{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:CJFDZKT23MYMZAFGD43DYHKNVL","short_pith_number":"pith:CJFDZKT2","schema_version":"1.0","canonical_sha256":"124a3caa7adb30cc80a61f363c1d4daae8c7b01c61778abca22082dfa4aff238","source":{"kind":"arxiv","id":"1908.06885","version":2},"attestation_state":"computed","paper":{"title":"Addition-deletion results for the minimal degree of logarithmic derivations of arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Alexandru Dimca, Gabriel Sticlaru, Takuro Abe","submitted_at":"2019-08-19T15:42:18Z","abstract_excerpt":"We study the change of the minimal degree of a logarithmic derivation of a hyperplane arrangement under the addition or the deletion of a hyperplane, and give a number of applications. First, we prove the existence of Tjurina maximal line arrangements in a lot of new situations. Then, starting with Ziegler's example of a pair of arrangements of $d=9$ lines with $n_3=6$ triple points in addition to some double points, having the same combinatorics, but distinct minimal degree of a logarithmic derivation, we construct new examples of such pairs, for any number $d\\geq 9$ of lines, and any number "},"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":"1908.06885","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-19T15:42:18Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"532ed422e107f9688ed2c3f606ca45d14fdde39ac33f97ccfed614f9f2b98fe1","abstract_canon_sha256":"7c0af72a719c5ab64b62369f70e6ebf760689f35cb65027d27efe762789085af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:04:43.978288Z","signature_b64":"7rlV4T0EasmQE7Seq8n5+KaJQG2V9NN+6gsS5JW2cBsb+Z8i6Qr9VMhyMObMQRjJ3ytXLPKGuUWEs5OrTnEVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"124a3caa7adb30cc80a61f363c1d4daae8c7b01c61778abca22082dfa4aff238","last_reissued_at":"2026-07-05T00:04:43.977879Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:04:43.977879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Addition-deletion results for the minimal degree of logarithmic derivations of arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Alexandru Dimca, Gabriel Sticlaru, Takuro Abe","submitted_at":"2019-08-19T15:42:18Z","abstract_excerpt":"We study the change of the minimal degree of a logarithmic derivation of a hyperplane arrangement under the addition or the deletion of a hyperplane, and give a number of applications. First, we prove the existence of Tjurina maximal line arrangements in a lot of new situations. Then, starting with Ziegler's example of a pair of arrangements of $d=9$ lines with $n_3=6$ triple points in addition to some double points, having the same combinatorics, but distinct minimal degree of a logarithmic derivation, we construct new examples of such pairs, for any number $d\\geq 9$ of lines, and any number "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06885","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06885/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.06885","created_at":"2026-07-05T00:04:43.977937+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.06885v2","created_at":"2026-07-05T00:04:43.977937+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06885","created_at":"2026-07-05T00:04:43.977937+00:00"},{"alias_kind":"pith_short_12","alias_value":"CJFDZKT23MYM","created_at":"2026-07-05T00:04:43.977937+00:00"},{"alias_kind":"pith_short_16","alias_value":"CJFDZKT23MYMZAFG","created_at":"2026-07-05T00:04:43.977937+00:00"},{"alias_kind":"pith_short_8","alias_value":"CJFDZKT2","created_at":"2026-07-05T00:04:43.977937+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/CJFDZKT23MYMZAFGD43DYHKNVL","json":"https://pith.science/pith/CJFDZKT23MYMZAFGD43DYHKNVL.json","graph_json":"https://pith.science/api/pith-number/CJFDZKT23MYMZAFGD43DYHKNVL/graph.json","events_json":"https://pith.science/api/pith-number/CJFDZKT23MYMZAFGD43DYHKNVL/events.json","paper":"https://pith.science/paper/CJFDZKT2"},"agent_actions":{"view_html":"https://pith.science/pith/CJFDZKT23MYMZAFGD43DYHKNVL","download_json":"https://pith.science/pith/CJFDZKT23MYMZAFGD43DYHKNVL.json","view_paper":"https://pith.science/paper/CJFDZKT2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.06885&json=true","fetch_graph":"https://pith.science/api/pith-number/CJFDZKT23MYMZAFGD43DYHKNVL/graph.json","fetch_events":"https://pith.science/api/pith-number/CJFDZKT23MYMZAFGD43DYHKNVL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CJFDZKT23MYMZAFGD43DYHKNVL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CJFDZKT23MYMZAFGD43DYHKNVL/action/storage_attestation","attest_author":"https://pith.science/pith/CJFDZKT23MYMZAFGD43DYHKNVL/action/author_attestation","sign_citation":"https://pith.science/pith/CJFDZKT23MYMZAFGD43DYHKNVL/action/citation_signature","submit_replication":"https://pith.science/pith/CJFDZKT23MYMZAFGD43DYHKNVL/action/replication_record"}},"created_at":"2026-07-05T00:04:43.977937+00:00","updated_at":"2026-07-05T00:04:43.977937+00:00"}