Primordial Substrate

A geometric program for unified physics. Primordial Substrate developsa mathematically explicit framework in which microphysics, gravitation, cosmology,and chemical and biological complexity are derived as regimes of a single nonlinearcontinuous medium. The fundamental variable is the map ΦA : M 4 → B, where Bcarries hyperbolic geometry and admissible finite-energy states satisfy |Φ| < 1. In thisformulation, the vacuum is not a passive background: observable fields, particles, andmacroscopic structures are induced phase states of one geometrically active Substrate.No-Fit paradigm and single-action closure. Dynamics are fixed by one DBIaction with minimal stabilization and without a standalone fundamental Einstein–Hilbert term. The dimensional sector is closed by a single scale Θfree = {μ}:after one-time calibration of μ, all remaining dimensional quantities and dimensionlessratios are derived in the same invariant class, without new fitting coefficients. Withinthis framework, key constants follow from topology and Cartan geometry, includingα−1 ≈ 137.035999177, mp/me ≈ 1836.152673426, and the selector structure Nc = 3672with N ∈ qpZ, qp = |Isom+(Mp)| = 24, ∆DBI ≈ 0.3053.Geometric discreteness, stability, and cross-scale reduction. The frameworkaddresses landscape and fine-tuning issues by replacing parameter scanning with rigidityconstraints of hyperbolic topology (Mostow–Prasad type) and DBI frustration.Discreteness is therefore a geometric consequence of admissible fillings, while particlesare modeled as stable topological defects (knots and links) with masses and channelsdetermined by defect class, curvature concentration, and tension overlap. Two universalreductions close the multiscale channel: classical holographic reduction (bulk → boundaryin the saturated regime) and rigidity of polyhedral packings together with directed metricdrift (Phase Avalanche) (selection of discrete stable packings and directed attractordescent from atomic to biomolecular structure).Verification and falsifiability. The theory is formulated as a quantitativelyfalsifiable program with explicit rejection criteria by block. Representative predictionsinclude a TeV-photon delay law ∆t ∝ E2, an UHECR per-nucleon wall Ecrit = 4.53 ×1019 eV, finite-core compact-remnant channels, bounded connected-coherence limits formany-body logic systems, and constrained neutrino/cosmological windows tied to thesame geometric constants. Thus, Primordial Substrate isposed as a closed geometric hypothesis in which one medium, one variational action,and one calibration scale generate a connected hierarchy of testable regimes.