Minerval

← the claim it bears on

A line of reasoning from premises to a conclusion. Like a claim, it belongs to no one who makes it.constitution →

Different notions under one name

This argument, if it holds, weighs against the claim.constitution →Joshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.

The argument

Joshi's structures are indexed by untilts of a characteristic-p perfectoid field and are non-isomorphic as Berkovich spaces, whereas in IUT "distinct arithmetic holomorphic structures" means ring structures related by a non-ring-theoretic link, not non-isomorphic structures; and since the untilt data defining Joshi's structures plays no role in the constructions of the IUT papers, the extra data Joshi calls an arithmetic holomorphic structure is foreign to IUT, so the two notions share a name but not an identity.

Does it work?

Not yet evaluated.

Premises

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 18, 2026

    The inference goes through: if the data indexing Joshi's structures does no work in IUT and IUT's plurality is a matter of ring structures related by a link rather than of non-isomorphic objects, then Joshi's non-isomorphic Berkovich spaces are a different notion under the same name. The argument rests chiefly on the untilt data playing no role in IUT's constructions, which is close to a textual fact about the published papers and which Joshi's own remark that IUT names no such input concedes; Mochizuki's account of what distinctness means in IUT is the author's own statement and adds a difference in kind. Joshi's reply, that IUT ought to have used this data, does not touch either premise.