{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:NB3LFBF7ALYCUWWGCRFNZEYCET","short_pith_number":"pith:NB3LFBF7","schema_version":"1.0","canonical_sha256":"6876b284bf02f02a5ac6144adc930224dc11d67cb0cbce6784962433af567f24","source":{"kind":"arxiv","id":"math/0612739","version":3},"attestation_state":"computed","paper":{"title":"The Euler multiplicity and addition-deletion theorems for multiarrangements","license":"","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.CV","authors_text":"Hiroaki Terao, Max Wakefield, Takuro Abe","submitted_at":"2006-12-23T09:34:12Z","abstract_excerpt":"The addition-deletion theorems for hyperplane arrangements, which were originally shown in [H. Terao, Arrangements of hyperplanes and their freeness I, II. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980), 293--320], provide useful ways to construct examples of free arrangements. In this article, we prove addition-deletion theorems for multiarrangements. A key to the generalization is the definition of a new multiplicity, called the Euler multiplicity, of a restricted multiarrangement. We compute the Euler multiplicities in many cases. Then we apply the addition-deletion theorems to various a"},"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":"math/0612739","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"2006-12-23T09:34:12Z","cross_cats_sorted":["math.AG","math.CO"],"title_canon_sha256":"b9a440e433d1629a7455e494df6073b7cf8921ba40baaf222960898c362506a6","abstract_canon_sha256":"356bb94b966f9e6ac50678fc07a50034ee23db32b06a491b24d67da6453384b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:45.338517Z","signature_b64":"IilqjCYC7r21qidJkrRrjMWt1ARc8GuD5Oetu8g2Ze7ux8Ti1qzNOdlSX0lJUIJypE4Uo8ObF8xH8Q5XtpcJDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6876b284bf02f02a5ac6144adc930224dc11d67cb0cbce6784962433af567f24","last_reissued_at":"2026-05-18T02:57:45.338002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:45.338002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Euler multiplicity and addition-deletion theorems for multiarrangements","license":"","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.CV","authors_text":"Hiroaki Terao, Max Wakefield, Takuro Abe","submitted_at":"2006-12-23T09:34:12Z","abstract_excerpt":"The addition-deletion theorems for hyperplane arrangements, which were originally shown in [H. Terao, Arrangements of hyperplanes and their freeness I, II. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980), 293--320], provide useful ways to construct examples of free arrangements. In this article, we prove addition-deletion theorems for multiarrangements. A key to the generalization is the definition of a new multiplicity, called the Euler multiplicity, of a restricted multiarrangement. We compute the Euler multiplicities in many cases. Then we apply the addition-deletion theorems to various a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612739","kind":"arxiv","version":3},"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":"math/0612739","created_at":"2026-05-18T02:57:45.338079+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0612739v3","created_at":"2026-05-18T02:57:45.338079+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612739","created_at":"2026-05-18T02:57:45.338079+00:00"},{"alias_kind":"pith_short_12","alias_value":"NB3LFBF7ALYC","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"NB3LFBF7ALYCUWWG","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"NB3LFBF7","created_at":"2026-05-18T12:25:54.717736+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/NB3LFBF7ALYCUWWGCRFNZEYCET","json":"https://pith.science/pith/NB3LFBF7ALYCUWWGCRFNZEYCET.json","graph_json":"https://pith.science/api/pith-number/NB3LFBF7ALYCUWWGCRFNZEYCET/graph.json","events_json":"https://pith.science/api/pith-number/NB3LFBF7ALYCUWWGCRFNZEYCET/events.json","paper":"https://pith.science/paper/NB3LFBF7"},"agent_actions":{"view_html":"https://pith.science/pith/NB3LFBF7ALYCUWWGCRFNZEYCET","download_json":"https://pith.science/pith/NB3LFBF7ALYCUWWGCRFNZEYCET.json","view_paper":"https://pith.science/paper/NB3LFBF7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0612739&json=true","fetch_graph":"https://pith.science/api/pith-number/NB3LFBF7ALYCUWWGCRFNZEYCET/graph.json","fetch_events":"https://pith.science/api/pith-number/NB3LFBF7ALYCUWWGCRFNZEYCET/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NB3LFBF7ALYCUWWGCRFNZEYCET/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NB3LFBF7ALYCUWWGCRFNZEYCET/action/storage_attestation","attest_author":"https://pith.science/pith/NB3LFBF7ALYCUWWGCRFNZEYCET/action/author_attestation","sign_citation":"https://pith.science/pith/NB3LFBF7ALYCUWWGCRFNZEYCET/action/citation_signature","submit_replication":"https://pith.science/pith/NB3LFBF7ALYCUWWGCRFNZEYCET/action/replication_record"}},"created_at":"2026-05-18T02:57:45.338079+00:00","updated_at":"2026-05-18T02:57:45.338079+00:00"}