ERB Framework: A Reconstruction of the Standard Model from a Single Mechanical Postulate

We present the Emergent Resonant Brane (ERB) framework, version 26, a systematic reconstruction program for quantum field theory from a single mechanical postulate: two colliding vacuum branes with mass-density ratio ξ = m_B/m_A = 3/2. This ratio is not chosen to fit data — it is the smallest ratio of two distinct primes, the unique fixed point at which a two-brane system reaches minimum entropy production and maximum resonance stability under the Callan-Symanzik flow.

From this single input, a strictly causal five-level chain (L0→L5) with zero upward information flow derives: the coupling constant g = 3/25 = 0.12 (Le Chatelier closure), the penetration scale k as a field eigenvalue (not a fit parameter), the complete CKM matrix (MAE = 6.94×10⁻⁴, zero free parameters in the mixing sector), the Jarlskog invariant J = 2.95×10⁻⁵ (1.69% error vs. PDG), the fine-structure constant α_EM = 1/137.071 (0.025% error, Berry-phase holonomy), and — new in v26 — the pion mass as the Goldstone mode of interface torsion: m_π(dimensionless) = √(ε₀·δ·m_eff)·(1−3θ_B) = 0.1393 (0.18% error vs. PDG).

CP violation is proven to be geometric: J = 0 exactly without the sgn(Δr) term in the Whip phase operator, verified in four independent cases. Three fermion generations emerge structurally from the SO(3) Bessel spectrum — not postulated. The quark-lepton mass hierarchy is explained by the gyroscope model: the moment of inertia I_i = m_i·r_i² of the top quark (I ≈ 5737) is 2.7×10⁵ times larger than that of the up quark (I ≈ 0.022), freezing the heavy generation at its topological Bessel radius while light quarks precess freely.

The PMNS near-maximal mixing follows as the evanescent limit of the same resonance operator: at the lepton penetration scale k_L = 4k_Q, the wave function spreads across all three Bessel nodes, driving mixing angles toward π/4. The gauge structure U(1)×SU(2)×SU(3) emerges as collective brane oscillations: the photon as a massless phase-gradient wave, the W/Z mass from the 3/2 mechanical mismatch without a Higgs field, and gluons as lattice shear waves with confinement via linear string tension.

Wilsonian renormalization is reinterpreted physically: the UV cutoff Λ = 464.1 GeV is the brane collision scale. Running couplings are the elastic substrate's response to different wavelength modes. Renormalization is not a mathematical trick — it is the transition from the discrete ERB substrate to the continuous QFT. The 3/2 attractor is stable by entropy minimisation: any deviation ξ = 3/2 + ε induces phase dissipation at rate dS/dt ∝ ε², forcing the system back to the fixed point.

All results, open problems, and derivation gaps are explicitly labelled (PROVEN / DERIVED / CANDIDATE / HYPOTHESIS / OPEN). The primary falsifiable prediction is δ_CP ≈ 352° for leptonic CP violation, testable by the DUNE experiment (~2030). Falsification criterion: |δ_CP(measured) − 352°| > 20°.