{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MLHTH5I4Q75CUYTCQNFAMNRYKQ","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":"bdeab19fe8174d7a168b6e7bf8b2bd92895626dc0cc1260fbe6321bfc47332b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-07-16T22:24:33Z","title_canon_sha256":"9a4888813bcb6f15fad0d3d7ecf24eb1f29354d56086ab62e49024ca35b3a97f"},"schema_version":"1.0","source":{"id":"1907.07280","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.07280","created_at":"2026-05-17T23:40:22Z"},{"alias_kind":"arxiv_version","alias_value":"1907.07280v1","created_at":"2026-05-17T23:40:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.07280","created_at":"2026-05-17T23:40:22Z"},{"alias_kind":"pith_short_12","alias_value":"MLHTH5I4Q75C","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MLHTH5I4Q75CUYTC","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MLHTH5I4","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:675a50fd5d81e69e06dc4b03e8a7d4ad6221797002d57bb6d2e18c1778cae817","target":"graph","created_at":"2026-05-17T23:40:22Z","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"},"paper":{"abstract_excerpt":"A surface with an involution can be viewed as a $C_2$-space where $C_2$ is the cyclic group of order two. Using the classification of $C_2$-surfaces given by Dugger, we compute the $RO(C_2)$-graded Bredon cohomology of all $C_2$-surfaces in constant $\\mathbb{Z}/2$ coefficients as modules over the cohomology of a point. We show the cohomology depends only on three numerical invariants in the nonfree case, and only on two numerical invariants in the free case.","authors_text":"Christy Hazel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-07-16T22:24:33Z","title":"The $RO(C_2)$-graded cohomology of $C_2$-surfaces in $\\underline{\\mathbb{Z}/2}$-coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07280","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:e2498e9dc4b05c8f70c1d0757e9700e35f166a30c1ee0fe52b86b87ae22395e6","target":"record","created_at":"2026-05-17T23:40:22Z","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":"bdeab19fe8174d7a168b6e7bf8b2bd92895626dc0cc1260fbe6321bfc47332b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-07-16T22:24:33Z","title_canon_sha256":"9a4888813bcb6f15fad0d3d7ecf24eb1f29354d56086ab62e49024ca35b3a97f"},"schema_version":"1.0","source":{"id":"1907.07280","kind":"arxiv","version":1}},"canonical_sha256":"62cf33f51c87fa2a6262834a063638540159c805ca8409fa388450ee78a829fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62cf33f51c87fa2a6262834a063638540159c805ca8409fa388450ee78a829fe","first_computed_at":"2026-05-17T23:40:22.826488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:22.826488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Il89G/2Czvujq0QHimtN5RvlgkoewTHQ2f/iis4PaoKA1rHlTjOTXVdfIB2xZh0Wc4Xll2g98ICaDWFfvKfxDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:22.827091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.07280","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2498e9dc4b05c8f70c1d0757e9700e35f166a30c1ee0fe52b86b87ae22395e6","sha256:675a50fd5d81e69e06dc4b03e8a7d4ad6221797002d57bb6d2e18c1778cae817"],"state_sha256":"c39e0181180cc33905f0a5df867e004abd9623485c6fc1049a06a875fbf69c59"}