RH as a HoTT Proposition: Decidability and Constructive Certification

We study the logical structure of the Riemann Hypothesis as a homotopy-type-theoretic proposition $ : $. Working in Book HoTT extended with the cubical Cauchy-real construction $$ and assuming the Volume II infrastructure that places $ : $ inside HoTT, we ask: independently of provability, is $$ decidable? We answer four interlocking questions. (i) $$ has h-level $-1$ (it is a proposition); the proof is short but conceptually load-bearing. (ii) Under the law of excluded middle ($$), $ $ is inhabited; without $$, decidability of $$ is equivalent to the existence of a constructive certifier, who…

Lean 4 Proof Verdict

# Lean proof verdict — oq6-rh-as-hott-proposition

_Generated by codex gpt-5.5 at xhigh reasoning effort, with workspace-write._

## Pre-verification `lake build` output

```
info: oq6-rh-as-hott-proposition: no previous manifest, creating one from scratch
trace: ././.lake/packages/mathlib> git fetch --tags --force origin
error: ././.lake/packages/mathlib/lakefile.lean:35:40: error: unexpected token ']'; expected term
error: ././.lake/packages/mathlib/lakefile.lean:45:38: error: unexpected token ']'; expected term
error: ././.lake/packages/mathlib/lakefile.lean:64:17: error: unknown identifier 'mathlibLeanOptions'
error: ././.lake/packages/mathlib/lakefile.lean:75:17: error: unknown identifier 'mathlibLeanOptions'
error: ././.lake/packages/mathlib/lakefile.lean:78:17: error: unknown identifier 'mathlibLeanOptions'
error: ././.lake/packages/mathlib/lakefile.lean:143:5: error: invalid field 'baseName', the environment does not contain 'Lake.Package.baseName'
  rootPkg
has type
  Package
error: ././.lake/packages/mathlib/lakefile.lean:143:24: error: invalid field 'baseName', the environment does not contain 'Lake.NPackage.baseName'
  pkg
has type
  NPackage _package.name
error: ././.lake/packages/mathlib/lakefile.lean:149:34: error: invalid field 'trimAscii', the environment does not contain 'String.trimAscii'
  toolchainContent
has type
  String
error: ././.lake/packages/mathlib/lakefile.lean:170:16: error: invalid field 'baseName', the environment does not contain 'Lake.NPackage.baseName'
  pkg
has type
  NPackage _package.name
error: ././.lake/packages/mathlib/lakefile.lean:151:13: error: invalid field 'trimAscii', the environment does not contain 'String.trimAscii'
  toolchainContent
has type
  String
error: ././.lake/packages/mathlib/lakefile.lean:153:29: error: invalid field notation, type is not of the form (C ...) where C is a constant
  toolchainVersion
has type
  ?m.3835 pkg rootPkg y✝ __do_lift✝ toolchainContent
error: ././.lake/packages/mathlib/lakefile.lea

… (truncated)