{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:A6Z3N7ERZQWYMC3E6HHCC2Q267","short_pith_number":"pith:A6Z3N7ER","canonical_record":{"source":{"id":"math/0402334","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2004-02-20T13:31:48Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"e468a9f370044a729c8f419759c4e1aaa033cb33125d44b01d99476c274df885","abstract_canon_sha256":"45814d4fd53c84da2f89b752df58fd792507f853df8619c050f2e03a5cab2aca"},"schema_version":"1.0"},"canonical_sha256":"07b3b6fc91cc2d860b64f1ce216a1af7fa8667e788f04ce7d228e0122c036db6","source":{"kind":"arxiv","id":"math/0402334","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0402334","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0402334v1","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0402334","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"pith_short_12","alias_value":"A6Z3N7ERZQWY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"A6Z3N7ERZQWYMC3E","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"A6Z3N7ER","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:A6Z3N7ERZQWYMC3E6HHCC2Q267","target":"record","payload":{"canonical_record":{"source":{"id":"math/0402334","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2004-02-20T13:31:48Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"e468a9f370044a729c8f419759c4e1aaa033cb33125d44b01d99476c274df885","abstract_canon_sha256":"45814d4fd53c84da2f89b752df58fd792507f853df8619c050f2e03a5cab2aca"},"schema_version":"1.0"},"canonical_sha256":"07b3b6fc91cc2d860b64f1ce216a1af7fa8667e788f04ce7d228e0122c036db6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:32.505973Z","signature_b64":"AAICvZoLSkoEcJLQmqjuyl00nbWL7UtJqTLemBF2UEmMOHAtXHEIAMcBkA6yg/OStf2JxFwyCmh27DNEyOvSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07b3b6fc91cc2d860b64f1ce216a1af7fa8667e788f04ce7d228e0122c036db6","last_reissued_at":"2026-05-18T02:41:32.505542Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:32.505542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0402334","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PPloNvvNYauREVA/629RcXgDlPxKE9IFNguLxBPVKhKXDLqGCFh1w2CN48yjexhMHcE8Cf5uS5eM9QNcput3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T11:59:30.887556Z"},"content_sha256":"a535337fdd6f53db6fb33a5734699154fcabc217f280dcd69560823ef0d57592","schema_version":"1.0","event_id":"sha256:a535337fdd6f53db6fb33a5734699154fcabc217f280dcd69560823ef0d57592"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:A6Z3N7ERZQWYMC3E6HHCC2Q267","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The boundary-Wecken classification of surfaces","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Michael R. Kelly, Robert F. Brown","submitted_at":"2004-02-20T13:31:48Z","abstract_excerpt":"Let X be a compact 2-manifold with nonempty boundary dX and let f: (X, dX) --> (X, dX) be a boundary-preserving map. Denote by MF_d[f] the minimum number of fixed point among all boundary-preserving maps that are homotopic through boundary-preserving maps to f. The relative Nielsen number N_d(f) is the sum of the number of essential fixed point classes of the restriction f-bar : dX --> dX and the number of essential fixed point classes of f that do not contain essential fixed point classes of f-bar. We prove that if X is the Moebius band with one (open) disc removed, then MF_d[f] - N_d(f) < 2 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402334","kind":"arxiv","version":1},"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":"2026-05-18T02:41:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WIRzKr67QIDbyEa+H2+KsRKcDRrgoQfQEg+bOTu1oXomzVoVkrE8TxRX1h0tFguaDqUgnYcHSPxiqLt66Xo6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T11:59:30.887901Z"},"content_sha256":"5e5f6c4dd3ba807000f0b0faaf4a98696c1c61cfd701226590c2470315c5aac0","schema_version":"1.0","event_id":"sha256:5e5f6c4dd3ba807000f0b0faaf4a98696c1c61cfd701226590c2470315c5aac0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A6Z3N7ERZQWYMC3E6HHCC2Q267/bundle.json","state_url":"https://pith.science/pith/A6Z3N7ERZQWYMC3E6HHCC2Q267/