ℝ ⊂ ℂ ⊂ ℍ ⊂ 𝕆, with G₂ = Aut (𝕆) as the gauge-content seed. **Core architecture. ** Each normed division algebra plays a forced physical role: - ℝ — classical measurement output - ℂ — quantum-mechanical scaffold (interference) - ℍ — spacetime (signature (1, 3) via H₂ (ℂ) Pauli identification) - 𝕆 — internal / gauge (SU (3) c via Stab₆䃒 (e₁) ; SU (2) L × U (1) Y from the residual G₂ structure) The Single-Scale Theorem reduces the framework to **1 dimensional input + 0 dimensionless inputs** generating ~50 catalogued observables. **Headline closed-form predictions. ** - **αEM⁻¹ = 137 = (|W (G₂) |−1) (|W (G₂) |+1) − h (G₂) ** A (closing relation in A integers; +0. 026 % with the residual closed by 1-loop QED VP at Q\* ≈ 3. 71 MeV) - **αₛ (MZ) = 3√3/44 = γPl²/11** A (Theorem G₂-SR: Callias-type index 8+3+0 = 11 + Killing-form equipartition on simple G₂; +0. 16 %) - **sin²θW = 3/13** B/structural (closing relation; −0. 19 %) - **Ngen = 3** A conditional on Axiom 3 from Hurwitz (1898) - **mH = mₜ / √2** ~1 % (PT λ=2 + IR fixed point) - **MPl structural formula**: ln (MPl/mₜ) = (3^ (3/4) /2) ·ΣSM ln (m₃/m₁) + NB·ln 7, −1. 8 % - **Λ = 27 · m_ν₁⁴** (cosmological lock, +0. 82 %) - **ΩDM / Ωb = 59/11** (−0. 013 % vs Planck 2026) - **Koide K = 2/3** at +0. 0009 % via Z₃ + CD equipartition - **δCKM = arctan √ (m₂/m₁) = 65. 905°** at +0. 008 % via 𝔽₂ rank counting + invariant-ring CP parity **Centerpiece (§17). ** The Λ⁴ (𝕆) integer bridge: **γPl² / αₛ = 11 = C (8, 4) · Ωb / Ωₘ** ties the QCD gauge coupling to the cosmological matter budget through pure integer arithmetic of 𝕆. **Visualisation. ** The Λ² (𝕆) panoramic chart organises the 28 SM+GR parameters as 4 concentric hexagons (28 = 4 × 6 + 4) over the SU (3) -stabiliser decomposition. **Methodology. ** All results carry an explicit tier label: A (algebraic theorem from D+N), A/identification (algebraic + named identification step), B/structural (one identification step beyond A), B/derived (derived from a B/structural identification), B/identification (multiple ranked alternatives selected by stated criteria), C/open. A retraction ledger (**67 LIVE / 12 decisive** triggers) commits the framework to falsifiable predictions tied to specific upcoming experiments (Hyper-K, DUNE, T2HK, LiteBIRD, HL-LHC, FCC, CMB-S4). **Reproducibility. ** 109 standalone Python scripts (numerical witnesses for every quantitative claim) ship alongside the paper. **Companion artefacts. ** - Full paper PDF + Markdown source - 1-page prediction sheet (PDF + Markdown) - 33-entry glossary - Λ² (𝕆) panoramic chart and 4-hexagon visualisation scripts - 109-script reproducer archive --- License: CC-BY 4. 0. ORCID: 0009-0005-0447-6748 (https: //orcid. org/0009-0005-0447-6748). Concept DOI: 10. 5281/zenodo. 19681810 (https: //doi. org/10. 5281/zenodo. 19681810). Supersedes v10 DOI 10. 5281/zenodo. 20069952 (https: //doi. org/10. 5281/zenodo. 20069952) (2026-05-07).