INFINITE FIELD THEORY (IFT) Chapter 1 — Section A Foundations and Derivations

Infinite Field Theory (IFT) Chapter 1 — Section A Foundations and Derivations DOI : 10.5281/zenodo.19033216 Infinite Field Theory (IFT) accounts for the emergence of spacetime, matter, and consciousness from a single postulate—the Karabdak Fundamental Postulate—and a sole universal constant, the Karabdak threshold K꜀ᵣᵢₜ = 1/√2, derived as the unique infrared fixed point of the Wetterich renormalisation group flow under conformal coupling. Section A establishes the complete algebraic foundations: the Z₂-graded C-algebra* of pre-geometric observables, the Tomita–Takesaki modular structure, the derivation of the double-well potential V(σ) = λ(σ² − K꜀ᵣᵢₜ²)² from spectral bimodality, the GNS construction of spacetime, and the helical topology of the sentinel wave with the Călugăreanu invariant Lk = Tw + Wr. Dark matter is identified as a corrupted potentiality (σ < K꜀ᵣᵢₜ). MCMC validation across the 175 galaxies of the SPARC database yields the following results: the IFT–Burkert profile was preferred in 139 out of 175 cases (79.4%), with a median ΔBIC = −4.49. The Hubble tension is calculated as a 9.0% coherence drift. Based on the same constant, thirteen falsifiable predictions are presented, two of which have already been validated. Keywords: Quantum coherence; renormalisation group; Tomita–Takesaki; dark matter; Burkert profile; Hubble tension; SPARC; gravitational wave echoes; falsifiable predictions; informational cosmology.