{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:CTEQORPWYQVQ6C4232K3PIYMO6","short_pith_number":"pith:CTEQORPW","schema_version":"1.0","canonical_sha256":"14c90745f6c42b0f0b9ade95b7a30c779221ac1eeab0ed931bf7c409331737d5","source":{"kind":"arxiv","id":"1203.6830","version":2},"attestation_state":"computed","paper":{"title":"Homological stability for moduli spaces of high dimensional manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Oscar Randal-Williams, Soren Galatius","submitted_at":"2012-03-30T14:33:34Z","abstract_excerpt":"We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to g(S^n x S^n), provided n > 2. This generalises Harer's stability theorem for the homology of mapping class groups. Combined with previous work of the authors, it gives a calculation of the homology of these moduli spaces in a range of degrees."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1203.6830","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-03-30T14:33:34Z","cross_cats_sorted":[],"title_canon_sha256":"f3fefe2a03041becf54d13f3475f562afe37abddbd51c3b9a1ed44aa93513761","abstract_canon_sha256":"8dd2cacdddea792ea4348d50fbea6371317b809910cfd8c526b44f6082ac419e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:31.391940Z","signature_b64":"XBQGbVqULOX1dRleDP4KdPgQRCf1K3f39nFwh74Bs7ElAr8NzEeuJvVUJBKnNd2fSEfL4j6ZqaE6xuWd4bqRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14c90745f6c42b0f0b9ade95b7a30c779221ac1eeab0ed931bf7c409331737d5","last_reissued_at":"2026-05-18T03:53:31.391253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:31.391253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homological stability for moduli spaces of high dimensional manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Oscar Randal-Williams, Soren Galatius","submitted_at":"2012-03-30T14:33:34Z","abstract_excerpt":"We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to g(S^n x S^n), provided n > 2. This generalises Harer's stability theorem for the homology of mapping class groups. Combined with previous work of the authors, it gives a calculation of the homology of these moduli spaces in a range of degrees."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6830","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1203.6830","created_at":"2026-05-18T03:53:31.391367+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.6830v2","created_at":"2026-05-18T03:53:31.391367+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6830","created_at":"2026-05-18T03:53:31.391367+00:00"},{"alias_kind":"pith_short_12","alias_value":"CTEQORPWYQVQ","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"CTEQORPWYQVQ6C42","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"CTEQORPW","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CTEQORPWYQVQ6C4232K3PIYMO6","json":"https://pith.science/pith/CTEQORPWYQVQ6C4232K3PIYMO6.json","graph_json":"https://pith.science/api/pith-number/CTEQORPWYQVQ6C4232K3PIYMO6/graph.json","events_json":"https://pith.science/api/pith-number/CTEQORPWYQVQ6C4232K3PIYMO6/events.json","paper":"https://pith.science/paper/CTEQORPW"},"agent_actions":{"view_html":"https://pith.science/pith/CTEQORPWYQVQ6C4232K3PIYMO6","download_json":"https://pith.science/pith/CTEQORPWYQVQ6C4232K3PIYMO6.json","view_paper":"https://pith.science/paper/CTEQORPW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.6830&json=true","fetch_graph":"https://pith.science/api/pith-number/CTEQORPWYQVQ6C4232K3PIYMO6/graph.json","fetch_events":"https://pith.science/api/pith-number/CTEQORPWYQVQ6C4232K3PIYMO6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CTEQORPWYQVQ6C4232K3PIYMO6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CTEQORPWYQVQ6C4232K3PIYMO6/action/storage_attestation","attest_author":"https://pith.science/pith/CTEQORPWYQVQ6C4232K3PIYMO6/action/author_attestation","sign_citation":"https://pith.science/pith/CTEQORPWYQVQ6C4232K3PIYMO6/action/citation_signature","submit_replication":"https://pith.science/pith/CTEQORPWYQVQ6C4232K3PIYMO6/action/replication_record"}},"created_at":"2026-05-18T03:53:31.391367+00:00","updated_at":"2026-05-18T03:53:31.391367+00:00"}