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AlienMuse/README.md

Vincent Liu — The Grothendieckian Programme, Series 00–07: the seven works as a seven-cell honeycomb, GAI-MUA at the centre

Mathematics and machine reasoning. I am the author of The Grothendieckian Programme, a programme for machine reasoning about mathematics, set out in seven works of the WiseMotif Monograph of Mathematical Intelligence (Series 01–07), with their overview (Series 00). WiseMotif.ai · Palo Alto, California.

ORCID 0009-0000-8718-222X Website alienmuse.github.io Google Scholar Vincent Liu Zenodo community The Grothendieckian Programme

The Grothendieckian Programme · Series 00–07

Cover of The Grothendieckian Programme
SERIES 00
The Grothendieckian Programme
the Programme's overview
one book · 53 pages
doi:10.5281/zenodo.23669107 		Cover of GAI-MUA: The Grothendieckian Machine
SERIES 01
GAI-MUA: The Grothendieckian Machine
the core
6 volumes · 14,905 pages
doi:10.5281/zenodo.23480696 		Cover of GM-Omega-Infinity: Topos-Native Intelligence
SERIES 02
GM-Omega-Infinity: Topos-Native Intelligence
the meta-reasoning kernel
5 volumes · 4,020 pages
doi:10.5281/zenodo.23538544 		Cover of Arithmetic Spectral Descent
SERIES 03
Arithmetic Spectral Descent
research subject 1 · RH and GRH
4 volumes · 1,549 pages
doi:10.5281/zenodo.23564898
Cover of Fractured Adelic Geometry
SERIES 04
Fractured Adelic Geometry
research subject 2 · BSD
4 volumes · 571 pages
doi:10.5281/zenodo.23585887 		Cover of The Archimedean Prism
SERIES 05
The Archimedean Prism
research subject 3 · Hodge
5 volumes · 1,309 pages
doi:10.5281/zenodo.23597954 		Cover of Strained Prismatic Geometry
SERIES 06
Strained Prismatic Geometry
research subject 4 · abc
5 volumes · 1,666 pages
doi:10.5281/zenodo.23610034 		Cover of The Arithmetic Topos
SERIES 07
The Arithmetic Topos
research subject 5 · Langlands
5 volumes · 2,001 pages
doi:10.5281/zenodo.23629681

7 works · 34 volumes · 26,021 pages · 995 chapters · 349,000+ formulas · 714 algorithms — each count taken by two independent methods from the sealed editions (STATISTICS.md). Each work has its own repository, its own DOI and its own boundary in its own words; the overview, Series 00, adds no mathematical result to them.

Approach

  • Worlds. At its centre, The Grothendieckian Machine (Series 01) holds mathematical worlds as typed, versioned and verifiable objects, with the status of every claim part of its type.
  • Descent. Over it, Topos-Native Intelligence (Series 02) reasons inside a world as inside a topos: a context is a site, the evidence a sheaf, a conclusion a global section that exists only where the local data glue, and a failure to glue an obstruction that can be located.
  • Recursive discovery. Around them, five research subjects (Series 03–07) — the Riemann Hypothesis and its generalisation, the conjecture of Birch and Swinnerton-Dyer, the Hodge conjecture, the abc conjecture and the Langlands programme — carry the method of recursive mathematical discovery through in full: a structure is proposed, tested against the cases in which the answer is known and abstracted where it survives, and the question is posed again; what fails is kept, as an obstruction, a gap or a test.

None of the seven works claims a proof of the problems it studies. Each says what it proves, what it reduces to stated hypotheses, and where it stops.

Contact

ORCID 0009-0000-8718-222X · Google Scholar · alienmuse.github.io (中文) · Zenodo community · vincent.liu@wisemotif.ai

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  1. grothendieckian-programme grothendieckian-programme Public

    The Grothendieckian Programme: seven works, 34 volumes, 26,021 pages on machine reasoning about mathematics — a core, a topos-native kernel and five research subjects (RH, BSD, Hodge, abc, Langland…

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  2. grothendieckian-machine grothendieckian-machine Public

    GAI-MUA: The Grothendieckian Machine, the core of the Grothendieckian Programme. Six volumes, 14,905 pages: Grothendieck's method of changing ambient worlds, turned into an architecture for verifia…

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  3. topos-native-intelligence topos-native-intelligence Public

    Five volumes, 4,020 pages: the meta-reasoning kernel of the Grothendieckian Programme. Reasoning native to a topos: a context is a site, evidence is a sheaf over it, and a conclusion is a global se…

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  4. arithmetic-spectral-descent arithmetic-spectral-descent Public

    Four volumes, 1,549 pages on the Riemann Hypothesis: 23 scoped no-go theorems, the Krein Index Theorem, a proved derivation of RH from three unconstructed realization hypotheses, and two obligation…

    Python 1

  5. the-arithmetic-topos the-arithmetic-topos Public

    Five volumes, 2,001 pages on the Langlands programme: a global arithmetic curve over Z, a geometry with a primitive trace, and a Main Conjecture of three equivalences and eight corollaries; 1,609 s…

    Python 1

  6. alienmuse.github.io alienmuse.github.io Public

    The website of Vincent Liu (WiseMotif.ai): The Grothendieckian Programme, Series 00–07 of the WiseMotif Monograph of Mathematical Intelligence — the overview and the seven works, with their DOIs.

    HTML 1