A Cubical Library for Analytic Continuation: Identity and Monodromy Theorems Constructively

This paper specifies and partially formalises a Cubical Agda library Cubical.Analysis.HolomorphicFunctions for constructive analytic continuation, targeting Gates 2 and 4 of the Volume II RH roadmap. We give explicit type-theoretic definitions of holomorphic functions, power series, and analytic continuation over the cubical Cauchy complex numbers \(C_c = R_c R_c\), where \(R_c\) is the higher inductive--inductive type (HIIT) of Cauchy reals from Booij and from Volume II Part II vol2partII\@. Five numbered statements are advanced: (i) density of dyadic rationals in \(C_c\); (ii) a constructive…

Lean 4 Proof Verdict

# Lean proof verdict — oq2-cubical-analytic-continuation

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

## Pre-verification `lake build` output

```
info: oq2-cubical-analytic-continuation: 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/mathli

… (truncated)