Strained Prismatic Geometry — Research Architecture Edition 1 (v1.0.0)

Strained Prismatic Geometry

Deformation over the Absolute Base and the abc Conjecture

Vincent Liu · Research Architecture Edition 1 · version 1.0.0 · first public edition

A monograph in five volumes bound as one — 10 parts, 62 chapters, 1,666 pages, 186 vector plates and 242 references — and the sixth work of the series: a self-contained research subject of the Grothendieckian Programme, following The Archimedean Prism (doi:10.5281/zenodo.23597954). It asks why the abc conjecture is a theorem over function fields and open over the integers: Spec ℤ has no base, and no 1-categorical repair can give it one (Obstruction 3.3.2, the no-go theorem for initial lifts); a global substrate glued from prismatic geometry, the Habiro ring and condensed analytic geometry gives it a relative cotangent direction, along which bad reduction is strain. Theorem C, trace invariance under groupoids of identifications, is proved unconditionally (Theorem 36.3.1); the master inequality (Theorem A) and abc over ℚ (Theorem B) are proved conditionally on a ledger of ninety-eight named obligations.

The abc conjecture remains open. This work does not prove it, and it neither verifies nor refutes inter-universal Teichmüller theory.

New here? Start with the preview (72.0 MB): the Series Note, the Abstract, the Preface, the Epistemic Status of This Book, the Leitfaden, notation, the contents and the whole of Part 0.

	File	Pages	Size
Preview	Strained-Prismatic-Geometry-v1.0.0-Preview.pdf	166	72.0 MB
Complete monograph (Volumes I–V and Appendices A–J)	Strained-Prismatic-Geometry-v1.0.0-Complete.pdf	1,666	83.0 MB
Companion code (Apache-2.0)	Strained-Prismatic-Geometry-v1.0.0-code.zip	—	60.7 KB

Permanent archive and citation — Zenodo, concept DOI 10.5281/zenodo.23610034 (this edition: 10.5281/zenodo.23610035). The files here are byte-identical to the Zenodo record.

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