Published paper
Role in dependence graphs
Proof-critical source
Winning property of counterexamples to Uniform Littlewood's Conjecture
This paper is included only for the following marked statement:
- Proposition 3.1 · VOR pp. 210–216, with Proposition 3.3 and §§3.4–3.5Constructs the increasing measurable partition subordinate to global unstable disks reused by Ledrappier–Young.
AI-generated audit
Audit summary
Not a correctness certificate. These reports do not replace expert scrutiny or formal verification.
Exact reviewed source
Cambridge version of record · Ergodic Theory and Dynamical Systems 2 (1982), 203–219
François Ledrappier and Jean-Marie Strelcyn. A proof of the estimation from below in Pesin's entropy formula. Ergodic Theory and Dynamical Systems 2 (1982), 203–219.
Open audited source ↗01Statements1 reported findingNo statement issues found
Proposition 3.1 constructs the measurable increasing partition subordinate to unstable disks that Ledrappier–Young reuses.
Proposition 3.1No issue found
A measurable partition can be made increasing and subordinate to global unstable leaves
Version of record pp. 210–216 · Proposition 3.1, Proposition 3.3, and §§ 3.4–3.5
Under the full-positive-unstable-dimension hypothesis, Proposition 3.1 produces an increasing measurable partition whose atoms contain neighborhoods inside global unstable leaves, exhaust those leaves under backward iterates, generate the ambient sigma-algebra, and admit measurable leaf volume. Ledrappier–Young's Lemma 3.1.1 explicitly reuses this disk-family construction for its subordinate partition.
02Proofs2 reported findingsNo proof issues found
The measurable-partition argument is complete once the explicitly cited invariant-manifold chapter is treated as a terminal monograph source.
Proposition 3.1 proofCorrect and complete with explicit imported input
The local-disk family yields subordination, exhaustion, and generation
Version of record pp. 211–216 · Propositions 3.2–3.3 and §§ 3.4–3.5
Proposition 3.2 supplies the radius-selection estimate. Proposition 3.3 gives uniform closed regular blocks and continuous local unstable disks. Sections 3.4–3.5 choose an admissible radius, form the leafwise partition, prove local subordination using contraction and Borel–Cantelli, establish exhaustion and separation under iterates, and extend the construction across countably many invariant components. The deductions from Proposition 3.3 are coherent.
Terminal source boundaryClosed at published-book terminals
The regular disk family comes from Katok–Strelcyn's invariant-manifold monograph chapter
Version of record p. 212 · Proposition 3.3 cites §§ 6–7 of Katok–Strelcyn's 1980 preprint; published form: Lecture Notes in Mathematics 1222 (1986), pp. 1–40, DOI 10.1007/BFb0099032
The paper explicitly derives Proposition 3.3 from the results and proofs of §§ 6–7 of the cited preprint, later published as the Part I invariant-manifold chapter in Katok–Strelcyn's Lecture Notes in Mathematics 1222. That exact chapter is a terminal monograph source for this graph. The remaining entropy theorem, Hopf argument, and other cited papers are not required for the selected disk-family construction.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.