{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:CPZRJ66JJF2EXH3CPWZFPG2EKR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f23de863ae0b7c16bdb67cad149c32947209487d8d63f89b1f70dc95e6d12371","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-08-09T15:34:21Z","title_canon_sha256":"144a76ecf9ceeb4124435a42effb04a742b704be4a044a9cec011193a60951f0"},"schema_version":"1.0","source":{"id":"2208.04855","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.04855","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"arxiv_version","alias_value":"2208.04855v1","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.04855","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"pith_short_12","alias_value":"CPZRJ66JJF2E","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"pith_short_16","alias_value":"CPZRJ66JJF2EXH3C","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"pith_short_8","alias_value":"CPZRJ66J","created_at":"2026-07-05T04:47:20Z"}],"graph_snapshots":[{"event_id":"sha256:e6bbcf9d3551630503f8f222be111a20282609c2a8c25bca9b1cb90d14e4b4cd","target":"graph","created_at":"2026-07-05T04:47:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2208.04855/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a cohomological interpretation of the Heaviside filtration on the Varchenko--Gelfand ring of a pair $(\\mathcal{A},\\mathcal{K})$, where $\\mathcal{A}$ is a real hyperplane arrangement and $\\mathcal{K}$ is a convex open subset of the ambient vector space. This builds on work of the first author, who studied the filtration from a purely algebraic perspective, as well as work of Moseley, who gave a cohomological interpretation in the special case where $\\mathcal{K}$ is the ambient vector space. We also define the Gelfand--Rybnikov ring of a conditional oriented matroid, which simultaneously","authors_text":"Galen Dorpalen-Barry, Jidong Wang, Nicholas Proudfoot","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-08-09T15:34:21Z","title":"Equivariant cohomology and conditional oriented matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.04855","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b322fe84824f063a935a06d5532b6fe05a650a1bb0d3576eb8b6418a9711282b","target":"record","created_at":"2026-07-05T04:47:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f23de863ae0b7c16bdb67cad149c32947209487d8d63f89b1f70dc95e6d12371","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-08-09T15:34:21Z","title_canon_sha256":"144a76ecf9ceeb4124435a42effb04a742b704be4a044a9cec011193a60951f0"},"schema_version":"1.0","source":{"id":"2208.04855","kind":"arxiv","version":1}},"canonical_sha256":"13f314fbc949744b9f627db2579b44544cc309709b38c6396cf4ce5bde0846e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13f314fbc949744b9f627db2579b44544cc309709b38c6396cf4ce5bde0846e0","first_computed_at":"2026-07-05T04:47:20.013638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:47:20.013638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9eEQY2iVsNHQA3FNWVH4FTc2yjj2HY2O/jiaeim3kQKxklkfLQ0lJvkaz6uSVvGEc/CLD9QCLY1Hc5JWPb5YAA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:47:20.014030Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.04855","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b322fe84824f063a935a06d5532b6fe05a650a1bb0d3576eb8b6418a9711282b","sha256:e6bbcf9d3551630503f8f222be111a20282609c2a8c25bca9b1cb90d14e4b4cd"],"state_sha256":"fff7df92476b71c6d31851767175b62a1ced67085dc03e264eccdc728322e8c5"}