{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:L3UR3W5K47AC3RMRDHUUVRU7GZ","short_pith_number":"pith:L3UR3W5K","schema_version":"1.0","canonical_sha256":"5ee91ddbaae7c02dc59119e94ac69f36603c50f0219e0a3ee0db76a615785a2d","source":{"kind":"arxiv","id":"1106.1759","version":1},"attestation_state":"computed","paper":{"title":"The Freeness and Minimal Free Resolutions of Modules of Differential Operators of a Generic Hyperplane Arrangement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Go Okuyama, Mutsumi Saito, Norihiro Nakashima","submitted_at":"2011-06-09T09:45:43Z","abstract_excerpt":"Let A be a generic hyperplane arrangement composed of r hyperplanes in an n-dimensional vector space, and S the polynomial ring in n variables. We consider the S-submodule D(m)(A) of the nth Weyl algebra of homogeneous differential operators of order m preserving the defining ideal of A.\n  We prove that if n \\geq 3, r > n,m > r - n + 1, then D(m)(A) is free (Holm's conjecture). Combining this with some results by Holm, we see that D(m)(A) is free unless n \\geq 3, r > n,m < r - n + 1. In the remaining case, we construct a minimal free resolution of D(m)(A) by generalizing Yuzvinsky's constructi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1106.1759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-09T09:45:43Z","cross_cats_sorted":[],"title_canon_sha256":"8640f79c36813cd051d4068c6001eacc02489b0d760673eae5485b4e7b83d3cf","abstract_canon_sha256":"84c8fd1262dd5845415d7f50381a6fcd40960266acfbb71e81c67807fb56c4a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:15.187022Z","signature_b64":"HNqwFmoxBBOlovjA6CMjHpa3sIEqYjvwlBpzef1bBftR8wE3nD2vVuv58WZh+hxyfzHvfL3xNeOmHvIHSEGgBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ee91ddbaae7c02dc59119e94ac69f36603c50f0219e0a3ee0db76a615785a2d","last_reissued_at":"2026-05-18T04:20:15.186490Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:15.186490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Freeness and Minimal Free Resolutions of Modules of Differential Operators of a Generic Hyperplane Arrangement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Go Okuyama, Mutsumi Saito, Norihiro Nakashima","submitted_at":"2011-06-09T09:45:43Z","abstract_excerpt":"Let A be a generic hyperplane arrangement composed of r hyperplanes in an n-dimensional vector space, and S the polynomial ring in n variables. We consider the S-submodule D(m)(A) of the nth Weyl algebra of homogeneous differential operators of order m preserving the defining ideal of A.\n  We prove that if n \\geq 3, r > n,m > r - n + 1, then D(m)(A) is free (Holm's conjecture). Combining this with some results by Holm, we see that D(m)(A) is free unless n \\geq 3, r > n,m < r - n + 1. In the remaining case, we construct a minimal free resolution of D(m)(A) by generalizing Yuzvinsky's constructi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1759","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1106.1759","created_at":"2026-05-18T04:20:15.186610+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.1759v1","created_at":"2026-05-18T04:20:15.186610+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1759","created_at":"2026-05-18T04:20:15.186610+00:00"},{"alias_kind":"pith_short_12","alias_value":"L3UR3W5K47AC","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"L3UR3W5K47AC3RMR","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"L3UR3W5K","created_at":"2026-05-18T12:26:34.985390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L3UR3W5K47AC3RMRDHUUVRU7GZ","json":"https://pith.science/pith/L3UR3W5K47AC3RMRDHUUVRU7GZ.json","graph_json":"https://pith.science/api/pith-number/L3UR3W5K47AC3RMRDHUUVRU7GZ/graph.json","events_json":"https://pith.science/api/pith-number/L3UR3W5K47AC3RMRDHUUVRU7GZ/events.json","paper":"https://pith.science/paper/L3UR3W5K"},"agent_actions":{"view_html":"https://pith.science/pith/L3UR3W5K47AC3RMRDHUUVRU7GZ","download_json":"https://pith.science/pith/L3UR3W5K47AC3RMRDHUUVRU7GZ.json","view_paper":"https://pith.science/paper/L3UR3W5K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.1759&json=true","fetch_graph":"https://pith.science/api/pith-number/L3UR3W5K47AC3RMRDHUUVRU7GZ/graph.json","fetch_events":"https://pith.science/api/pith-number/L3UR3W5K47AC3RMRDHUUVRU7GZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L3UR3W5K47AC3RMRDHUUVRU7GZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L3UR3W5K47AC3RMRDHUUVRU7GZ/action/storage_attestation","attest_author":"https://pith.science/pith/L3UR3W5K47AC3RMRDHUUVRU7GZ/action/author_attestation","sign_citation":"https://pith.science/pith/L3UR3W5K47AC3RMRDHUUVRU7GZ/action/citation_signature","submit_replication":"https://pith.science/pith/L3UR3W5K47AC3RMRDHUUVRU7GZ/action/replication_record"}},"created_at":"2026-05-18T04:20:15.186610+00:00","updated_at":"2026-05-18T04:20:15.186610+00:00"}