{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:QGT3Q6ICMNWRMGJNIQTV2XWNM3","short_pith_number":"pith:QGT3Q6IC","schema_version":"1.0","canonical_sha256":"81a7b87902636d16192d44275d5ecd66f983f8b61cf1f13b4e8c7d1bb3547d37","source":{"kind":"arxiv","id":"2608.06767","version":1},"attestation_state":"computed","paper":{"title":"Vector fields of graphic arrangements and face rings of simplicial posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Satoshi Murai, Takuro Abe","submitted_at":"2026-08-07T03:41:55Z","abstract_excerpt":"A graphic arrangement $\\A_G$ associated with a simple graph $G$ is a classical and well-studied object in the theory of hyperplane arrangements. In this note, we show that, for a connected graph $G$, a slight modification of the logarithmic vector field $D(\\A_G)$ of $\\A_G$ is isomorphic to the face ring of a certain simplicial poset. This allows us to give formulas for several algebraic invariants of $D(\\A_G)$, such as its Hilbert series, local cohomology, projective dimension, and Castelnuovo--Mumford regularity, in terms of combinatorial and topological information about the corresponding si"},"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":"2608.06767","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-08-07T03:41:55Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"fd197dd82ecbd62e520df46f0a10a009c4201eced4906a2b5044b0c9ea7fb584","abstract_canon_sha256":"3d16cd2dcc15262aeedfb01789baae8f55430cecafd647198d3bca7ac66a9e4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-10T01:11:58.393791Z","signature_b64":"/Phkd9niZvFI58/xgClJ2zOUjLg/mfLH9FMrECs73lKyhz6S8UOgeZC4rhp++B7Dy0TUzJK8ME6d1l19nyuPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81a7b87902636d16192d44275d5ecd66f983f8b61cf1f13b4e8c7d1bb3547d37","last_reissued_at":"2026-08-10T01:11:58.391392Z","signature_status":"signed_v1","first_computed_at":"2026-08-10T01:11:58.391392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vector fields of graphic arrangements and face rings of simplicial posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Satoshi Murai, Takuro Abe","submitted_at":"2026-08-07T03:41:55Z","abstract_excerpt":"A graphic arrangement $\\A_G$ associated with a simple graph $G$ is a classical and well-studied object in the theory of hyperplane arrangements. In this note, we show that, for a connected graph $G$, a slight modification of the logarithmic vector field $D(\\A_G)$ of $\\A_G$ is isomorphic to the face ring of a certain simplicial poset. This allows us to give formulas for several algebraic invariants of $D(\\A_G)$, such as its Hilbert series, local cohomology, projective dimension, and Castelnuovo--Mumford regularity, in terms of combinatorial and topological information about the corresponding si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06767","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/2608.06767/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":"2608.06767","created_at":"2026-08-10T01:11:58.392400+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.06767v1","created_at":"2026-08-10T01:11:58.392400+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06767","created_at":"2026-08-10T01:11:58.392400+00:00"},{"alias_kind":"pith_short_12","alias_value":"QGT3Q6ICMNWR","created_at":"2026-08-10T01:11:58.392400+00:00"},{"alias_kind":"pith_short_16","alias_value":"QGT3Q6ICMNWRMGJN","created_at":"2026-08-10T01:11:58.392400+00:00"},{"alias_kind":"pith_short_8","alias_value":"QGT3Q6IC","created_at":"2026-08-10T01:11:58.392400+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/QGT3Q6ICMNWRMGJNIQTV2XWNM3","json":"https://pith.science/pith/QGT3Q6ICMNWRMGJNIQTV2XWNM3.json","graph_json":"https://pith.science/api/pith-number/QGT3Q6ICMNWRMGJNIQTV2XWNM3/graph.json","events_json":"https://pith.science/api/pith-number/QGT3Q6ICMNWRMGJNIQTV2XWNM3/events.json","paper":"https://pith.science/paper/QGT3Q6IC"},"agent_actions":{"view_html":"https://pith.science/pith/QGT3Q6ICMNWRMGJNIQTV2XWNM3","download_json":"https://pith.science/pith/QGT3Q6ICMNWRMGJNIQTV2XWNM3.json","view_paper":"https://pith.science/paper/QGT3Q6IC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.06767&json=true","fetch_graph":"https://pith.science/api/pith-number/QGT3Q6ICMNWRMGJNIQTV2XWNM3/graph.json","fetch_events":"https://pith.science/api/pith-number/QGT3Q6ICMNWRMGJNIQTV2XWNM3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QGT3Q6ICMNWRMGJNIQTV2XWNM3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QGT3Q6ICMNWRMGJNIQTV2XWNM3/action/storage_attestation","attest_author":"https://pith.science/pith/QGT3Q6ICMNWRMGJNIQTV2XWNM3/action/author_attestation","sign_citation":"https://pith.science/pith/QGT3Q6ICMNWRMGJNIQTV2XWNM3/action/citation_signature","submit_replication":"https://pith.science/pith/QGT3Q6ICMNWRMGJNIQTV2XWNM3/action/replication_record"}},"created_at":"2026-08-10T01:11:58.392400+00:00","updated_at":"2026-08-10T01:11:58.392400+00:00"}