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A6Z3N7ERZQWYMC3E6HHCC2Q267/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":"2026-06-21T11:59:30Z","links":{"resolver":"https://pith.science/pith/A6Z3N7ERZQWYMC3E6HHCC2Q267","bundle":"https://pith.science/pith/A6Z3N7ERZQWYMC3E6HHCC2Q267/bundle.json","state":"https://pith.science/pith/A6Z3N7ERZQWYMC3E6HHCC2Q267/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A6Z3N7ERZQWYMC3E6HHCC2Q267/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:A6Z3N7ERZQWYMC3E6HHCC2Q267","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":"45814d4fd53c84da2f89b752df58fd792507f853df8619c050f2e03a5cab2aca","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.AT","submitted_at":"2004-02-20T13:31:48Z","title_canon_sha256":"e468a9f370044a729c8f419759c4e1aaa033cb33125d44b01d99476c274df885"},"schema_version":"1.0","source":{"id":"math/0402334","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0402334","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0402334v1","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0402334","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"pith_short_12","alias_value":"A6Z3N7ERZQWY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"A6Z3N7ERZQWYMC3E","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"A6Z3N7ER","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:5e5f6c4dd3ba807000f0b0faaf4a98696c1c61cfd701226590c2470315c5aac0","target":"graph","created_at":"2026-05-18T02:41:32Z","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 X be a compact 2-manifold with nonempty boundary dX and let f: (X, dX) --> (X, dX) be a boundary-preserving map. Denote by MF_d[f] the minimum number of fixed point among all boundary-preserving maps that are homotopic through boundary-preserving maps to f. The relative Nielsen number N_d(f) is the sum of the number of essential fixed point classes of the restriction f-bar : dX --> dX and the number of essential fixed point classes of f that do not contain essential fixed point classes of f-bar. We prove that if X is the Moebius band with one (open) disc removed, then MF_d[f] - N_d(f) < 2 ","authors_text":"Michael R. Kelly, Robert F. Brown","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2004-02-20T13:31:48Z","title":"The boundary-Wecken classification of surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402334","kind":"arxiv","version":1},"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:a535337fdd6f53db6fb33a5734699154fcabc217f280dcd69560823ef0d57592","target":"record","created_at":"2026-05-18T02:41:32Z","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":"45814d4fd53c84da2f89b752df58fd792507f853df8619c050f2e03a5cab2aca","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.AT","submitted_at":"2004-02-20T13:31:48Z","title_canon_sha256":"e468a9f370044a729c8f419759c4e1aaa033cb33125d44b01d99476c274df885"},"schema_version":"1.0","source":{"id":"math/0402334","kind":"arxiv","version":1}},"canonical_sha256":"07b3b6fc91cc2d860b64f1ce216a1af7fa8667e788f04ce7d228e0122c036db6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07b3b6fc91cc2d860b64f1ce216a1af7fa8667e788f04ce7d228e0122c036db6","first_computed_at":"2026-05-18T02:41:32.505542Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:32.505542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AAICvZoLSkoEcJLQmqjuyl00nbWL7UtJqTLemBF2UEmMOHAtXHEIAMcBkA6yg/OStf2JxFwyCmh27DNEyOvSBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:32.505973Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0402334","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a535337fdd6f53db6fb33a5734699154fcabc217f280dcd69560823ef0d57592","sha256:5e5f6c4dd3ba807000f0b0faaf4a98696c1c61cfd701226590c2470315c5aac0"],"state_sha256":"068c76d6a69d264bcb510da56c4b70abca4d750b4506d0dc4f9f7ebc4c44aa8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sl3htYujeo/RM9HUBCMb5wYQbCurCrNmMnTn/GRmuHNNnn//XcdMsFO0vWgDjde/OF2SeFTcPsn5y/1O3L5GBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T11:59:30.889773Z","bundle_sha256":"bdc2a7a5d0c7f3764477fa03083b5bf9f65e4983731b9db0c0d1ecdd8b05e419"}}