Title: Autoconsistency as an Organizing Principle: From qubit substrate to Standard Model via E₈ foam (v3.0)

This is version 3. 0 of the Autoconsistency as an Organizing Principle framework, a structural-derivational programme in fundamental physics. The framework articulates a single variational principle on a minimal qubit substrate (φ: ℳ → ℂP¹) whose stationary configurations form a definite chain C₃ → K₄ → cluster → 600-cell → 2I → E₈-roots → E₈-lattice → foam, with each transition realised as a quantum-field-theoretic instanton. The chain operationalises the framework's organising principle of maximal mutual determination: the structural relations among substrate, chain stages, and macroscopic content mutually constrain each other to a self-consistent configuration. Spacetime, gravity, matter, quantum mechanics, and Standard Model phenomenology emerge as derived consequences of the variational structure, rather than being separately postulated. Principal v3. 0 innovations relative to v2: The variational principle as foundational dynamics: many v2 distributed-proof claims collapse to Stratum-1 theorems via Noether's theorem and instanton spectroscopy. Chirality propagation as unified Noether theorem: a single primordial chirality bit χ generates ten distinct ℤ₂ phenomena across the chain, including the matter-antimatter asymmetry. The W (E₈) representation theory: rigorous GAP-verified identification of the foam vacuum with the irreducible V₁₁₂, with three Standard Model generations derived from its ℤ₃-eigenspace decomposition. Foam at percolation criticality: the framework's free parameter λ identified with the percolation critical density pc ≈ 1/163 on the E₈ foam graph, measured by direct Monte-Carlo simulation up to N = 1. 68 × 10⁶ vertices. Quantitative predictions verified against PDG 2024: Koide combination Q = 2/3 as a theorem of V₁₁₂'s ℤ₃ structure (empirical precision 10−5, framework saturates current measurement). Koide angle θ = 2/9 as algebraic invariant C₂ (3) / (2h∨) (compatibility at 0. 91σ). Charged lepton masses mμ, mτ predicted at 10−5–10−4 precision. Cosmological constant Λ ≈ 4. 67 × 10−123 (factor 2 from observed). Baryon asymmetry ηB ≈ 1. 84 × 10−9 (factor 3 from observed). SU (3) Isolation Identity: 1 − cos (arccos (1/N) ) = C₂ (N) /2 if and only if N ∈ 1, 3. Fritzsch relation sinθC ≈ √ (md/ms) at 1. 5% precision. Sector-precision hierarchy theorem articulating the structural precision ceiling for each Standard Model sector. Additional content: The framework is articulated in 7 Parts across 47 sections (137 pages): substrate foundations and variational principle (Part I) ; the chain stage-by-stage with chirality verification (Parts II–IV) ; Standard Model phenomenology including Koide, unified coupling, RG matching, quark/mirror/neutrino sectors and beyond-leptons extensions (Part V) ; relational ontology with physical themes including the Dirac equation from autoconsistency converging with Prandel's general-systems formulation, photons and wave-particle duality, extreme curvature with black-hole singularity resolution, the residuo principle and cyclic cosmology, golden-ratio phenomenology, and connections with related programmes including causal sets, loop quantum gravity, relational quantum mechanics (Rovelli), causal dynamical triangulations, tensor networks, twistor theory, non-commutative geometry, and asymptotic safety (Part VI) ; and a complete epistemic stratification with explicit open problems and falsification tests (Part VII). Status: This version is explicitly work-in-progress. The epistemic stratification (five strata: rigorous theorems, distributed proofs, structural articulations, open problems, predictive precision) classifies every claim with its current level of formal support. Two principal targets remain in the open roadmap: a category-theoretic formalisation of autoconsistency, and a complete dynamical articulation of the bounce action in SU (3) 1 Chern–Simons theory. Three formal-status targets enumerated in v2 have been closed in v3. 0 (Cartan A₂ unified articulation, stage-by-stage μn classification, ℤ₃-lattice gauge theory formal setup). Reproducibility: All computational results (the W (E₈) representation decomposition, the V₁₁₂ uniqueness theorem, and the percolation criticality estimate) are accompanied by reproducible scripts (GAP for representation theory, Python for percolation Monte-Carlo simulation), available as supplementary computational material. Keywords: fundamental physics; exceptional Lie algebras; E₈; foundations of quantum mechanics; relational ontology; emergent spacetime; Standard Model phenomenology; Koide relation; percolation criticality; autoconsistency; Prandel; cosmological constant; baryon asymmetry; foam models; variational principle.