04/14/2026
Infinite‑Finite Cosmology is a radical reconstruction of the universe’s foundations. Instead of beginning with geometry, fields, or spacetime, this framework starts with the simplest arithmetic act imaginable:
Suc(n) = n + 1 — the successor operation.
From this single primitive, the manuscript shows how the universe’s structure unfolds step by step. The mod‑4 residue cycle forces the first differentiation of the arithmetic substrate, generating proto‑rotation, polarity, curvature, and the unique 1 + 3 rail architecture that becomes time (the active rail) and space (the three inert rails) .
Refinement compresses the residue structure into finite Möbius‑bounded interiors, where curvature and torsion arise automatically from arithmetic asymmetry. Matter appears when refinement crosses the 4·π threshold, locking curvature and torsion into stable knotted configurations — the proton, electron, and neutrino triplet .
Entropy emerges as the loss of residue‑specific information under finite projection, driving each interior toward a curvature‑neutral saddle. Because the successor field has no minimal element, the universe becomes a bi‑infinite chain of eons, each generated by refinement acting on the arithmetic substrate .
The manuscript positions this as a compression claim: the shortest known generative description of the universe’s large‑scale regularities. It is fully falsifiable — either by a shorter competitor or by failed predictions listed in Appendix C, including CMB rotation, gravitational wave spectra, lensing anomalies, and the persistence of the Hubble tension .
In short:
Arithmetic generates geometry.
Geometry generates matter.
Matter generates cosmic evolution.
The universe is not built from space — space is built from succession.
Infinite‑Finite Cosmology is a radical reconstruction of the universe’s foundations. Instead of beginning with geometry, fields, or spacetime, this framework...