Maximal Mutual Determination: from Qubit Substrate to the Standard Model via E8 Foam

This paper articulates a research programme in fundamental physics: that the entire content of physics — spacetime, quantum mechanics, gravity, matter, and the Standard Model — can be derived as structural consequences of a single variational principle on a minimal qubit substrate, rather than separately postulated. The framework is a continuous-qubit-field action Sφ with φ: M → CP¹ on a smooth substrate manifold, whose stationary configurations form a definite chain of nine categorial stages from the symmetric vacuum φ0 to the foam — the terminal asymptotic equilibrium that supports Standard Model phenomenology and the gravitational sector. v5. 0 structural milestones (relative to v4. 0): Stratum-1 bridge programme. Eight new theorems, one lemma, one conjecture articulating all six bridge claims (emergent exact Lorentz invariance, exact SM gauge invariance, unitarity, locality, correct spectrum of masses and mixings, and effective Einstein–Hilbert gravity) at Stratum 2 conditional or better, with a joint promotion path through high-statistics partial-order-tracking simulation. BPS-rigorous derivation. The bond-bias structural parameter εstructBPS = 1/4 derived at Stratum 1 from E8 simply-lacedness; refined empirical εmacro = 0. 1622 ± 0. 0031 (7, 680 trials at L ∈ 16, 24, 32) ; rejection at 5. 3σ of the renormalisation-group-flow interpretation in favour of the kinematic 2/3 projection from chain triality. Foam continuum limit. The 4D macroscopic Lorentzian spacetime articulated within the Bombelli–Lee–Meyer–Sorkin causal-sets framework via cut-and-project from the 8D E8 lattice to the chain's D4 base. Dark energy two-component decomposition. Structural prediction ΩΛ = ΩΛ (s) + ΩΛ (c) with observable signatures in parity-odd CMB correlations and gravitational-wave polarisation. Numerical verification of the 3-fold merger pattern. 53, 611 combined events at L ∈ 6, 8, confirming the 1/4 unanimous / 3/4 split prediction at z = −0. 39σ. Single-foam reframing of the Z/2 substrate symmetry, with the gravitational cluster integrity theorem and the t0 encounter mechanism articulating dark matter as the gravitationally integral but electromagnetically invisible opposite-time-direction sector of the same percolating foam. Structural reorganisation of the text for reading fluency: introductory part streamlined to its essential overview function, contents redistributed across the eight Parts to follow the natural progression of the framework's articulation, sections renumbered, narrative thread tightened. Key quantitative predictions preserved from v3. 0/v4. 0: the Koide combination Q = 2/3 at unconditional Stratum 1; charged lepton mass predictions to 10−5 precision; the unified coupling α−1E8 ≈ 25. 4; the cosmological constant Λ ≈ 4. 17 × 10−123 (factor 2. 7 from observed) ; the baryon asymmetry ηB ≈ 5. 97 × 10−10 from the cosmological 3-fold merger algebra (0. 56% match to observed under the conjectured geometric correction). Epistemic stratification. Every claim in the framework is explicitly classified across five strata, from Stratum 1 (rigorous theorem) to Stratum 5 (programmatic target), with falsification tests articulated for each prediction. The work-in-progress character is preserved through this explicit stratification: the reader can distinguish rigorously-derived results from structural articulations and open commitments. The paper is articulated in 8 Parts with 56 theorems, 10 lemmas, 17 propositions, 17 corollaries, 7 conjectures, 3 foundational axioms, 16 definitions, 93 remarks, and 145 bibliographic references across 285 pages. Public release trajectory: v2 → v2. 1 → v3. 0 → v4. 0 → v5. 0 (this release). The foundational commitments — substrate ontology, variational principle, chain of stages, chirality propagation, V112 vacuum identification, PMMD as organising principle — are unchanged across all releases; the Koide derivations, charged lepton mass predictions, the unified coupling, and the cosmological constant are preserved from v3. 0/v4. 0. Earlier release notes are documented in the corresponding Zenodo archive entries.