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 StabG₂(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.** - **α_EM⁻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) - **α_s(M_Z) = 3√3/44 = γ_Pl²/11** [A] (Theorem G₂-SR: Callias-type index 8+3+0 = 11 + Killing-form equipartition on simple G₂; +0.16 %) - **sin²θ_W = 3/13** [B/structural] (closing relation; −0.19 %) - **N_gen = 3** [A conditional on Axiom 3] from Hurwitz (1898) - **m_H = m_t / √2** ~1 % (PT λ=2 + IR fixed point) - **M_Pl structural formula**: ln(M_Pl/m_t) = (3^(3/4)/2)·[Σ_SM ln(m₃/m₁) + N_B·ln 7], −1.8 % - **Λ = 27 · m_ν₁⁴** (cosmological lock, +0.82 %) - **Ω_DM / Ω_b = 59/11** (−0.013 % vs Planck 2026) - **Koide K = 2/3** at +0.0009 % via Z₃ + CD equipartition - **δ_CKM = arctan √(m_2/m_1) = 65.905°** at +0.008 % via 𝔽₂ rank counting + invariant-ring CP parity **Centerpiece (§17).** The Λ⁴(𝕆) integer bridge: **γ_Pl² / α_s = 11 = C(8,4) · Ω_b / Ω_m** 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).