grothendieckian-programme

Five volumes, 1,666 pages on the abc conjecture: a global substrate over which Spec Z acquires a base, strain, the Theta-dilation, an unconditional trace-invariance theorem, Theorems A and B conditional on 98 named obligations, and abctk. The abc conjecture remains open. DOI 10.5281/zenodo.23610034.

The official site of Grothendieck Lab (WiseMotif.ai) and of the Grothendieckian Programme: the overview and the seven works, the method, the machine, the open problems.

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 verifiable, self-evolving AI for mathematics — typed worlds, bridges and proof obligations. Open access, DOI 10.5281/zenodo.23480696.

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 obligations posed to be attacked or falsified. RH remains open. Open access, DOI 10.5281/zenodo.23564898.

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, Langlands). Series 00, their overview, adds no mathematical result; none of the seven claims a proof of the problems it studies. DOI 10.5281/zenodo.23669107.

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 section that exists only where the local evidence glues. Open access, DOI 10.5281/zenodo.23538544.

Five volumes, 1,309 pages on the Hodge Conjecture: algebraicity as a descent datum along a definable prism, twelve axioms, an unconditional equivalence of five formulations, nine obstructions of which two are live. The Hodge conjecture remains open. Open access, DOI 10.5281/zenodo.23597954.

Profile of Vincent Liu (WiseMotif.ai): mathematics and machine reasoning — The Grothendieckian Programme, Series 00–07.

Four volumes, 571 pages on the Birch and Swinnerton-Dyer conjecture: Frobenius–Arakelov–Prismatic spaces, the Master Identity as one determinant line with two trivialisations, a proved conditional descent, twelve conjectures and fourteen obstructions. BSD remains open. Open access, DOI 10.5281/zenodo.23585887.

Three papers on the Grothendieckian Programme — an overview, twelve theses and 57 open problems for mathematics and machine reasoning, with problem cards, problems.json and Lean statements. Take 57.

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 status-marked statements, 17 falsification tests, aletheia, a Lean 4 skeleton. Not a proof of the Langlands correspondence. DOI 10.5281/zenodo.23629681.

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.