{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6BDVPNGUSQXGGAY3COOMAQMFP6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3fbc3d157fc2a940d2dd3e45c55f5563821f555a1422551f1d45aa59a87f1714","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-01-17T18:57:44Z","title_canon_sha256":"874ad19d02e0dce52066ad3607c97f092ea3b7f14dcbfda465cb8db8d45f459f"},"schema_version":"1.0","source":{"id":"1201.3594","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3594","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3594v4","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3594","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"pith_short_12","alias_value":"6BDVPNGUSQXG","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6BDVPNGUSQXGGAY3","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6BDVPNGU","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:0cc857f02b20f2e331281399d9581a8d815d5fdd15b9af3bb6eb510e006398ae","target":"graph","created_at":"2026-05-18T01:37:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we prove that the Bernstein-Sato polynomial of any free divisor for which the $D[s]$-module $D[s] h^s$ admits a Spencer logarithmic resolution satisfies the symmetry property $b(-s-2) = \\pm b(s)$. This applies in particular to locally quasi-homogeneous free divisors (for instance, to free hyperplane arrangements), or more generally, to free divisors of linear Jacobian type. We also prove that the Bernstein-Sato polynomial of an integrable logarithmic connection $E$ and of its dual $E^*$ with respect to a free divisor of linear Jacobian type are related by the equality $b_{E}(s)=\\","authors_text":"Luis Narv\\'aez Macarro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-01-17T18:57:44Z","title":"A duality approach to the symmetry of Bernstein-Sato polynomials of free divisors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3594","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:99a6f1b15c2bed504907fc34ae424b182fbe3c34f413a8626c5fea2ae2c3ff07","target":"record","created_at":"2026-05-18T01:37:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3fbc3d157fc2a940d2dd3e45c55f5563821f555a1422551f1d45aa59a87f1714","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-01-17T18:57:44Z","title_canon_sha256":"874ad19d02e0dce52066ad3607c97f092ea3b7f14dcbfda465cb8db8d45f459f"},"schema_version":"1.0","source":{"id":"1201.3594","kind":"arxiv","version":4}},"canonical_sha256":"f04757b4d4942e63031b139cc041857faaf8d409a8320ac557f9b6b33c551f18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f04757b4d4942e63031b139cc041857faaf8d409a8320ac557f9b6b33c551f18","first_computed_at":"2026-05-18T01:37:51.577152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:51.577152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yTCvBX19oG7S6qg9iD59sHV5Me3VjR/74S4nH2eg53+Zel7dCJ6CRAJojYCAZSSIFEE8s2vhpEPkFW9H2wgJCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:51.577866Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3594","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99a6f1b15c2bed504907fc34ae424b182fbe3c34f413a8626c5fea2ae2c3ff07","sha256:0cc857f02b20f2e331281399d9581a8d815d5fdd15b9af3bb6eb510e006398ae"],"state_sha256":"890bbc090288979406e3be0771a31ffbcb49d310d038594b02bc46afa4c9ea49"}