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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:
- Theorem C · Annals pp. 540–545; proof Sections 9–11Metric entropy decomposes as Lyapunov exponents times transverse conditional dimensions.
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Version of record · Annals of Mathematics 122 (1985), no. 3, 540–574
François Ledrappier and Lai-Sang Young. The metric entropy of diffeomorphisms. Part II: Relations between entropy, exponents and dimension. Annals of Mathematics 122 (1985), no. 3, 540–574.
Open audited source ↗01Statements1 reported findingNo statement issues found
The selected Ledrappier–Young entropy formula is correct.
Theorem CNo issue found
Metric entropy decomposes into Lyapunov exponents times conditional dimensions
Annals pp. 540–545 and Sections 9–11 · Theorem C
For the increasing unstable foliations, Theorem C identifies each partial-entropy increment with the corresponding Lyapunov exponent times the transverse conditional dimension. Summing gives the formula used in EK03 Corollary 7.2.
02Proofs2 reported findingsNo proof issues found
The partial-entropy comparison and transverse-dimension argument prove Theorem C, with explicitly identified inputs from Part I.
Proof of Theorem CNo issue found in the reviewed proof
Each Lyapunov layer contributes exactly its conditional-dimension increment
Annals pp. 556–570 · Sections 9–11
Section 9 handles the terminal partial entropy using Part I. Sections 10–11 compare Bowen-like plaques at adjacent Lyapunov scales and prove both inequalities for each entropy increment. The nested conditional measures and distortion estimates have the needed uniformity on Pesin blocks.
Part I dependencyCorrect source use
The Part I import is Proposition 5.1 and Corollary 5.3, not the broader Part I Theorems A–B
VOR p. 543 · Corollary 7.2.2; pp. 556–557 · Section 9; pp. 568–570 · Proposition 11.2 and proof of Theorem C
Corollary 7.2.2 explicitly combines Part I Section 5 with the Section 9 discussion to obtain , and its proof names Part I Corollary 5.3. Proposition 11.2 then revisits the Part I Proposition 5.1 argument at each Lyapunov layer. The graph therefore selects only Proposition 5.1 and Corollary 5.3 and recursively represents their actual source inputs; the Ruelle-inequality and Pesin-formula branches for Part I Theorems A–B are not needed here.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.