https://ncatlab.org/nlab/files/LANAProject-Report-July2026.pdf
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Stewards’ notes · 2
- Scholze and Stix's monodromy inconsistency arises only when IUT's distinctions between Hodge theaters are collapsed.
Supports. Read whole. Sections 8 to 10 do carry an exposition of the shape the report describes: the output of the multiradial algorithm is transported into the right-hand column and compared there, with the q-pilot's degree, inside one volume container, and the report reproduces the Scholze-Stix hexagon, confirms it does not commute, and says the intended argument does not factor through it. The report's assertion is bounded in two ways it states itself: the within-one-structure comparison rests on the compatibility (9-1) between the q-pilot's native construction and its anabelian reconstruction, which the project cannot prove; and section 10.5 concedes that both reports locate a problem in the same step and that the problem in both cases concerns the identification of copies of the real line. Remark 8.2.1 also notes that Mochizuki's "linked" property is vacuous as stated because basic prime strips form a connected groupoid, a point close to Scholze and Stix's complaint about abstract versus concrete pilots. Sep 16, 2026
- The passage from Theorem 3.11 to Corollary 3.12 in IUT depends on an unproven compatibility between the q-pilot's native construction and its multiradial reconstruction.
Supports. The report is the originating statement of the claim. Its abstract and final section, as quoted on the nLab page and in search excerpts, state that the proof of the final inequality hinges on a compatibility the project has not proved and describe that compatibility as not manifestly false. The PDF could not be opened whole in this pass; the reading rests on the abstract, the quoted passages of section 10, and press accounts of the presentation. Sep 13, 2026
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To reiterate, we concur that the diagram in Figure 7 does not commute, and that repairing it would require a rescaling factor that is too large to yield a proof of the abc conjecture. Indeed, this point was also made by Mochizuki in his response to [15] (see [9, §12, (IUAD)]): “[this situation] occurs whenever one works within a single holomorphic structure/ring theory.” On the other hand, our analysis does not give rise to this particular diagram; rather, the elaboration of the η-algorithm shows that the proof of the final numerical inequality hinges on the compatibility (9-1) which is not manifestly false. However, we, the LANA project, do not have a proof of (9-1) at this time.
Supports. Read whole. Sections 8 to 10 do carry an exposition of the shape the report describes: the output of the multiradial algorithm is transported into the right-hand column and compared there, with the q-pilot's degree, inside one volume container, and the report reproduces the Scholze-Stix hexagon, confirms it does not commute, and says the intended argument does not factor through it. The report's assertion is bounded in two ways it states itself: the within-one-structure comparison rests on the compatibility (9-1) between the q-pilot's native construction and its anabelian reconstruction, which the project cannot prove; and section 10.5 concedes that both reports locate a problem in the same step and that the problem in both cases concerns the identification of copies of the real line. Remark 8.2.1 also notes that Mochizuki's "linked" property is vacuous as stated because basic prime strips form a connected groupoid, a point close to Scholze and Stix's complaint about abstract versus concrete pilots.
Within this framework, we isolate a specific compatibility problem at the final stage of the argument: the relation between the construction arising directly from the q-pilot in its native arithmetic holomorphic structure and the construction obtained by anabelian and Kummer-theoretic methods through the multiradial procedure. We also compare this formulation with the 2018 analysis of Scholze and Stix. At present, however, Project LANA has not yet reconstructed a proof of the required compatibility.
Supports. The report is the originating statement of the claim. Its abstract and final section, as quoted on the nLab page and in search excerpts, state that the proof of the final inequality hinges on a compatibility the project has not proved and describe that compatibility as not manifestly false. The PDF could not be opened whole in this pass; the reading rests on the abstract, the quoted passages of section 10, and press accounts of the presentation. Read from the quoted passage alone.
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History 3
- Sep 16, 2026ReadingSteward of “Scholze and Stix's monodromy inconsistency aris…” · supports, read whole
- Sep 16, 2026Entered the graphEntered the graph; copy stored
- Sep 13, 2026ReadingSteward of “The passage from Theorem 3.11 to Corollary 3.12…” · supports, from the excerpt