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

Version 7.0 of a framework that articulates a programme of structural derivation: the content of physics—spacetime, quantum mechanics, gravity, matter, and the Standard Model—is to emerge as derived consequences of a single organising principle, maximal mutual determination, applied to a minimal qubit system, rather than being separately postulated. This version refines and improves on earlier ones (v2, v2.1, v3.0, v4.0, v5.0, v5.1, v5.2, and v6.0; all on Zenodo). Its principal departure from v6.0 is that the discrete relational action is made operative—with stationarity δS = 0 as the working principle—and the flavour sector is closed through it: the full quark mixing from the electroweak gateway with every input derived at leading order, the neutrino oscillation sector at zero parameters from derived constants, the colour-flux census laws measured on 1.46×1010 lattice loops, and three exact flavour–gauge bridges, all recorded under an explicit adjudication ledger (forty-four falsification tests, eleven self-inflicted). The framework carries no free continuous parameter at the foundational level (sector-level effective models may carry measured coordinates, each recorded with its epistemic status and its named decider). Framework summary The framework articulates physics as the structural unfolding of a single organising principle—maximal mutual determination—on a closed, minimal qubit system, with dynamics given by a discrete relational action on nodes, edges, and triangular faces (no manifold, no metric, no integral, and no fields: the perpendicular “phason” content is a per-facet share of each relation, and the familiar fields are the continuum shadows of relation densities). The system’s stationary patterns form a chain of progressive stages, generated by stochastic vertex-by-vertex margin growth from the primordial C3 and terminating at percolation criticality on the E8 foam: C3 → K4 → cluster → 600-cell → 2I → E8-roots → E8-lattice → foam, with derivation rather than postulation at each step. The continuum description (a configuration φ: M → CP1 with action S[φ]) is recovered as an emergent limit, and the Standard Model is recognised as the framework’s continuum shadow, with universality supplying the flow coefficients in the continuum window and the golden self-similarity of the lattice (parallel ×φ, perpendicular ×1/φ per inflation step) acting as its renormalisation group. Principal structural results System-primary foundation; no free continuous parameter at the foundational level: the dynamics is a discrete relational action, both couplings fixed (θ = π by spin-½; β → ∞ is maximal mutual determination itself), so λ = pc is the structural percolation threshold of the E8 foam graph. In v7.0 the action is operative in the equivalent sector form S = −Σrelations M + Σtransports(leak share), with δS = 0 as the classical principle and quantum-occupancy weighting forced by granularity. The qubit value-space CP1 derived, not posited: relationality forces projectivity, the equitable triadic balance forces the complex structure, minimality forces CP1. Three generations of matter from the W(E8) representation V112’s ℤ3-cyclic decomposition (Coxeter element of an A2 ⊂ E8, GAP-verified). Koide relation as a theorem of the ℤ3-cyclic structure—angle θ = 2/9 a derived SU(3) Casimir invariant, value Q = 2/3 re-grounded in v7.0 as maximal shared indetermination between the generation loop and its two neighbour-chains (the √2 from the cyclic channel’s dimension)—charged-lepton mass ratios at 10−5 precision. The flavour sector closed (new in v7.0). Quark mixing: the full CKM—|Vus|, |Vcb|, |Vub|, and the Jarlskog invariant—from the spurion’s exact weak–generation gateway (the phason-shadow adjacency, with the w-root as the sole lattice bridge), the connector’s magnitude and phase derived (transport universality, promoted by granularity-forced factorisation; winding minus spinor half-angle), and the two virtual-gap coordinates delivered at leading order by the action’s excursion curvature Δp = 3·My(ρp) (unique double landing among eight pre-declared candidates; Δ5 = 4/3 exact in form): a zero-free-parameter CKM at the 3–15% level, χ²/dof = 0.55 at the data-pinned refinements, CP violation structurally necessary and the CP branch data-sealed. Neutrino oscillations: closed at zero parameters from three derived constants—the ℤ3 trisection of the free-sector angle (holonomy locking), r² = D = 3/4 (granularity-forced self-counting stationarity, unique fixed point), and the Majorana core κ = −5/12 (gateway slot-service counting, cyclic protection by the exact Σω2g = 0 theorem)—χ² = 1.42 with sinδCP = −1 exact. Colour-flux census laws (new in v7.0), from 1.46×1010 exhaustively enumerated lattice loops: exact flux quantisation Φ ∈ (2/√3)ℤ; the closed-form conversion κ = 4π/(3√3) with the plaquette identity κq = 8π/9 = 2π·pinv(1u); quantum universality across loop lengths; exact