{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:66PF33WN4EPOFDDBPAH7YF7IWD","short_pith_number":"pith:66PF33WN","canonical_record":{"source":{"id":"0909.4278","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-09-23T18:39:38Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"3f7c7e3530b0c3ec82e64ab6707e405b41db6bd6f20024e03aa1e7708a4d83e2","abstract_canon_sha256":"2d5e6a7445cac50c508e4c7a72f60c60dbffb51ae71f93bfa245b99f9262f32e"},"schema_version":"1.0"},"canonical_sha256":"f79e5deecde11ee28c61780ffc17e8b0cd683fbb9c00a8373d597d0ed2cd0269","source":{"kind":"arxiv","id":"0909.4278","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.4278","created_at":"2026-05-18T02:24:47Z"},{"alias_kind":"arxiv_version","alias_value":"0909.4278v4","created_at":"2026-05-18T02:24:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.4278","created_at":"2026-05-18T02:24:47Z"},{"alias_kind":"pith_short_12","alias_value":"66PF33WN4EPO","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"66PF33WN4EPOFDDB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"66PF33WN","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:66PF33WN4EPOFDDBPAH7YF7IWD","target":"record","payload":{"canonical_record":{"source":{"id":"0909.4278","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-09-23T18:39:38Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"3f7c7e3530b0c3ec82e64ab6707e405b41db6bd6f20024e03aa1e7708a4d83e2","abstract_canon_sha256":"2d5e6a7445cac50c508e4c7a72f60c60dbffb51ae71f93bfa245b99f9262f32e"},"schema_version":"1.0"},"canonical_sha256":"f79e5deecde11ee28c61780ffc17e8b0cd683fbb9c00a8373d597d0ed2cd0269","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:47.101943Z","signature_b64":"u4XTnHDZlyhErmtSrFY+qEA8w2OIFmbXpAy6IJXDbfA96iszmiAM8ojEJeeIuiM2qyidpMWaaS6MXwDGBVBqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f79e5deecde11ee28c61780ffc17e8b0cd683fbb9c00a8373d597d0ed2cd0269","last_reissued_at":"2026-05-18T02:24:47.101404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:47.101404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.4278","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B+8iqthOEeF9G57v4L8F46EgkkoCRxs5+f5AMluZtT3TLTmNsQ/YV8z4le2DNwpJXCdbR/kstWfKBFlZwnDWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:30:18.556649Z"},"content_sha256":"907502f4561a6f0edf9d00b913699e2f4ab6687b57f02ed3611ae5a3d21e4636","schema_version":"1.0","event_id":"sha256:907502f4561a6f0edf9d00b913699e2f4ab6687b57f02ed3611ae5a3d21e4636"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:66PF33WN4EPOFDDBPAH7YF7IWD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Resolutions of moduli spaces and homological stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Oscar Randal-Williams","submitted_at":"2009-09-23T18:39:38Z","abstract_excerpt":"We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and give explicit stability ranges in many new cases. In each of these cases the stable homology can be identified using the methods of Galatius, Madsen, Tillmann and Weiss."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4278","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aHiYlhPCfBPr1/kw+fY8CKgA8DIV/qNm+7H0r5SORtYxKxshK/cGXZ7PT7qab4QaVgQ9MePxL39Z+yrHB6nFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:30:18.557292Z"},"content_sha256":"1dd9e1eeb44beb4ff6bfdaa2ad05677de69242199c3e4db2487dc72c02779d12","schema_version":"1.0","event_id":"sha256:1dd9e1eeb44beb4ff6bfdaa2ad05677de69242199c3e4db2487dc72c02779d12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/66PF33WN4EPOFDDBPAH7YF7IWD/bundle.json","state_url":"https://pith.science/pith/66PF33WN4EPOFDDBPAH7YF7IWD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/66PF33WN4EPOFDDBPAH7YF7IWD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T18:30:18Z","links":{"resolver":"https://pith.science/pith/66PF33WN4EPOFDDBPAH7YF7IWD","bundle":"https://pith.science/pith/66PF33WN4EPOFDDBPAH7YF7IWD/bundle.json","state":"https://pith.science/pith/66PF33WN4EPOFDDBPAH7YF7IWD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/66PF33WN4EPOFDDBPAH7YF7IWD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:66PF33WN4EPOFDDBPAH7YF7IWD","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":"2d5e6a7445cac50c508e4c7a72f60c60dbffb51ae71f93bfa245b99f9262f32e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-09-23T18:39:38Z","title_canon_sha256":"3f7c7e3530b0c3ec82e64ab6707e405b41db6bd6f20024e03aa1e7708a4d83e2"},"schema_version":"1.0","source":{"id":"0909.4278","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.4278","created_at":"2026-05-18T02:24:47Z"},{"alias_kind":"arxiv_version","alias_value":"0909.4278v4","created_at":"2026-05-18T02:24:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.4278","created_at":"2026-05-18T02:24:47Z"},{"alias_kind":"pith_short_12","alias_value":"66PF33WN4EPO","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"66PF33WN4EPOFDDB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"66PF33WN","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:1dd9e1eeb44beb4ff6bfdaa2ad05677de69242199c3e4db2487dc72c02779d12","target":"graph","created_at":"2026-05-18T02:24:47Z","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":"We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and give explicit stability ranges in many new cases. In each of these cases the stable homology can be identified using the methods of Galatius, Madsen, Tillmann and Weiss.","authors_text":"Oscar Randal-Williams","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-09-23T18:39:38Z","title":"Resolutions of moduli spaces and homological stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4278","kind":"arxiv","version":4},"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":"sha256:907502f4561a6f0edf9d00b913699e2f4ab6687b57f02ed3611ae5a3d21e4636","target":"record","created_at":"2026-05-18T02:24:47Z","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":"2d5e6a7445cac50c508e4c7a72f60c60dbffb51ae71f93bfa245b99f9262f32e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-09-23T18:39:38Z","title_canon_sha256":"3f7c7e3530b0c3ec82e64ab6707e405b41db6bd6f20024e03aa1e7708a4d83e2"},"schema_version":"1.0","source":{"id":"0909.4278","kind":"arxiv","version":4}},"canonical_sha256":"f79e5deecde11ee28c61780ffc17e8b0cd683fbb9c00a8373d597d0ed2cd0269","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f79e5deecde11ee28c61780ffc17e8b0cd683fbb9c00a8373d597d0ed2cd0269","first_computed_at":"2026-05-18T02:24:47.101404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:47.101404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u4XTnHDZlyhErmtSrFY+qEA8w2OIFmbXpAy6IJXDbfA96iszmiAM8ojEJeeIuiM2qyidpMWaaS6MXwDGBVBqBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:47.101943Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.4278","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:907502f4561a6f0edf9d00b913699e2f4ab6687b57f02ed3611ae5a3d21e4636","sha256:1dd9e1eeb44beb4ff6bfdaa2ad05677de69242199c3e4db2487dc72c02779d12"],"state_sha256":"4f79b691f66e5b6118a31243ce0a798dca1c31d8765504660f86ee22d53e552f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cez+luIl6TJAThRqqB+pCGUBvCL3B4/RZNnXqsibco71eEqz+8EPYK5qYFhjrB5tpEGWSuOJNxm0dyinZ6NqDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T18:30:18.560515Z","bundle_sha256":"4593153efc58882298177c4059c1a8293900d19b16748c1b6b7d3773fafd2749"}}