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

Book IContents

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 · Version 4 · 21 June 2026
The Mathematics of Generative Transitions
The current Volume I. Six assumptions, five operators, the operator chain G = U∘F∘K∘C, Whitney A1–A3 classification and symplectic structure, with the Lean 4 status of each constant. This is the copy the rest of the series links to.
../vol1-mathematics.html Volume II · Version 2a · 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 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

The Second Edition is not superseded in every respect. Version 4 revised the mathematics, but it dropped the note “A note on ‘orthogenesis’” — the passage separating orthogonal genesis from the dead nineteenth-century biological theory of the same name, and reading Waddington’s canalisation as a curvature picture. That note currently exists only in the Second Edition below. Until it is carried forward, this page keeps the older edition reachable rather than quietly retiring it.
Volume I · Second Edition · April 2026
The Mathematics of Generative Transitions — earlier edition
Superseded as mathematics by Version 4; retained because it carries the orthogenesis note. Read it as history, and cite Version 4.
book1/vol1-mathematics.html 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, Second Edition, April 2026. The current Volume I (Version 4) is at ../vol1-mathematics.html.
vol2-dashboard.html Misnamed. Despite the filename this is the Volume II text (Contact Realization, Version 2a), not a dashboard. The interactive dashboard is ../vol2-dashboard.html; the Volume II text is also at ../vol2-contact.html.
verification-registry.html The 2026-07-03 Lean status snapshot described above.
vol1-mathematics.html.bak An editor backup that is tracked in git and therefore published. It is not part of the volume and should be removed from the repository.