The series is being written into the Lean 4 proof assistant with the Mathlib library. Some results are proved and machine-checkable; many steps still carry an open sorry, and several hypotheses are stated as explicit axioms rather than derived. Across 121 of the authors’ own files the library is unfinished — and the pages say so. The full directory and the theorem registry remain open for inspection.
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A closed de Sitter universe contracts to a throat and rebounds, never reaching zero. Written up as the Orthogonal Witness; its scalar core is formalized in Lean, kernel-check pending.
Its mirror: a closed dust universe, born from nothing to a Big Crunch. The classical Friedmann cycloid of 1922 — here paired and formalized, not claimed as new.
A closed universe’s fate turns on its contents: a cosmological constant bounces; ordinary matter recollapses. The two are guardrails; the measured universe lies between them.
I · GOMC Science. The origin volume →
II · TOGT. Contact geometry →
III · The Mini-Beast. The living eBook →
IV · GTCT. Dimensional theory →
V · The Seed. Completeness →
VI · Roots. $i$, the rotation; $o$, the point →
VII · The Scientist Gallery. Portraits of scientists →
VIII · The Monster. Dark matter, horizons, quanta →
Ω · The Space of Possibility. Above the ladder →
Openly licensed CC BY-NC-ND 4.0 · series DOI 10.5281/zenodo.19117399 · ORCID 0009-0000-6496-2186. The complete series index lives at the geometry site →
Hour House is an adult English programme whose lessons are built on the teacher’s own published work. Tiers run A2 through C1, alongside a career track in IT for the court system. The materials are free.
The dm³-101 course runs sixteen weeks and chains straight through, Week 1 to Week 16 — a first door that leads onward without dead ends.
Offered in the spirit of Pope Leo XIV’s Magnifica Humanitas: the guard against a dominating technology is understanding — freely given, first steps to the frontier.
Every folder and chapter of the repository — the books, the Lean sources, the companion papers — laid out in full.
The catalogue of formalized statements, each linked to its source, with its status shown honestly rather than summarized.
This journal is the front door; the directory is the whole house. Nothing here is hidden behind the masthead.