Proof-critical dependence graph
Bernstein inequality and holonomic modules
Bounded statement-restricted first-order citation graph for arXiv:1501.01260v4. It has one focal node and fourteen selected direct ancestor nodes. It is not a full recursive closure: selected source proof citations are unexpanded/unverified, and superseded Gies is excluded because the focal manuscript re-proves its lemma. It does not repair T1.1.
Graph scope15 nodes23 proof-critical linksChecked August 31, 2026
Oriented proof graph
Dependence map
Arrows point from a prerequisite toward the paper whose marked statement uses it.
- Solid arrow: headline proof lineage
- Dashed arrow: a separately marked side or appendix claim
- Dashed square: a terminal book
Hover over, or focus, a square to see its full citation.
Every visible arrow is documented in the evidence ledger below. A non-book leaf means that no earlier proof-critical source was identified for the marked statement—not that the paper has no other citations.
Evidence ledger
Proof-critical links
Poisson traces and D-modules on Poisson varieties→Bernstein inequality and holonomic modulesHeadline lineageSource link partially checked
Completion flatness is explicitly cited in the focal setup.
Citation location: Focal arXiv:1501.01260v4 §2.4 p. 7; [L3, Lemma A.2].- Lemma 3.7Imported-input step in the unsupported T1.1 route.
Poisson traces and D-modules on Poisson varieties→Bernstein inequality and holonomic modulesHeadline lineageSource link partially checked
Corollary 3.19 supplies selected slice finiteness.
Citation location: Focal Lemma 3.7 p. 9; [ES, Cor. 3.19].- Lemma 3.7Imported-input step in the unsupported T1.1 route.
Quantized symplectic actions and W-algebras→Bernstein inequality and holonomic modulesHeadline lineageSource link partially checked
Selected ideal tensor-factorization input.
Citation location: Focal Lemma 3.7 p. 9; [Wquant, Lemma 3.4.3].- Lemma 3.7Imported-input step in the unsupported T1.1 route.
Finite dimensional representations of W-algebras→Bernstein inequality and holonomic modulesHeadline lineageSource link partially checked
Closedness input for Euler stability.
Citation location: Focal Lemma 3.7 p. 9; [HC, Lemma 2.4.4].- Lemma 3.7Imported-input step in the unsupported T1.1 route.
Completions of symplectic reflection algebras→Bernstein inequality and holonomic modulesAncillary claimSource link partially checked
Comparison citation near P3.8, whose proof is supplied in the focal manuscript.
Citation location: Focal P3.8 p. 10; [sraco, Prop. 3.7.2].Verification note: Not a proof-critical P3.8 edge.- SRA completion comparisonContextual compare-with citation; focal paper supplies its own Proposition 3.8 proof.
Completions of symplectic reflection algebras→Bernstein inequality and holonomic modulesHeadline lineageSource link partially checked
Restriction/right-adjoint route in the independent RCA proof.
Citation location: Focal §4.1 pp. 12–14; [sraco, §3.6].- Theorem 1.3(iii)Rational-Cherednik sufficient conditions.
The integrability of the characteristic variety→Bernstein inequality and holonomic modulesHeadline lineageSource chain not fully resolved
Unresolved formal involutivity use.
Citation location: Focal Cor. 3.4 p. 8; [Ga].- Corollary 3.4Formal coisotropicity step.
The integrability of the characteristic variety→Bernstein inequality and holonomic modulesAncillary claimSource chain not fully resolved
Unresolved appendix involutivity use.
Citation location: Focal Appendix p. 17; [Ga].- Appendix Lemma 5.2Localization holonomicity comparison with repairable errors.
Quantizations of conical symplectic resolutions I: local and global structure→Bernstein inequality and holonomic modulesAncillary claimSource link partially checked
Conical-resolution setup citation, not T1.3(i) proof support.
Citation location: Focal §2.2 pp. 4–5; [BPW, §2].Verification note: Contextual role only.- BPW conical-resolution setupContextual definition/setup citation; not asserted as proof support for T1.3(i).
Quantizations of conical symplectic resolutions I: local and global structure→Bernstein inequality and holonomic modulesHeadline lineageSource link partially checked
Localization input in §4.3.
Citation location: Focal §4.3 pp. 15–16; [BPW, §5/§5.3].- Theorem 1.3(i)Conical-resolution sufficient conditions.
