{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:PK6XWZP2PI5RLOXYY7NPJRNWYU","short_pith_number":"pith:PK6XWZP2","canonical_record":{"source":{"id":"0907.4226","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-24T06:46:05Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"5bf9cd7655543a7dd0631cd9bdda3f05ed558d1d60ad213c9e19fbf79e86fe4c","abstract_canon_sha256":"7a12b0287443ecedaf90c3698dce5970c11c6724c7681d900608bd94e23f0be9"},"schema_version":"1.0"},"canonical_sha256":"7abd7b65fa7a3b15baf8c7daf4c5b6c5330ed493839a8e453d7d77084f60bd2c","source":{"kind":"arxiv","id":"0907.4226","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.4226","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"0907.4226v2","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.4226","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"PK6XWZP2PI5R","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"PK6XWZP2PI5RLOXY","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"PK6XWZP2","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:PK6XWZP2PI5RLOXYY7NPJRNWYU","target":"record","payload":{"canonical_record":{"source":{"id":"0907.4226","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-24T06:46:05Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"5bf9cd7655543a7dd0631cd9bdda3f05ed558d1d60ad213c9e19fbf79e86fe4c","abstract_canon_sha256":"7a12b0287443ecedaf90c3698dce5970c11c6724c7681d900608bd94e23f0be9"},"schema_version":"1.0"},"canonical_sha256":"7abd7b65fa7a3b15baf8c7daf4c5b6c5330ed493839a8e453d7d77084f60bd2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:18.794172Z","signature_b64":"j+gVS3Ubl692L9UB8uqPC4HSqfAY7VSF+3CjtsJKXQnpOKgn89NoamzRkJpHZWIHcsWfL/9Ra4gtbdqq95rEAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7abd7b65fa7a3b15baf8c7daf4c5b6c5330ed493839a8e453d7d77084f60bd2c","last_reissued_at":"2026-05-18T02:38:18.793534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:18.793534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.4226","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":"2026-05-18T02:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iwJLvUIQ4b+Sc5bm4EI7Yz7T//t2YRhO2c+w9WhZK5kCyjwxWq+i3t6xgZk+QiPIV2xNI7ZuwrLQBgU2h/12AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:40:28.164944Z"},"content_sha256":"1b2c2306ab402345d28e39d6f82878e01a57238c37b8584b64ae550457d5a7dc","schema_version":"1.0","event_id":"sha256:1b2c2306ab402345d28e39d6f82878e01a57238c37b8584b64ae550457d5a7dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:PK6XWZP2PI5RLOXYY7NPJRNWYU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Madsen-Weiss for geometrically minded topologists","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Nikolai Mishachev, Soren Galatius, Yakov Eliashberg","submitted_at":"2009-07-24T06:46:05Z","abstract_excerpt":"We give an alternative proof of Madsen-Weiss' generalized Mumford conjecture. Our proof is based on ideas similar to Madsen-Weiss' original proof, but it is more geometrical and less homotopy theoretical in nature. At the heart of the argument is a geometric version of Harer stability, which we formulate as a theorem about folded maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4226","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":"2026-05-18T02:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Yq98inTRU7N9PntJ/AmPNiuVAceITY6XqvTM/FnoIUtWXJ3rdmcHE47JgXALMahQgNarhhLKxremFUqMQDBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:40:28.165588Z"},"content_sha256":"f37b4be51a8129d5824948a6e4df16c3caa3ed602037963d9fd934390b6160b9","schema_version":"1.0","event_id":"sha256:f37b4be51a8129d5824948a6e4df16c3caa3ed602037963d9fd934390b6160b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PK6XWZP2PI5RLOXYY7NPJRNWYU/bundle.json","state_url":"https://pith.science/pith/PK6XWZP2PI5RLOXYY7NPJRNWYU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PK6XWZP2PI5RLOXYY7NPJRNWYU/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":"2026-05-28T16:40:28Z","links":{"resolver":"https://pith.science/pith/PK6XWZP2PI5RLOXYY7NPJRNWYU","bundle":"https://pith.science/pith/PK6XWZP2PI5RLOXYY7NPJRNWYU/bundle.json","state":"https://pith.science/pith/PK6XWZP2PI5RLOXYY7NPJRNWYU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PK6XWZP2PI5RLOXYY7NPJRNWYU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:PK6XWZP2PI5RLOXYY7NPJRNWYU","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":"7a12b0287443ecedaf90c3698dce5970c11c6724c7681d900608bd94e23f0be9","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-24T06:46:05Z","title_canon_sha256":"5bf9cd7655543a7dd0631cd9bdda3f05ed558d1d60ad213c9e19fbf79e86fe4c"},"schema_version":"1.0","source":{"id":"0907.4226","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.4226","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"0907.4226v2","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.4226","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"PK6XWZP2PI5R","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"PK6XWZP2PI5RLOXY","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"PK6XWZP2","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:f37b4be51a8129d5824948a6e4df16c3caa3ed602037963d9fd934390b6160b9","target":"graph","created_at":"2026-05-18T02:38:18Z","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 give an alternative proof of Madsen-Weiss' generalized Mumford conjecture. Our proof is based on ideas similar to Madsen-Weiss' original proof, but it is more geometrical and less homotopy theoretical in nature. At the heart of the argument is a geometric version of Harer stability, which we formulate as a theorem about folded maps.","authors_text":"Nikolai Mishachev, Soren Galatius, Yakov Eliashberg","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-24T06:46:05Z","title":"Madsen-Weiss for geometrically minded topologists"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4226","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":"sha256:1b2c2306ab402345d28e39d6f82878e01a57238c37b8584b64ae550457d5a7dc","target":"record","created_at":"2026-05-18T02:38:18Z","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":"7a12b0287443ecedaf90c3698dce5970c11c6724c7681d900608bd94e23f0be9","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-24T06:46:05Z","title_canon_sha256":"5bf9cd7655543a7dd0631cd9bdda3f05ed558d1d60ad213c9e19fbf79e86fe4c"},"schema_version":"1.0","source":{"id":"0907.4226","kind":"arxiv","version":2}},"canonical_sha256":"7abd7b65fa7a3b15baf8c7daf4c5b6c5330ed493839a8e453d7d77084f60bd2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7abd7b65fa7a3b15baf8c7daf4c5b6c5330ed493839a8e453d7d77084f60bd2c","first_computed_at":"2026-05-18T02:38:18.793534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:18.793534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j+gVS3Ubl692L9UB8uqPC4HSqfAY7VSF+3CjtsJKXQnpOKgn89NoamzRkJpHZWIHcsWfL/9Ra4gtbdqq95rEAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:18.794172Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.4226","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b2c2306ab402345d28e39d6f82878e01a57238c37b8584b64ae550457d5a7dc","sha256:f37b4be51a8129d5824948a6e4df16c3caa3ed602037963d9fd934390b6160b9"],"state_sha256":"516f19e7b3387270fbbafc3b2c59f087418a0a5812d2981eed6616226709c04b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JKiOCF7f3WnGHWKQc4HG+aAjHPViGQ3K1KHXAmRK7N7Nmzkrm0BsSjGSC2UdQj0IK7kGe3Zz2Dd2qxdSaW+zCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:40:28.167932Z","bundle_sha256":"287554a5e375fe168a4dcfbab7dd57d1d7694262419b7fca02ae18cbe243a891"}}