{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:AHUWGCTXX2ZJ3AAJESKVLBKCYL","short_pith_number":"pith:AHUWGCTX","canonical_record":{"source":{"id":"math/0501304","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2005-01-19T21:49:46Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"807de0b13cff8539ba2719f52a7d6986a45fd16751574d275c67a6bd3af56ddf","abstract_canon_sha256":"98b91788d125d4cf607a5c165b99ae1fb868894b8ae0a69cb5a768f4af0bfb99"},"schema_version":"1.0"},"canonical_sha256":"01e9630a77beb29d80092495558542c2e45a80a2c5dd12b513fdd7fed071d6a7","source":{"kind":"arxiv","id":"math/0501304","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0501304","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"arxiv_version","alias_value":"math/0501304v2","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501304","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"pith_short_12","alias_value":"AHUWGCTXX2ZJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"AHUWGCTXX2ZJ3AAJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"AHUWGCTX","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:AHUWGCTXX2ZJ3AAJESKVLBKCYL","target":"record","payload":{"canonical_record":{"source":{"id":"math/0501304","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2005-01-19T21:49:46Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"807de0b13cff8539ba2719f52a7d6986a45fd16751574d275c67a6bd3af56ddf","abstract_canon_sha256":"98b91788d125d4cf607a5c165b99ae1fb868894b8ae0a69cb5a768f4af0bfb99"},"schema_version":"1.0"},"canonical_sha256":"01e9630a77beb29d80092495558542c2e45a80a2c5dd12b513fdd7fed071d6a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:35.818620Z","signature_b64":"ylnkmKY+WgkkvqYHN10elSipj1WlJG/pYt1Lelj0yDbBNtssgD1gTm7cNTCrnpyteT+I90eTmLJeni8Bj8VmCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01e9630a77beb29d80092495558542c2e45a80a2c5dd12b513fdd7fed071d6a7","last_reissued_at":"2026-05-18T04:08:35.818058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:35.818058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0501304","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:08:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KnbaOiMwjIMbL0tb5QXeGzYFv8asQhGpT+LvQY+sYN5MS1dSlxozUgt2oH3gLxQlguNLEk5ZVH8TkbeJJibKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:54:33.479923Z"},"content_sha256":"6e51c85a33789aa27b2a4bfa14e1bef5d62f254168735c365fbb1f8812b386cf","schema_version":"1.0","event_id":"sha256:6e51c85a33789aa27b2a4bfa14e1bef5d62f254168735c365fbb1f8812b386cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:AHUWGCTXX2ZJ3AAJESKVLBKCYL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The unstable integral homology of the mapping class groups of a surface with boundary","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Veronique Godin","submitted_at":"2005-01-19T21:49:46Z","abstract_excerpt":"We construct a graph complex calculating the integral ho- mology of the bordered mapping class groups. We compute the ho- mology of the bordered mapping class groups of various surfaces. Using the circle action on this graph complex, we build a double complex and a spectral sequence converging to the homology of the unbordered mapping class groups. We compute the homology of the punctured mapping class groups associated to certain surfaces. Finally, we use Miller's operad to get the first Kudo-Araki and Browder operations on our graph complex. We also consider an unstable version of the higher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501304","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:08:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3l3qTx5Y0CAMbIUfM/sk3bpO5vhRwJvPbWwED1cumhv32jmklESi0/+SEMRwzqw2XT9NqF3nbxi9DqM9fdqABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:54:33.480259Z"},"content_sha256":"f1259a26f29902be9b235ff15a6f0f313d110e860301a6c623359657743d0d13","schema_version":"1.0","event_id":"sha256:f1259a26f29902be9b235ff15a6f0f313d110e860301a6c623359657743d0d13"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AHUWGCTXX2ZJ3AAJESKVLBKCYL/bundle.json","state_url":"https://pith.science/pith/AHUWGCTXX2ZJ3AAJESKVLBKCYL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AHUWGCTXX2ZJ3AAJESKVLBKCYL/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":"2026-06-01T19:54:33Z","links":{"resolver":"https://pith.science/pith/AHUWGCTXX2ZJ3AAJESKVLBKCYL","bundle":"https://pith.science/pith/AHUWGCTXX2ZJ3AAJESKVLBKCYL/bundle.json","state":"https://pith.science/pith/AHUWGCTXX2ZJ3AAJESKVLBKCYL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AHUWGCTXX2ZJ3AAJESKVLBKCYL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:AHUWGCTXX2ZJ3AAJESKVLBKCYL","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":"98b91788d125d4cf607a5c165b99ae1fb868894b8ae0a69cb5a768f4af0bfb99","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.AT","submitted_at":"2005-01-19T21:49:46Z","title_canon_sha256":"807de0b13cff8539ba2719f52a7d6986a45fd16751574d275c67a6bd3af56ddf"},"schema_version":"1.0","source":{"id":"math/0501304","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0501304","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"arxiv_version","alias_value":"math/0501304v2","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501304","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"pith_short_12","alias_value":"AHUWGCTXX2ZJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"AHUWGCTXX2ZJ3AAJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"AHUWGCTX","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:f1259a26f29902be9b235ff15a6f0f313d110e860301a6c623359657743d0d13","target":"graph","created_at":"2026-05-18T04:08:35Z","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 construct a graph complex calculating the integral ho- mology of the bordered mapping class groups. We compute the ho- mology of the bordered mapping class groups of various surfaces. Using the circle action on this graph complex, we build a double complex and a spectral sequence converging to the homology of the unbordered mapping class groups. We compute the homology of the punctured mapping class groups associated to certain surfaces. Finally, we use Miller's operad to get the first Kudo-Araki and Browder operations on our graph complex. We also consider an unstable version of the higher","authors_text":"Veronique Godin","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2005-01-19T21:49:46Z","title":"The unstable integral homology of the mapping class groups of a surface with boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501304","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":"sha256:6e51c85a33789aa27b2a4bfa14e1bef5d62f254168735c365fbb1f8812b386cf","target":"record","created_at":"2026-05-18T04:08:35Z","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":"98b91788d125d4cf607a5c165b99ae1fb868894b8ae0a69cb5a768f4af0bfb99","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.AT","submitted_at":"2005-01-19T21:49:46Z","title_canon_sha256":"807de0b13cff8539ba2719f52a7d6986a45fd16751574d275c67a6bd3af56ddf"},"schema_version":"1.0","source":{"id":"math/0501304","kind":"arxiv","version":2}},"canonical_sha256":"01e9630a77beb29d80092495558542c2e45a80a2c5dd12b513fdd7fed071d6a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01e9630a77beb29d80092495558542c2e45a80a2c5dd12b513fdd7fed071d6a7","first_computed_at":"2026-05-18T04:08:35.818058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:35.818058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ylnkmKY+WgkkvqYHN10elSipj1WlJG/pYt1Lelj0yDbBNtssgD1gTm7cNTCrnpyteT+I90eTmLJeni8Bj8VmCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:35.818620Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0501304","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e51c85a33789aa27b2a4bfa14e1bef5d62f254168735c365fbb1f8812b386cf","sha256:f1259a26f29902be9b235ff15a6f0f313d110e860301a6c623359657743d0d13"],"state_sha256":"057389b80d0ac443b89f1b4396e60ef2ce4a4eab574db1fa7e2ccf5e4e04c6cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+qyjchqCuN3N/Bq9Bux/vyXR92SkMI4UL3JRax/jflJffazOyLS5NspOLDcvlPpqdptxpEE4peRp5hQ1yUMdAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:54:33.482080Z","bundle_sha256":"0b525b04c2df7317d881c222aab844a901b37a2b2803d88dfa56d917617ed2c6"}}