{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4E2LJ2OOHZTB2NMXRYPEQG7ICS","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":"aaf066d9ae89cfa6c4a365f572bb98e08a085d345aba9b4dd4b8ab7ccd1a7038","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-26T06:10:50Z","title_canon_sha256":"6de12b785ce0812f538a27a7e1fff5a7b8febacc4c58db0d79c12e8f3d7f4404"},"schema_version":"1.0","source":{"id":"1603.08077","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08077","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08077v1","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08077","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"4E2LJ2OOHZTB","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4E2LJ2OOHZTB2NMX","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4E2LJ2OO","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:d576de965f7a359b4fb147536ea2eaac5000028a56a9ecdd1b7218e86eabce34","target":"graph","created_at":"2026-05-18T01:18:13Z","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":"Suppose an orientation preserving action of a finite group $G$ on the closed surface $\\Sigma_g$ of genus $g>1$ extends over the 3-torus $T^3$ for some embedding $\\Sigma_g\\subset T^3$. Then $|G|\\le 12(g-1)$, and this upper bound $12(g-1)$ can be achieved for $g=n^2+1, 3n^2+1, 2n^3+1, 4n^3+1, 8n^3+1, n\\in \\mathbb{Z}_+$. Those surfaces in $T^3$ realizing the maximum symmetries can be either unknotted or knotted. Similar problems in non-orientable category is also discussed.\n  Connection with minimal surfaces in $T^3$ is addressed and when the maximum symmetric surfaces above can be realized by mi","authors_text":"Chao Wang, Sheng Bai, Shicheng Wang, Vanessa Robins","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-26T06:10:50Z","title":"The most symmetric surfaces in the 3-torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08077","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:e1c1c931e712e7c0b2932b874a48659ae640000ccbbcce786cfa4dccabecae8f","target":"record","created_at":"2026-05-18T01:18:13Z","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":"aaf066d9ae89cfa6c4a365f572bb98e08a085d345aba9b4dd4b8ab7ccd1a7038","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-26T06:10:50Z","title_canon_sha256":"6de12b785ce0812f538a27a7e1fff5a7b8febacc4c58db0d79c12e8f3d7f4404"},"schema_version":"1.0","source":{"id":"1603.08077","kind":"arxiv","version":1}},"canonical_sha256":"e134b4e9ce3e661d35978e1e481be814adcab573cba43ea755cc6c985bcf9b16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e134b4e9ce3e661d35978e1e481be814adcab573cba43ea755cc6c985bcf9b16","first_computed_at":"2026-05-18T01:18:13.381583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:13.381583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1lmNBtXLRwO7dh+C6n9Ub+L1+kby+obdG5HhMrligJafbAAv9JZIsi99aYmEbhIJ8wtGD2IKjA4aADHEIgX+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:13.382192Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08077","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1c1c931e712e7c0b2932b874a48659ae640000ccbbcce786cfa4dccabecae8f","sha256:d576de965f7a359b4fb147536ea2eaac5000028a56a9ecdd1b7218e86eabce34"],"state_sha256":"4efcaa5fa544a82432f34d3d755467a4f48a271730e7287f926784910a769273"}