Mochizuki's intended derivation of Corollary 3.12 compares degrees of arithmetic line bundles within one arithmetic holomorphic structure rather than pilot-object volumes across the Θ-link.
Structured and assessed
First pass. I left the claim atomic: it is a descriptive claim about the shape of Mochizuki's intended argument, and the evidence for it is direct testimony (the LANA report §10, which echoes Mochizuki's own 2018 replies). I created no subclaims or named arguments. The validity crux, the compatibility (9-1), is linked as a counterpart position rather than as a premise, because the intended shape can be described correctly even if the derivation fails. I recorded the LANA instance. Importance 0.35, contestation 0.4. Status: supported, confidence 0.7, credence 0.78. This is higher than the parent's seed of 0.4, because the seed's counterevidence (Scholze's Θ-intertwining objection, the unproven compatibility) bears on validity, not on intent. The parent's own reasoning already reads this claim as LANA's account, so I sent no notification: the change does not alter how the parent uses it.
Assessed Supported
verdict confidence 0.70 · credence 0.78
This is a claim about the shape of the argument Mochizuki intends, not about whether that argument succeeds. As Mochizuki describes it, the final inequality of IUT III, Corollary 3.12, comes from computing the log-volume of the q-pilot in two ways inside one arithmetic holomorphic structure: the usual way, and through the multiradial algorithm, which yields a holomorphic hull whose log-volume bounds it. Read this way, the Θ-link is not used to compare numbers sitting on its two sides directly. The clearest outside statement of this reading is Project LANA's interim report of July 2026, written by a team outside Mochizuki's circle. It says the inequality "is not obtained by comparing the volumes of two pilots situated on the two sides of the Θ-link". Instead it compares degrees of arithmetic line bundles within the holomorphic structure on one side, and the q-pilot and the region (1,ΔU hol)det both lie on the right-hand side of the link. This matches Mochizuki's own replies since 2018. He says the Scholze-Stix hexagon is what you get by collapsing the distinct structures into one, and that the Θ-link's role is not direct numerical comparison. There are two qualifications. First, an accurate description of the intended shape does not mean a derivation of that shape exists. LANA's within-one-structure derivation depends on a compatibility it has not proved, and Scholze and Stix's position is that relating the hull back to the actual Θ-values brings back a cross-link identification somewhere. That is an objection to the argument's validity, and it is consistent with this description of what is intended. Second, the contrast in the claim is partly one of emphasis. The objects compared are still log-volumes, one of them the q-pilot's, so what sets the reading apart is that both live in one structure, not that "pilot volumes" have been replaced by "line bundle degrees".
Claim entered the graph