Quantizations of conical symplectic resolutions I: local and global structure→Bernstein inequality and holonomic modulesHeadline lineageSource link partially checked
Opposite-reduction input.
Citation location: Focal §2.3 p. 5 and §4.2 p. 15; [BPW, Lemma 3.14].- Theorem 1.3(ii)Hamiltonian-reduction regular-bimodule finite length.
Quantizations of conical symplectic resolutions I: local and global structure→Bernstein inequality and holonomic modulesHeadline lineageSource link partially checked
HC translation-bimodule input.
Citation location: Focal §4.3 p. 16; [BPW, §6.1].- Theorem 1.3(i)Conical-resolution sufficient conditions.
Fundamental groups of symplectic singularities→Bernstein inequality and holonomic modulesHeadline lineageSource link partially checked
Leafwise use of finite pi-one theorem; transfer unresolved.
Citation location: Focal §4.3 p. 15; [Namikawa_fund].Verification note: Exact statement located; leafwise applicability unresolved.- Theorem 1.3(i)Conical-resolution sufficient conditions.
Symplectic singularities from the Poisson point of view→Bernstein inequality and holonomic modulesHeadline lineageSource link partially checked
Finite-leaf structure input.
Citation location: Focal §2.2 p. 4; [Kaledin].- Theorem 1.3(i)Conical-resolution sufficient conditions.
Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism→Bernstein inequality and holonomic modulesHeadline lineageSource link partially checked
PBW source in RCA setup.
Citation location: Focal §2.4 p. 6; [EG, Thm. 1.3].- Theorem 1.3(iii)Rational-Cherednik sufficient conditions.
On the category O for rational Cherednik algebras→Bernstein inequality and holonomic modulesHeadline lineageSource link partially checked
Highest-weight/projective source in RCA branch.
Citation location: Focal §§2.4,4.1; [GGOR, Thm. 2.19].- Theorem 1.3(iii)Rational-Cherednik sufficient conditions.
On the category O for rational Cherednik algebras→Bernstein inequality and holonomic modulesHeadline lineageSource link partially checked
Finite-length source in RCA branch.
Citation location: Focal §§2.4,4.1; [GGOR, Cor. 2.16].- Theorem 1.3(iii)Rational-Cherednik sufficient conditions.
Normality of Marsden-Weinstein reductions for representations of quivers→Bernstein inequality and holonomic modulesAncillary claimSource link partially checked
Quiver-specific compare-with citation, not T1.3(ii) proof support.
Citation location: Focal §2.3 p. 5; [CB_norm, §4].Verification note: The scope boundary is explicitly retained.- Crawley–Boevey comparisonContextual compare-with citation; not asserted as proof support for T1.3(ii).
Isomorphisms of quantizations via quantization of resolutions→Bernstein inequality and holonomic modulesAncillary claimSource link partially checked
Parameter setup citation, not a theorem parent.
Citation location: Focal §2.2 p. 4; [quant, §2].Verification note: Contextual role only.- Quantization parameter setupConceptual parameter and opposite-parameter setup, not a standalone theorem parent.
Isomorphisms of quantizations via quantization of resolutions→Bernstein inequality and holonomic modulesAncillary claimSource link partially checked
Opposite-parameter setup citation, not a theorem parent.
Citation location: Focal §2.2 p. 5; [quant, §2.3].Verification note: Contextual role only.- Quantization parameter setupConceptual parameter and opposite-parameter setup, not a standalone theorem parent.
Isomorphisms of quantizations via quantization of resolutions→Bernstein inequality and holonomic modulesAncillary claimSource link partially checked
Special Gamma-n spherical SRA result, not general T1.3(iii) proof support.
Citation location: Focal Remark:SRA p. 16; [quant, §6.2, Thm. 6.2.1].Verification note: Coverage boundary retained.- Special spherical SRA remarkSpecial Gamma-n case; not proof support for general T1.3(iii).
Kempf–Ness stratification.
Citation location: Focal Prop. 4.1 p. 14; [PV, §5.6].- Theorem 1.3(ii)Hamiltonian-reduction regular-bimodule finite length.
Representation theory and complex geometry→Bernstein inequality and holonomic modulesAncillary claimSource-chain endpoint
Isotropic-subvariety criterion.
Citation location: Focal Appendix p. 17; [Chriss_Ginzburg, Prop. 1.3.30].- Appendix Lemma 5.1Isotropicity comparison with repairable errors.