{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:PJQU7H6PJCTERHSOKCUCX2M6NP","short_pith_number":"pith:PJQU7H6P","schema_version":"1.0","canonical_sha256":"7a614f9fcf48a6489e4e50a82be99e6bcfae792c140a92954e5de3b1b9e7eb93","source":{"kind":"arxiv","id":"2606.20421","version":1},"attestation_state":"computed","paper":{"title":"On Ziegler pairs of line arrangements: from non-existence to abundance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC","math.CO"],"primary_cat":"math.AG","authors_text":"Alexandru Dimca, Piotr Pokora","submitted_at":"2026-06-18T16:05:35Z","abstract_excerpt":"We study Ziegler pairs of line arrangements from both numerical and homological perspectives. First, we show that for arrangements of $d<9$ lines the intersection lattice determines the exponent data considered here. Then we list six distinct Ziegler pair with $d=10$. In particular, we construct higher-degree examples with the same intersection lattice, the same minimal degree of a Jacobian relation, and the same Hilbert function of the Milnor algebra, but with different minimal graded free resolutions."},"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":"2606.20421","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-18T16:05:35Z","cross_cats_sorted":["math.AC","math.CO"],"title_canon_sha256":"0e18ff9105cc92288a3d369783a4a2691586b7d9e410788009426ece3870bf23","abstract_canon_sha256":"29ec5ec0ef47a6dd671a0e648f7382e2635e1fd48f5250d0bff9560ed6d7dea2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:13:12.032678Z","signature_b64":"dpK5OVwqk9qLbrwoqp39FirLuzW+AoiL+zUcpPvCCpU2ifPhG02M9ZXBoMj/TFab2zKG4ok3/g12C0o9Zl+0BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a614f9fcf48a6489e4e50a82be99e6bcfae792c140a92954e5de3b1b9e7eb93","last_reissued_at":"2026-06-19T16:13:12.032270Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:13:12.032270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Ziegler pairs of line arrangements: from non-existence to abundance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC","math.CO"],"primary_cat":"math.AG","authors_text":"Alexandru Dimca, Piotr Pokora","submitted_at":"2026-06-18T16:05:35Z","abstract_excerpt":"We study Ziegler pairs of line arrangements from both numerical and homological perspectives. First, we show that for arrangements of $d<9$ lines the intersection lattice determines the exponent data considered here. Then we list six distinct Ziegler pair with $d=10$. In particular, we construct higher-degree examples with the same intersection lattice, the same minimal degree of a Jacobian relation, and the same Hilbert function of the Milnor algebra, but with different minimal graded free resolutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20421","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.20421/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":"2606.20421","created_at":"2026-06-19T16:13:12.032351+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.20421v1","created_at":"2026-06-19T16:13:12.032351+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20421","created_at":"2026-06-19T16:13:12.032351+00:00"},{"alias_kind":"pith_short_12","alias_value":"PJQU7H6PJCTE","created_at":"2026-06-19T16:13:12.032351+00:00"},{"alias_kind":"pith_short_16","alias_value":"PJQU7H6PJCTERHSO","created_at":"2026-06-19T16:13:12.032351+00:00"},{"alias_kind":"pith_short_8","alias_value":"PJQU7H6P","created_at":"2026-06-19T16:13:12.032351+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/PJQU7H6PJCTERHSOKCUCX2M6NP","json":"https://pith.science/pith/PJQU7H6PJCTERHSOKCUCX2M6NP.json","graph_json":"https://pith.science/api/pith-number/PJQU7H6PJCTERHSOKCUCX2M6NP/graph.json","events_json":"https://pith.science/api/pith-number/PJQU7H6PJCTERHSOKCUCX2M6NP/events.json","paper":"https://pith.science/paper/PJQU7H6P"},"agent_actions":{"view_html":"https://pith.science/pith/PJQU7H6PJCTERHSOKCUCX2M6NP","download_json":"https://pith.science/pith/PJQU7H6PJCTERHSOKCUCX2M6NP.json","view_paper":"https://pith.science/paper/PJQU7H6P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.20421&json=true","fetch_graph":"https://pith.science/api/pith-number/PJQU7H6PJCTERHSOKCUCX2M6NP/graph.json","fetch_events":"https://pith.science/api/pith-number/PJQU7H6PJCTERHSOKCUCX2M6NP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PJQU7H6PJCTERHSOKCUCX2M6NP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PJQU7H6PJCTERHSOKCUCX2M6NP/action/storage_attestation","attest_author":"https://pith.science/pith/PJQU7H6PJCTERHSOKCUCX2M6NP/action/author_attestation","sign_citation":"https://pith.science/pith/PJQU7H6PJCTERHSOKCUCX2M6NP/action/citation_signature","submit_replication":"https://pith.science/pith/PJQU7H6PJCTERHSOKCUCX2M6NP/action/replication_record"}},"created_at":"2026-06-19T16:13:12.032351+00:00","updated_at":"2026-06-19T16:13:12.032351+00:00"}