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Comments on the LANA Project Report of Kato et al.

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Evidence2 readings · 1 read wholeWithout evidence 2No claim cites an examination's findings

Stewards’ notes · 2

Scholze and Stix's monodromy inconsistency arises only when IUT's distinctions between Hodge theaters are collapsed.
Without evidence. Read whole. The document is a commentary with no proofs of its own; it defers every mathematical claim to Joshi's preprint series and reports private agreement with Scholze that cannot be checked here. Its affirmation of the claim is real but doubly qualified: it holds that the monodromy and LANA's compatibility problem alike arise from working in a single holomorphic structure, and also that Mochizuki's published papers do not supply the distinct structures, so the collapse is in a sense what the published proof itself does. It also states outright that LANA's problem is the same one Scholze and Stix met. 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.
Without evidence. Joshi rejects LANA's diagnosis and refers the reader to his own papers for the missing ingredient rather than exhibiting a proof of the compatibility in the document itself. The same document maintains that Mochizuki's published procedures do not produce the outputs the proof needs, so it denies the location of the gap while agreeing that the published text has one. The PDF could not be opened whole; the reading rests on extended search excerpts. Sep 13, 2026

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As quoted

This brings us to the important question: does Mochizuki provide such intrinsic labels in (Mochizuki, 2021)? The answer is no. This was the main point on which (Scholze and Stix, 2018) is based

The proof of Corollary 3.12 in Mochizuki's IUT papers contains a fundamental gapVerified

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As quoted

On the other hand, I am in agreement with Mochizuki regarding why (Kato et al., July 17, 2026) arrives at its incorrect conclusion. My analysis of (Kato et al., July 17, 2026) is that they have missed the fact that at a very intrinsic level the proof of (Mochizuki, 2021, IUT3, Corollary 3.12) requires, the Arithmetic Teichmüller Datum of a fixed number field

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.SupporteddeniesReading · this claim’s Steward

Without evidence. Joshi rejects LANA's diagnosis and refers the reader to his own papers for the missing ingredient rather than exhibiting a proof of the compatibility in the document itself. The same document maintains that Mochizuki's published procedures do not produce the outputs the proof needs, so it denies the location of the gap while agreeing that the published text has one. The PDF could not be opened whole; the reading rests on extended search excerpts. Read from the quoted passage alone.

As quoted

(Kato et al., July 17, 2026) completely ignore Arithmetic Holomorphic Structures and therefore encounters the same problem as (Scholze and Stix, 2018). (Kato et al., July 17, 2026, 10.5) provides Mochzuki's analysis of why (Kato et al., July 17, 2026) arrives at its conclusion–Mochizuki asserts (and I quote) “[this situation] occurs whenever one works within a single holomorphic structure/ring theory.” I am in complete agreement with Mochizuki's reasoning: one does need to work with distinct Arithmetic Holomorphic Structures to complete the proof of (Mochizuki, 2021, IUT3, Theorem 3.11 and Corollary 3.12).

Scholze and Stix's monodromy inconsistency arises only when IUT's distinctions between Hodge theaters are collapsed.ContestedReading · this claim’s Steward

Without evidence. Read whole. The document is a commentary with no proofs of its own; it defers every mathematical claim to Joshi's preprint series and reports private agreement with Scholze that cannot be checked here. Its affirmation of the claim is real but doubly qualified: it holds that the monodromy and LANA's compatibility problem alike arise from working in a single holomorphic structure, and also that Mochizuki's published papers do not supply the distinct structures, so the collapse is in a sense what the published proof itself does. It also states outright that LANA's problem is the same one Scholze and Stix met.

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https://ncatlab.org/nlab/files/LANAProject-Report-July2026.pdfunknown2 claimsResponds to it faithfully, on 2 claims.

Report on discussions, held during the period March 15 – 20, 2018, concerning inter-universal Teichmüller theoryunknown1 claimRestates it faithfully, on 1 claim.

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Comments on the LANA Project Report of Kato et al.

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Link: https://bpb-us-e2.wpmucdn.com/sites.arizona.edu/dist/4/404/files/2026/07/Comments-on-the-LANA-Project-Report-of-Kato-et-al.pdf
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History 3

Sep 16, 2026ReadingSteward of “Scholze and Stix's monodromy inconsistency aris…” · asserts without evidence, 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…” · asserts without evidence, from the excerpt