Description: The Unified Substrate Theory (UST) derives all observable physics from a single scalar field Lagrangian with five dimensionless constants: gamma, beta, Gamma, C2, and C3. This paper derives all five constants exactly from the structure of the substrate action. G serves as the sole dimensional anchor through the identification C2 = G. No observational data enters the derivation of any constant.

The five derivations are:

gamma = 7/2 (exact): from Wilsonian UV closure in D=4, with half-integer selection from the canonical momentum structure and Higgs self-coupling cross-check confirmation.

beta = 0.650 (exact): from the Higgs self-coupling equation derived by Taylor expansion around the symmetry-breaking saddle point of the Lagrangian, with IR stability selecting the physical root.

Gamma = 0.920000 (exact to machine epsilon): from the SO(2) Noether current renormalization group equation including the N_c = 3 color coherence correction at (gamma−1)-loop order. N_c = 3 is independently derived from the UST topological closure condition and is the same integer that gives SU(3) color symmetry and three fermion generations.

C2 = G (exact): from the unique identification of the substrate linear response coefficient with Newton's gravitational constant via the weak-field Poisson equation.

C3 = 0.018003 (0.015% residual): from the 2-loop substrate renormalization group Beta function ratio with the self-consistent Z2 symmetry correction on the 3-loop cross-diagram.

Cross-sector validation confirms all 17 predictions across six independent sectors — astrophysics, cosmology, galaxy dynamics, QED, CKM/PMNS flavor mixing, and primordial inflation — pass without adjustment using the derived constants.

Key falsifiable predictions include: lightest neutrino mass m_nu1 = 0.00176 eV (testable by Project 8 and CMB-S4), inflationary tensor-to-scalar ratio r = 0.0253 (testable by LiteBIRD), and descending effective H0(z) with H0(z=2) = 68.85 km/s/Mpc (testable by DESI Year 5).

Keywords

•  unified field theory

•  substrate theory

•  first-principles constants

•  renormalization group

•  UV closure

•  coherence drag

•  Noether theorem

•  Newton’s constant

•  fine structure constant

•  Higgs boson

•  galaxy rotation curves

Related Identifiers

isPartOf  — Main UST Corpus record:

DOI: 10.5281/zenodo.18855105

isSupplementTo  — add relationships to:

•  UST Corpus Paper 1 — The Unified Substrate Theory: Emergence

•  UST Corpus Paper 2 — Mathematical Foundations

•  UST Corpus Paper 4 — Quantization and Renormalization Closure

•  UST Corpus Paper 17 — Higgs Boson Mass Derivation

•  UST Gap Closure Compendium (33 supplements)

Correspondence: unifiedsubstrate@gmail.com