Last updated 2026-08-19 · from git history, not hand-typed
Principia Orthogona · Book I

Book IContents

Chapter 0 · Definitions and notation — every defined term in this book, with its status (decided, verified, open).

This page is an index, not a text. The Volume I paper itself lives at the series root; everything below points at the file that is actually current.

The text

Volume I · page text: Second Edition, April 2026 · deposit: Version 7, August 2026
The Mathematics of Generative Transitions
The canonical Volume I page. Six assumptions, five operators, the operator chain G = U∘F∘K∘C, Whitney A1–A3 classification and symplectic structure. The Zenodo deposit is Version 7 (10.5281/zenodo.22084842), which changes no mathematics and adds the kernel-checked PrincipiaVol1.lean (58 theorems). Cite Version 7.
book1/vol1-mathematics.html Volume II · Version 5 · August 2026
Contact Realization of Generative Transitions
The companion volume: fold–contact correspondence, the threshold equivalence κ* ↔ τ, and the singularity–bifurcation theorem.
../vol2-contact.html TOGT · Version 4 · September 2026 · correction release
Contact-Geometric Theory of Generative Transitions
The synthesis paper built on Volumes I and II: foundations, contact realization, seven proofs that the fold recurrence grows at the Tribonacci constant η ≈ 1.8393, and conjectural applications to nuclear matter. The page gives the Version 4 status of every tag, the kernel-checked files, and the tags that are not yet backed by a deposited declaration. Zenodo 10.5281/zenodo.20682933.
book1/vol1-proofs.html Interactive
dm³ Dashboard
The interactive companion to the dm³ toy model — the explicit contact-geometric realisation used in Volume I §14 and Volume II.
../vol2-dashboard.html

Kept for the record

Why the Volume I page carries the Second Edition text. Later versions revised the mathematics but dropped the note “A note on ‘orthogenesis’” — the passage separating orthogonal genesis from the nineteenth-century biological theory of the same name, and reading Waddington’s canalisation as a curvature picture. It exists only in the Second Edition, so that is the text the page keeps, with a banner giving the current deposit. The old root copy ../vol1-mathematics.html is now a redirect to it.
Snapshot · 3 July 2026
Formal Verification Registry
Per-file, per-lemma tracking for five Lean 4 files as they stood on one audit date, when none of them had yet been compiled. Its counts are not the current counts — the live figures, and the distinction between a statement written, a proof sorry-free in source, and a proof individually kernel-audited, are in the theorem registry. Kept because it records what was true then.
book1/verification-registry.html

Every file in this directory

Listed in full, including the ones that are duplicates or misnamed, so that nothing in book1/ is reachable only by guessing at a URL.
FileWhat it actually is
index.html This page.
vol1-mathematics.html Volume I, canonical page. Text: Second Edition, April 2026; banner and badges give the current deposit, Version 7. ../vol1-mathematics.html redirects here.
vol2-dashboard.html Misnamed. Despite the filename this is the Volume II text (Contact Realization, an older Version 2a copy), not a dashboard. The interactive dashboard is ../vol2-dashboard.html; the current Volume II text (Version 5) is ../vol2-contact.html.
vol1-proofs.html Guide to the TOGT paper (Nuclear Physics B), Version 4, 2026-09-24. Despite the filename it is not the Volume I Lean repository (TOTOGT/vol1-proofs), though it cites that repository’s PrincipiaVol1.lean at commit be9a20b.
verification-registry.html The 2026-07-03 Lean status snapshot described above.