Primordial Substrate

A geometric program for unified physics. Primordial Substrate develops
a mathematically explicit framework in which microphysics, gravitation, cosmology,
and chemical and biological complexity are derived as regimes of a single nonlinear
continuous medium. The fundamental variable is the map ΦA : M 4 → B, where B
carries hyperbolic geometry and admissible finite-energy states satisfy |Φ| < 1. In this
formulation, the vacuum is not a passive background: observable fields, particles, and
macroscopic structures are induced phase states of one geometrically active Substrate.

No-Fit paradigm and single-action closure. Dynamics are fixed by one DBI
action 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 dimensionless
ratios are derived in the same invariant class, without new fitting coefficients. Within
this framework, key constants follow from topology and Cartan geometry, including
α−1 ≈ 137.035999177, mp/me ≈ 1836.152673426, and the selector structure Nc = 3672
with N ∈ qpZ, qp = |Isom+(Mp)| = 24, ∆DBI ≈ 0.3053.

Geometric discreteness, stability, and cross-scale reduction. The framework
addresses landscape and fine-tuning issues by replacing parameter scanning with rigidity
constraints of hyperbolic topology (Mostow–Prasad type) and DBI frustration.
Discreteness is therefore a geometric consequence of admissible fillings, while particles
are modeled as stable topological defects (knots and links) with masses and channels
determined by defect class, curvature concentration, and tension overlap. Two universal
reductions close the multiscale channel: classical holographic reduction (bulk → boundary
in the saturated regime) and rigidity of polyhedral packings together with directed metric
drift (Phase Avalanche) (selection of discrete stable packings and directed attractor
descent from atomic to biomolecular structure).

Verification and falsifiability. The theory is formulated as a quantitatively
falsifiable program with explicit rejection criteria by block. Representative predictions
include 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 for
many-body logic systems, and constrained neutrino/cosmological windows tied to the
same geometric constants. Thus, Primordial Substrate is
posed as a closed geometric hypothesis in which one medium, one variational action,
and one calibration scale generate a connected hierarchy of testable regimes.