Published paper
Abstract
Selected proof-dependency source recorded for the bounded audit of arXiv:1501.01260v4.
Role in dependence graphs
Proof-critical source
Bernstein inequality and holonomic modules
This paper is included only for the following marked statements:
- Appendix A Lemma A.2 · arXiv:0908.3868v4, PDF p. 23Completion exactness/flatness.
- Corollary 3.19 · arXiv:0908.3868v4, PDF p. 13Formal finiteness input.
AI-generated audit
Audit summary
Not a correctness certificate. These reports do not replace expert scrutiny or formal verification.
Exact reviewed source
Frozen exact arXiv:0908.3868v4
Poisson traces and D-modules on Poisson varieties
The exact versioned arXiv PDF was frozen and inspected because publisher full text was not acquired for this review. It is a fallback, not a claimed version of record.
Open audited source ↗01Statements2 reported findingsSuspected unsupported statements
Selected claim text and its focal use were checked in the frozen exact versioned source. The source proofs and antecedent citations are outside this bounded first-order shell, so no selected claim is certified merely from its locator.
Claim content and focal mappingStatement located; proof closure not independently verified
Corollary 3.19
arXiv:0908.3868v4, Corollary 3.19, PDF p. 13; Focal arXiv:1501.01260v4, §2.4 and Lemma 3.7 proof, PDF pp. 7–9.
The selected corollary is the formal-deformation finiteness result invoked for the completed slice module. Losev uses it only after passing to the completed slice setting in Lemma 3.7; this audit does not extend it to arbitrary Poisson modules or reprove its deformation hypotheses. The audit verifies this statement-to-focal-role mapping only; it does not certify the source proof or any unexpanded antecedent.
Official arXiv:0908.3868v4 ↗Claim content and focal mappingStatement located; proof closure not independently verified
Appendix A, Lemma A.2
arXiv:0908.3868v4, Appendix A, Lemma A.2, PDF p. 23; Focal arXiv:1501.01260v4, §2.4 and Lemma 3.7 proof, PDF pp. 7–9.
The selected appendix lemma supplies exactness and flatness for the completion operation used in the focal completed local algebra. The focal completion notation is matched only at that local step; no general equivalence of every completion formalism is asserted. The audit verifies this statement-to-focal-role mapping only; it does not certify the source proof or any unexpanded antecedent.
Official arXiv:0908.3868v4 ↗02Proofs1 reported findingFurther proof verification needed
The selected proof route is bounded: the source's own proof dependencies have not been recursively closed in this audit.
Proof boundaryProof closure not independently verified
No recursive closure is claimed
Focal arXiv:1501.01260v4, §2.4 and Lemma 3.7 proof, PDF pp. 7–9.
The selected source proofs and their antecedent citations are not recursively audited.
Frozen exact arXiv:0908.3868v4 ↗03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.