The obstruction relocates rather than disappears
The argument
Identifications made along isomorphisms can be undone by tracking the isomorphisms, so an inconsistency visible after identification should be present before it. Given that no specific step of Scholze and Stix's argument has been shown to fail without their simplifications, that the passage from Theorem 3.11 to Corollary 3.12 depends on an unproven compatibility even in the formulation that avoids the diagram, and that this compatibility is the same obstruction Scholze and Stix identified, keeping the distinctions relocates the difficulty rather than removing it, and the monodromy is not an artifact of the collapse.
Does it work?
Not yet evaluated.
Premises
- InconclusiveThe evidence and argument have been examined and do not come down on either side.constitution →The compatibility the LANA project isolated at the final stage of IUT is the same obstruction Scholze and Stix identified in 2018.
- SupportedThe evidence favors the claim, but the examination is incomplete or the evidence is indirect.constitution →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.
- UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →Mochizuki has not identified a specific step in Scholze and Stix's argument that fails without their simplifications.
Where it is made
Passages where sources make, criticize or mention this argument. They record where it appears, not how strong it is, and none has precedence over another.
No source is recorded as making it.
Earlier ratings
- Sep 16, 2026
The tracking principle is standard and the inference from it is valid: if the identifications discard nothing, an inconsistency visible after them was already present. The argument's weight rests on whether the compatibility LANA isolated is the Scholze-Stix obstruction restated, which remains open but has gained support from the LANA report's own statement that both analyses locate a problem at the same step concerning the identification of copies of the real line, and from Joshi's remark that LANA meets the same problem Scholze and Stix did. The dependence on an unproven compatibility is conceded by LANA and now assessed as supported; the absence of a named failing step holds, though LANA's answer is that the intended argument has a different shape rather than that a step fails. If the compatibility proves to be a different problem from the j² discrepancy, the argument loses most of its force even with its other premises intact.
- Sep 13, 2026
The tracking principle is standard and the inference from it is valid: if the identifications discard nothing, an inconsistency that appears after them was already there. The argument's weight rests on whether the compatibility LANA isolated is the Scholze-Stix obstruction restated, which is the one genuinely open premise; the dependence on an unproven compatibility is conceded by LANA itself, and the absence of a named failing step has held since 2018 but is now qualified by LANA's report that the intended argument has a different shape rather than a failing step. If the compatibility turns out to be a different problem from the monodromy, the argument loses most of its force even though its other premises stand.