{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:MJKMKYWPWDNKS4MXXX4SMDI77X","short_pith_number":"pith:MJKMKYWP","canonical_record":{"source":{"id":"math/0201091","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2002-01-10T18:07:04Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"943f05a473250deb01f6e52320a57e14f21dcea5a986ffe69d64d4bd989a928f","abstract_canon_sha256":"fa51d0310009146a9094e7783f974486904495009aaad8a0c2f95d0726304dc0"},"schema_version":"1.0"},"canonical_sha256":"6254c562cfb0daa97197bdf9260d1ffdd00c4eeadd4b05614556b7113763d492","source":{"kind":"arxiv","id":"math/0201091","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0201091","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/0201091v2","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0201091","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"MJKMKYWPWDNK","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"MJKMKYWPWDNKS4MX","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"MJKMKYWP","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:MJKMKYWPWDNKS4MXXX4SMDI77X","target":"record","payload":{"canonical_record":{"source":{"id":"math/0201091","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2002-01-10T18:07:04Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"943f05a473250deb01f6e52320a57e14f21dcea5a986ffe69d64d4bd989a928f","abstract_canon_sha256":"fa51d0310009146a9094e7783f974486904495009aaad8a0c2f95d0726304dc0"},"schema_version":"1.0"},"canonical_sha256":"6254c562cfb0daa97197bdf9260d1ffdd00c4eeadd4b05614556b7113763d492","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:36.686078Z","signature_b64":"U71oIrj4UI/F4m/ahm9IgxHuVNkTxukvnCwQm6SgUdkAWwwtyWCiGMTCcBNpNdSdmf/J0sYrPdXLQc7fYfoOAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6254c562cfb0daa97197bdf9260d1ffdd00c4eeadd4b05614556b7113763d492","last_reissued_at":"2026-05-18T01:14:36.685389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:36.685389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0201091","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":"2026-05-18T01:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PWJPHn9J0K0nY6dCTWnkKqhwSlFl3TwWWPuUY08S2yuBumnqh2KIqZEEEpJK9zOQ0/gDmyjx5X8FiJcLCN4EDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:02:51.513033Z"},"content_sha256":"0324094f0c937d00ddeeaf8c18644a2c491352685d6309167e7ef2ffc34e3aa2","schema_version":"1.0","event_id":"sha256:0324094f0c937d00ddeeaf8c18644a2c491352685d6309167e7ef2ffc34e3aa2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:MJKMKYWPWDNKS4MXXX4SMDI77X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Gromov-Lawson-Rosenberg conjecture for cocompact Fuchsian groups","license":"","headline":"","cross_cats":["math.KT"],"primary_cat":"math.DG","authors_text":"James F. Davis, Kimberly Pearson","submitted_at":"2002-01-10T18:07:04Z","abstract_excerpt":"We prove the Gromov-Lawson-Rosenberg conjecture for cocompact Fuchsian groups, thereby giving necessary and sufficient conditions for a closed spin manifold of dimension greater than four with fundamental group cocompact Fuchsian to admit a metric of positive scalar curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0201091","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":"2026-05-18T01:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bPLQtgkqJK74NcPvs/q2V2YGi9rfdBxAjhhfFcp2antT5a8zttMVGA1k+FCK88SxNz+T42kdKpqsC08e5JR/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:02:51.513552Z"},"content_sha256":"117bcabced3850db394f528f6520f39276937be246664570103afb0737fc9f6f","schema_version":"1.0","event_id":"sha256:117bcabced3850db394f528f6520f39276937be246664570103afb0737fc9f6f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MJKMKYWPWDNKS4MXXX4SMDI77X/bundle.json","state_url":"https://pith.science/pith/MJKMKYWPWDNKS4MXXX4SMDI77X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MJKMKYWPWDNKS4MXXX4SMDI77X/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":"2026-05-28T20:02:51Z","links":{"resolver":"https://pith.science/pith/MJKMKYWPWDNKS4MXXX4SMDI77X","bundle":"https://pith.science/pith/MJKMKYWPWDNKS4MXXX4SMDI77X/bundle.json","state":"https://pith.science/pith/MJKMKYWPWDNKS4MXXX4SMDI77X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MJKMKYWPWDNKS4MXXX4SMDI77X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:MJKMKYWPWDNKS4MXXX4SMDI77X","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":"fa51d0310009146a9094e7783f974486904495009aaad8a0c2f95d0726304dc0","cross_cats_sorted":["math.KT"],"license":"","primary_cat":"math.DG","submitted_at":"2002-01-10T18:07:04Z","title_canon_sha256":"943f05a473250deb01f6e52320a57e14f21dcea5a986ffe69d64d4bd989a928f"},"schema_version":"1.0","source":{"id":"math/0201091","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0201091","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/0201091v2","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0201091","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"MJKMKYWPWDNK","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"MJKMKYWPWDNKS4MX","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"MJKMKYWP","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:117bcabced3850db394f528f6520f39276937be246664570103afb0737fc9f6f","target":"graph","created_at":"2026-05-18T01:14:36Z","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 prove the Gromov-Lawson-Rosenberg conjecture for cocompact Fuchsian groups, thereby giving necessary and sufficient conditions for a closed spin manifold of dimension greater than four with fundamental group cocompact Fuchsian to admit a metric of positive scalar curvature.","authors_text":"James F. Davis, Kimberly Pearson","cross_cats":["math.KT"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2002-01-10T18:07:04Z","title":"The Gromov-Lawson-Rosenberg conjecture for cocompact Fuchsian groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0201091","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":"sha256:0324094f0c937d00ddeeaf8c18644a2c491352685d6309167e7ef2ffc34e3aa2","target":"record","created_at":"2026-05-18T01:14:36Z","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":"fa51d0310009146a9094e7783f974486904495009aaad8a0c2f95d0726304dc0","cross_cats_sorted":["math.KT"],"license":"","primary_cat":"math.DG","submitted_at":"2002-01-10T18:07:04Z","title_canon_sha256":"943f05a473250deb01f6e52320a57e14f21dcea5a986ffe69d64d4bd989a928f"},"schema_version":"1.0","source":{"id":"math/0201091","kind":"arxiv","version":2}},"canonical_sha256":"6254c562cfb0daa97197bdf9260d1ffdd00c4eeadd4b05614556b7113763d492","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6254c562cfb0daa97197bdf9260d1ffdd00c4eeadd4b05614556b7113763d492","first_computed_at":"2026-05-18T01:14:36.685389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:36.685389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U71oIrj4UI/F4m/ahm9IgxHuVNkTxukvnCwQm6SgUdkAWwwtyWCiGMTCcBNpNdSdmf/J0sYrPdXLQc7fYfoOAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:36.686078Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0201091","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0324094f0c937d00ddeeaf8c18644a2c491352685d6309167e7ef2ffc34e3aa2","sha256:117bcabced3850db394f528f6520f39276937be246664570103afb0737fc9f6f"],"state_sha256":"1857a40854bf82c9e856fe9b1d21fec6d2af34aa9f4f6896d8960814a0c3eb80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MO1ntr1/qTcPZZ0UhG0e77ZLY64OJ0BFLelY9xxvt+1SS4iT+lPGPYI/QEaSGnSx6MiM8VNNonQdf1jOiE1IDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:02:51.517096Z","bundle_sha256":"9a2a90bb1699c8a3b48e6e55734b5f6bb2f4f4d3b549cb32e7d57e66c7fa2880"}}