{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QKTD2JPWNQTJFSFQWOIK644RD2","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":"a16357bf02c1e7e2aef527daec2535361ee49a305f9786a9c0253c19f0720af0","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-08T16:22:46Z","title_canon_sha256":"95eea1de99f29443a819daf7a11abae9dc0a60a1dfa4f8e7f36ea4aef2c4bb88"},"schema_version":"1.0","source":{"id":"2606.09702","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09702","created_at":"2026-06-09T02:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09702v1","created_at":"2026-06-09T02:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09702","created_at":"2026-06-09T02:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"QKTD2JPWNQTJ","created_at":"2026-06-09T02:09:04Z"},{"alias_kind":"pith_short_16","alias_value":"QKTD2JPWNQTJFSFQ","created_at":"2026-06-09T02:09:04Z"},{"alias_kind":"pith_short_8","alias_value":"QKTD2JPW","created_at":"2026-06-09T02:09:04Z"}],"graph_snapshots":[{"event_id":"sha256:ae06b45a26122541a3a2c7cdfaa4301b768aac8cae72313a00de9beff6f6393b","target":"graph","created_at":"2026-06-09T02:09:04Z","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/2606.09702/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The second homology group is of central importance in the study of profinite rigidity of $3$-manifold groups. Although general and deep results imply that the integral homology of cocompact hyperbolic $3$-orbifold groups is computable in principle, the resulting algorithm is not practical. We develop an effective method for computing $H_2$ in the case of orbifold groups arising as finite extensions of the fundamental group of hyperbolic rational homology $3$-spheres. As a special case, this yields explicit computations of the second homology groups of all cocompact lattices between $\\pi_1(\\mat","authors_text":"Carl-Fredrik Nyberg-Brodda","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-08T16:22:46Z","title":"On profinite rigidity, Grothendieck pairs, and the second homology of some $3$-orbifold groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09702","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:ed5ca4cb168117cc0fcdef2b6d3ddf7d74a074fa420f77aa961d9103dfc0cdf3","target":"record","created_at":"2026-06-09T02:09:04Z","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":"a16357bf02c1e7e2aef527daec2535361ee49a305f9786a9c0253c19f0720af0","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-08T16:22:46Z","title_canon_sha256":"95eea1de99f29443a819daf7a11abae9dc0a60a1dfa4f8e7f36ea4aef2c4bb88"},"schema_version":"1.0","source":{"id":"2606.09702","kind":"arxiv","version":1}},"canonical_sha256":"82a63d25f66c2692c8b0b390af73911e9dc6a8bb7c809a8ce309c0a3d46d4e02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82a63d25f66c2692c8b0b390af73911e9dc6a8bb7c809a8ce309c0a3d46d4e02","first_computed_at":"2026-06-09T02:09:04.700633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:09:04.700633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R1sUJk1kqcbzpOImx/C2tdA73HbcVdjLlOhKFF84x+N0kZG4nxRLVdXCg27ZuXHghjSifCer4Zgl2BGgXIFgBQ==","signature_status":"signed_v1","signed_at":"2026-06-09T02:09:04.701593Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.09702","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed5ca4cb168117cc0fcdef2b6d3ddf7d74a074fa420f77aa961d9103dfc0cdf3","sha256:ae06b45a26122541a3a2c7cdfaa4301b768aac8cae72313a00de9beff6f6393b"],"state_sha256":"a7102a7332a042bad1082cee6253d7d4e38757d60bf557d330a737fd9913a7c4"}