{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:M3PYQB6WHQHIDCG7VTWFAS6J6S","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":"0f0e20a48001bfe83cc0fda34adac4f57ed851314a8bfd40ce1ba92f7538587c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-04-17T10:58:50Z","title_canon_sha256":"0fbc431e258d0864017e066e0bac8f10e1b16a265581e4d41dae3deecaab7344"},"schema_version":"1.0","source":{"id":"1904.08181","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.08181","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"arxiv_version","alias_value":"1904.08181v1","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.08181","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"pith_short_12","alias_value":"M3PYQB6WHQHI","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"M3PYQB6WHQHIDCG7","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"M3PYQB6W","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:ab067e5dac48aabb66056a825edd054f64c05bb44ae6b200ff998459258eb904","target":"graph","created_at":"2026-05-17T23:48:18Z","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":"We consider the function $f(g)$ that assigns to an orientable surface $M$ of genus $g$ the maximal number of free commuting independent involutions on $M$. We show that the surface of minimal genus $g$ with $f(g)=n$ is a real moment-angle complex $R_K$, where $K$ is the boundary of an $(n+2)$-gon. The genus is given by the formula $g = 1 + 2^{n-1}(n-2)$.","authors_text":"Tatiana Neretina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-04-17T10:58:50Z","title":"Free commuting involutions on closed two-dimensional surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08181","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":"sha256:11f1a9c5fc40b76492d2eab96b1788c577b2637726aff1564fdc19811ca58308","target":"record","created_at":"2026-05-17T23:48:18Z","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":"0f0e20a48001bfe83cc0fda34adac4f57ed851314a8bfd40ce1ba92f7538587c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-04-17T10:58:50Z","title_canon_sha256":"0fbc431e258d0864017e066e0bac8f10e1b16a265581e4d41dae3deecaab7344"},"schema_version":"1.0","source":{"id":"1904.08181","kind":"arxiv","version":1}},"canonical_sha256":"66df8807d63c0e8188dfacec504bc9f4841505206d9af1b2d6ef5863ae8b617d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66df8807d63c0e8188dfacec504bc9f4841505206d9af1b2d6ef5863ae8b617d","first_computed_at":"2026-05-17T23:48:18.487851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:18.487851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gRTtrFEqcwpz7TQLLKRCuvZwmclTuIR2svHqgNlWj6/3ETHHSeGor1/izqODfDQ/7BIbyoUb3vli8uSCi4MvCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:18.488280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.08181","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11f1a9c5fc40b76492d2eab96b1788c577b2637726aff1564fdc19811ca58308","sha256:ab067e5dac48aabb66056a825edd054f64c05bb44ae6b200ff998459258eb904"],"state_sha256":"e148dada105b22a269e45a7a886f9afce9b7c14ba292a12c64c6a507de0c1d7f"}