{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:T5YSXEHRAR42GW6FVSTPJARAJU","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":"f1c7d3e2b36c6a8e192ec13d545ef3a7b847ecd06b395c2ef21fd3a2e74d44d7","cross_cats_sorted":["math.AT","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-26T20:08:22Z","title_canon_sha256":"08449c28dc8c25c10b0b3e26e4b8bd5522169ef1fd6237a7e4d5bd4eee1de35f"},"schema_version":"1.0","source":{"id":"1408.6242","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6242","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6242v3","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6242","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"pith_short_12","alias_value":"T5YSXEHRAR42","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T5YSXEHRAR42GW6F","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T5YSXEHR","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:76904572c65e1a2e2f8aeec84cf4e806b4cda179a31f8a827c60159e11bbc54d","target":"graph","created_at":"2026-05-18T00:21:00Z","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":"Let IA_n be the Torelli subgroup of Aut(F_n). We give an explicit finite set of generators for H_2(IA_n) as a GL_n(Z)-module. Corollaries include a version of surjective representation stability for H_2(IA_n), the vanishing of the GL_n(Z)-coinvariants of H_2(IA_n), and the vanishing of the second rational homology group of the level l congruence subgroup of Aut(F_n). Our generating set is derived from a new group presentation for IA_n which is infinite but which has a simple recursive form.","authors_text":"Andrew Putman, Matthew B. Day","cross_cats":["math.AT","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-26T20:08:22Z","title":"On the second homology group of the Torelli subgroup of Aut(F_n)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6242","kind":"arxiv","version":3},"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":"sha256:365bf04f14dc805d9651aaedb75b16a5c21da5db3fc0c4120eaef3ab831ef22a","target":"record","created_at":"2026-05-18T00:21:00Z","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":"f1c7d3e2b36c6a8e192ec13d545ef3a7b847ecd06b395c2ef21fd3a2e74d44d7","cross_cats_sorted":["math.AT","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-26T20:08:22Z","title_canon_sha256":"08449c28dc8c25c10b0b3e26e4b8bd5522169ef1fd6237a7e4d5bd4eee1de35f"},"schema_version":"1.0","source":{"id":"1408.6242","kind":"arxiv","version":3}},"canonical_sha256":"9f712b90f10479a35bc5aca6f482204d17a4f22d21f762c0995e5f8c02baba48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f712b90f10479a35bc5aca6f482204d17a4f22d21f762c0995e5f8c02baba48","first_computed_at":"2026-05-18T00:21:00.825974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:00.825974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K7JQBzAP683A3bmveCPWlqCXMrtCJ9OGdsAC130w3v2K5gofO7l0QW1taGrJvuoR103bM+lKeSYPbaVNnhE4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:00.826625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6242","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:365bf04f14dc805d9651aaedb75b16a5c21da5db3fc0c4120eaef3ab831ef22a","sha256:76904572c65e1a2e2f8aeec84cf4e806b4cda179a31f8a827c60159e11bbc54d"],"state_sha256":"eb118f9b095c5bc0ddbd372b4372169933d0bb19436d9708f50fcbaf870e1d97"}