Isomorphic copies without an intrinsic distinction
The argument
Because the Hodge theaters on the two sides of the Θ-link are isomorphic, any two structures the papers call distinct are copies of one structure, and since the papers give no definition under which two arithmetic holomorphic structures can be proved unequal, the distinctness is asserted by labeling rather than established by proof.
Does it work?
Not yet evaluated.
Premises
- 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 →The Hodge theaters on the two sides of IUT's Θ-link are isomorphic as abstract mathematical objects.
- 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's IUT papers give no definition of arithmetic holomorphic structure precise enough to prove that two such structures differ.
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 13, 2026
The inference is valid: isomorphic copies with no definable inequality between them cannot have been proved distinct in any sense stronger than labeling. Its first premise, that the Hodge theaters on the two sides of the Θ-link are isomorphic, is not seriously disputed. The argument's weight rests on the absence in the IUT papers of a definition under which two arithmetic holomorphic structures can be proved unequal, which Joshi asserts and Mochizuki denies; the papers' treatment of the term as a gloss on ring structure rather than as a defined object favors Joshi, but no third party has adjudicated it.