zero-flux controls (W = +1.00000); and the unit-diffusivity law ⟨q²⟩ ≈ A at 29.6σ, with the persistent zero-flux backbone quantified as the obstruction the determination-cost weight must remove. The strong-coupling boundary and the confinement dictionary (new in v7.0): the bare string tension in closed form, σ̂UV = 4√3π²/(81φ6); the strong coupling at the cell scale landing at the protection scale (1/αs(E*) = 49.6 at two loops against 147/3 = 49); and the calibrated two-way dictionary c = 0.583 ⇔ (αs(MZ), √σ) jointly, the native-scheme matching constant c being the single named decider of the strong-sector story. Foam at percolation criticality: Monte-Carlo through L = 12, finite-size scaling rejecting the algebraic conjecture at >8σ, branching-criticality origin of λ = pc, and the macroscopic dimensionality dBS = 4 verified on the ideal lattice and the growth ensemble. Cosmological constant: the ∼120-order smallness as a structural output of the foam area-law, wDE = −1 exact. Baryon asymmetry: ηB/JCKM = pc·μ9cosmo, now rendered fully input-free by the zero-parameter Jarlskog of the closed flavour sector, bracketing the measured ηB. Matter–antimatter, dark matter, and primordial black holes: dark matter as Standard-Model matter propagating in the temporally opposite direction; τ-demarcation surfaces as event horizons; the heavy-tailed ΩDM/ΩB distribution. Gravitational sector: Einstein–Hilbert effective action, graviton spin-2 from foam homotopy, the strong equivalence principle, and the Bekenstein–Hawking 1/4 coefficient, all foam-emergent; ℓ*/ℓP = 2φ5. The continuum as emergent: rigorous in d = 2 (Γ-convergence to the SU(2)1 WZW fixed point), the physical d = 4 framed as asymptotic safety with the E8 foam as finite ultraviolet completion—in v7.0 sharpened by the inflation-invariance theorem: the flavour shapes are fixed-point quantities of the golden renormalisation group, with scheme covariance verified (χ² 5118 → 19.6 at 2 GeV) and φ-suppressed deviations from Standard-Model running predicted, in principle, near the cell scale. Three emergent facets: space, time, and quantum mechanics as three structurally distinct facets of the qubit system. v7.0 release content (v6.0 → v7.0) The principal additions of this release (the intermediate working label v6.1 was never archived; its four sharpenings are items 1–4): Self-duality derived via Mordell’s theorem, removing an axiom-level input of the chain. The intrinsic Stage 4–5 reformulation, stating the 600-cell → 2I passage in system-primary terms. The two coherence thresholds, articulating the growth dynamics’ ordering. The Koide value re-grounded as maximal shared indetermination (joint coherence over the two V112 relation-chains), robust to the measure. The electroweak gateway and the CKM closure (see above), including the lattice-level reading of the gateway, the exclusion ladder of falsified alternatives, the data-sealed configuration and CP branch, scheme covariance by the per-unit prescription, and the excursion-curvature derivation of the gaps. The neutrino mechanism: trisection by holonomy locking, D = 3/4 by self-counting stationarity (with the budget and node walls formalised), and the −5/12 Majorana core by slot-service counting with the exact cyclic-protection theorem. The relational action made operative: δS = 0; the D = 3/4 derivation; the closed-form bare tension; the golden inflation as renormalisation group; the inheritance of Standard-Model running re-founded as a limit theorem (universality), the native language remaining primary. The colour-flux census (n = 5, 6; 1.46×1010 loops): quantisation, closed-form κ, universality, exact controls, unit diffusivity. Three exact flavour–gauge bridges and the strong-coupling boundary, with the two-loop adjudication and the c-dictionary for (αs(MZ), √σ). The honest ledger and publication passes: forty-four adjudications (eleven self-inflicted, including the multiplicity demotion of the golden-gap labels and the two-loop demotion of the one-loop αs exactness), every claim carrying its epistemic status with supersessions recorded in place, and a closing Predictions and named deciders summary. All numerical results of v6.0 are preserved except where explicitly superseded in the recorded ledger; each supersession is stated in place with its adjudicating test. Document structure and counts The framework is articulated in 8 Parts plus the changelog Part, with 61 theorems, 12 lemmas, 28 propositions, 25 corollaries, 7 conjectures, 3 foundational axioms, 18 definitions, 164 remarks, and 167 bibliographic references (~408 pages): Foundations; the chain of stages; Standard-Model phenomenology (now including the closed flavour sector); the relational ontology and the gravitational sector; epistemic stratification and open problems; the chain-uniqueness programme; and the v6.0 → v7.0 changelog with the campaign ledger and the predictions summary. Computational reproducibility is provided by GAP and Python scripts in the proj