pith. sign in

arxiv: 2605.06674 · v1 · submitted 2026-04-21 · 🧮 math.AG · math.LO

Corrigendum to `Evaluation of motivic functions, non-nullity, and integrability in fibers', Advances in Mathematics, Vol. 409, Part A, Paper No. 108635, 29 pages, doi:10.1016/j.aim.2022.108635 (2022)

Raf Cluckers , Immanuel Halupczok This is my paper

Pith reviewed 2026-05-11 01:11 UTC · model grok-4.3

classification 🧮 math.AG math.LO
keywords motivic functionsnon-nullityintegrabilityfiberscorrigendumevaluationalgebraic geometry
0
0 comments X

The pith

Corrections to two auxiliary propositions on motivic functions allow the main integrability and non-nullity theorems to hold after proof adjustments.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper corrects the statements and proofs of Propositions 4.1 and 4.2 from the authors' earlier work on the evaluation of motivic functions, non-nullity, and integrability in fibers. It then details how the arguments for the primary results can be modified to rely on these updated propositions instead. A sympathetic reader cares because these auxiliary statements form the technical backbone for the claims about integrability and non-nullity, so fixing them preserves the overall conclusions without requiring a full rewrite of the theory.

Core claim

The central claim is that after correcting the statements and proofs of the auxiliary Propositions 4.1 and 4.2, the proofs of the main results can be adapted to work with the corrected versions, thereby maintaining the validity of the theorems on the evaluation of motivic functions, non-nullity, and integrability in fibers.

What carries the argument

The corrected Propositions 4.1 and 4.2, which handle evaluation of motivic functions along with non-nullity and integrability properties in fibers, and the adaptation steps that replace their use in the original main proofs.

If this is right

  • The main theorems on non-nullity of motivic functions in fibers continue to hold.
  • Integrability statements in fibers remain valid under the adapted proofs.
  • The overall framework for evaluating motivic functions requires only local fixes rather than global revision.
  • Related applications that relied on the original propositions can be updated via the same adaptation method.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The robustness of the main results to these corrections suggests the theory is stable against small technical errors in auxiliary statements.
  • Authors working on similar motivic integration results in algebraic geometry might benefit from applying comparable self-correction checks to their own auxiliary propositions.
  • Independent verification of the corrected propositions could be done by specializing to concrete cases such as specific varieties or functions over finite fields.

Load-bearing premise

That the corrections to Propositions 4.1 and 4.2 are accurate enough to let the main results' proofs be adapted without introducing new errors or gaps.

What would settle it

A specific fiber or motivic function where one of the corrected propositions fails to hold would show that the adaptation cannot preserve the main theorems.

read the original abstract

We correct the statements and proofs of the (auxiliary) Propositions 4.1 and 4.2 of our paper `Evaluation of motivic functions, non-nullity, and integrability in fibers' in Advances in Mathematics, Vol. 409, Part A, Paper No. 108635, 29 pages (2022), and we explain how the proofs of the main results can be adapted to work with those corrected propositions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 0 minor

Summary. This corrigendum corrects the statements and proofs of the auxiliary Propositions 4.1 and 4.2 from the authors' 2022 paper 'Evaluation of motivic functions, non-nullity, and integrability in fibers' (Advances in Mathematics, Vol. 409, Part A, Paper No. 108635) and explains the adaptations required for the proofs of the main results to remain valid with the corrected propositions.

Significance. If the corrections to the auxiliary propositions are accurate and the adaptations are complete, the corrigendum preserves the validity of the original results on motivic functions, non-nullity, and integrability in fibers. This is important for maintaining the reliability of published work in motivic integration and algebraic geometry, as the auxiliary results underpin the main theorems.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the corrigendum and for recommending acceptance. The report accurately summarizes the purpose of the note, which is to correct the statements and proofs of the auxiliary Propositions 4.1 and 4.2 while confirming that the main theorems remain valid after the necessary adaptations.

Circularity Check

0 steps flagged

Corrigendum provides direct corrections; self-reference is contextual only

full rationale

The document is a corrigendum that explicitly corrects the statements and proofs of auxiliary Propositions 4.1 and 4.2 from the authors' 2022 paper and states how the main results' proofs can be adapted. No derivation chain is presented that reduces a claimed prediction or uniqueness result to a fitted input or unverified self-citation by construction. The reference to the prior paper serves only to identify the corrected statements; the corrigendum itself supplies the fixes and adaptation outline without invoking any load-bearing theorem from the same authors as external justification. This is a standard, transparent self-correction with no circularity in the sense of the enumerated patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No new parameters, axioms or entities are introduced; the focus is on correcting existing mathematical statements.

pith-pipeline@v0.9.0 · 5412 in / 916 out tokens · 37122 ms · 2026-05-11T01:11:22.334357+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

  1. [1]

    Cluckers and I

    R. Cluckers and I. Halupczok,Evaluation of motivic functions, non-nullity, and integra- bility in fibers, Adv. Math.409(2022), Paper No. 108635

    work page 2022

  2. [2]

    Cluckers and F

    R. Cluckers and F. Loeser,Constructible motivic functions and motivic integration, In- ventiones Mathematicae173(2008), no. 1, 23–121

    work page 2008

  3. [3]

    ,Constructible exponential functions, motivic Fourier transform and transfer prin- ciple, Annals of Mathematics171(2010), 1011–1065. Univ. Lille, CNRS, UMR 8524 - Laboratoire Paul Painlevé, F-59000 Lille, France, and KU Leuven, Department of Mathematics, B-3001 Leuven, Belgium Email address:Raf.Cluckers@univ-lille.fr URL:http://rcluckers.perso.math.cnrs.f...

    work page 2010