{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YBF42PLXIEUQ7J5NMTRAG4SDZK","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":"f6f813eed16471f326a809e3b9746427f79db09ab077043a300cf512b3da6a32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-12-19T11:29:27Z","title_canon_sha256":"6e2b30697e1b70c80ef0236bc8d84701637351647db2eaaaf9325f9d954554d3"},"schema_version":"1.0","source":{"id":"2512.17465","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.17465","created_at":"2026-06-04T01:08:38Z"},{"alias_kind":"arxiv_version","alias_value":"2512.17465v2","created_at":"2026-06-04T01:08:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.17465","created_at":"2026-06-04T01:08:38Z"},{"alias_kind":"pith_short_12","alias_value":"YBF42PLXIEUQ","created_at":"2026-06-04T01:08:38Z"},{"alias_kind":"pith_short_16","alias_value":"YBF42PLXIEUQ7J5N","created_at":"2026-06-04T01:08:38Z"},{"alias_kind":"pith_short_8","alias_value":"YBF42PLX","created_at":"2026-06-04T01:08:38Z"}],"graph_snapshots":[{"event_id":"sha256:b43a0fb33a6a6c21e1cb65e2e67af094cae7d070ca0bdd40b132400e6702457a","target":"graph","created_at":"2026-06-04T01:08:38Z","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/2512.17465/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $S(n)$ be the infinite-type surface with infinite genus and $n \\in \\mathbb{N}$ ends, all of which are accumulated by genus. The mapping class group of this surface, $\\mathrm{Map}(S(n))$, is a Polish group that is not countably generated, but it is countably topologically generated. This paper focuses on finding minimal sets of generators for $\\mathrm{Map}(S(n))$. We show that for $n \\ge 8$, $\\mathrm{Map}(S(n))$ is topologically generated by three elements, and for $n \\ge 3$, it is topologically generated by four elements. We also establish a generating set of two elements for the Loch Ness","authors_text":"Celal Can Bellek, Emir G\\\"ul, Mehmetcik Pamuk, O\\u{g}uz Y{\\i}ld{\\i}z, T\\\"ulin Altun\\\"oz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-12-19T11:29:27Z","title":"Small Sets of Topological Generators for Big Mapping Class Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.17465","kind":"arxiv","version":2},"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":"sha256:356bff3d6ae91ceeb62f20ab2468d23182f3bfbab3014ba9a00fbfdfe59ec2ec","target":"record","created_at":"2026-06-04T01:08:38Z","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":"f6f813eed16471f326a809e3b9746427f79db09ab077043a300cf512b3da6a32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-12-19T11:29:27Z","title_canon_sha256":"6e2b30697e1b70c80ef0236bc8d84701637351647db2eaaaf9325f9d954554d3"},"schema_version":"1.0","source":{"id":"2512.17465","kind":"arxiv","version":2}},"canonical_sha256":"c04bcd3d7741290fa7ad64e2037243caa661f08657b43da24710b5f71ec4e84a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c04bcd3d7741290fa7ad64e2037243caa661f08657b43da24710b5f71ec4e84a","first_computed_at":"2026-06-04T01:08:38.213920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:08:38.213920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/FpvTcnkwdHpQIpud1TGcVsVJP6MDBnyrcWHFzhBuD52UC+fx6RmVEdLcdwUyxCPQazfR5XFtXsiCoxje89rDg==","signature_status":"signed_v1","signed_at":"2026-06-04T01:08:38.214634Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.17465","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:356bff3d6ae91ceeb62f20ab2468d23182f3bfbab3014ba9a00fbfdfe59ec2ec","sha256:b43a0fb33a6a6c21e1cb65e2e67af094cae7d070ca0bdd40b132400e6702457a"],"state_sha256":"c57c16f1e787e5f401f8d24b2802fca8580efe9d759645d24144bd18eb0266b7"}