{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OSGIY4F6SKIXHMPH3ER2ECICSF","short_pith_number":"pith:OSGIY4F6","canonical_record":{"source":{"id":"1808.08737","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-08-27T08:53:18Z","cross_cats_sorted":[],"title_canon_sha256":"3b8feacaf4d09bbfb73a11eb2295d42898b10eab4ce6dcffb2bba6969e3efb69","abstract_canon_sha256":"f3cd605215fa3f5c690958508be74bcfa15681c67270f936ca36945d47ca0383"},"schema_version":"1.0"},"canonical_sha256":"748c8c70be929173b1e7d923a209029158b9898e365d214f5adc72ed0993a983","source":{"kind":"arxiv","id":"1808.08737","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08737","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08737v3","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08737","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"pith_short_12","alias_value":"OSGIY4F6SKIX","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OSGIY4F6SKIXHMPH","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OSGIY4F6","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OSGIY4F6SKIXHMPH3ER2ECICSF","target":"record","payload":{"canonical_record":{"source":{"id":"1808.08737","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-08-27T08:53:18Z","cross_cats_sorted":[],"title_canon_sha256":"3b8feacaf4d09bbfb73a11eb2295d42898b10eab4ce6dcffb2bba6969e3efb69","abstract_canon_sha256":"f3cd605215fa3f5c690958508be74bcfa15681c67270f936ca36945d47ca0383"},"schema_version":"1.0"},"canonical_sha256":"748c8c70be929173b1e7d923a209029158b9898e365d214f5adc72ed0993a983","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:38.407556Z","signature_b64":"CK9FKsDIgcl07uC6V7A5NrIn5TTJFcAQLaNFATHy0m37DljUe+wrGqa6cnNb1s8qJTVQPYa6hcAj6fqfQynWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"748c8c70be929173b1e7d923a209029158b9898e365d214f5adc72ed0993a983","last_reissued_at":"2026-05-17T23:55:38.407163Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:38.407163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.08737","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"du8cf1bbD9Fp5RoHgEFJq0BuE1trwmav4405Wv6qkeX3L+zcPDVWFGRPK8P1SQ5YP5Vz59CkA25Jx7FnwsT8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:29:46.321291Z"},"content_sha256":"523bdf410dd68fda92e2d73556821096cbb0a5ff01147b12af8e28616f934167","schema_version":"1.0","event_id":"sha256:523bdf410dd68fda92e2d73556821096cbb0a5ff01147b12af8e28616f934167"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OSGIY4F6SKIXHMPH3ER2ECICSF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting maximally broken Morse trajectories on aspherical manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Caterina Campagnolo, Roman Sauer","submitted_at":"2018-08-27T08:53:18Z","abstract_excerpt":"We prove a lower bound on the number of maximally broken trajectories of the negative gradient flow of a Morse-Smale function on a closed aspherical manifold in terms of integral (torsion) homology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08737","kind":"arxiv","version":3},"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":"2026-05-17T23:55:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oUdu0hc1AtzKUXyi/jQNUfg3Q6kzCTBWv4VeXfid6niOCMCr+gAOpCbd4XB1tHlwG+6vz4p1K+U9MWzFz54jCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:29:46.321645Z"},"content_sha256":"125d95bbf50471039aa4cd1a53b694ae89687890aaf282f557c272d4d320bccf","schema_version":"1.0","event_id":"sha256:125d95bbf50471039aa4cd1a53b694ae89687890aaf282f557c272d4d320bccf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OSGIY4F6SKIXHMPH3ER2ECICSF/bundle.json","state_url":"https://pith.science/pith/OSGIY4F6SKIXHMPH3ER2ECICSF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OSGIY4F6SKIXHMPH3ER2ECICSF/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":"2026-06-03T16:29:46Z","links":{"resolver":"https://pith.science/pith/OSGIY4F6SKIXHMPH3ER2ECICSF","bundle":"https://pith.science/pith/OSGIY4F6SKIXHMPH3ER2ECICSF/bundle.json","state":"https://pith.science/pith/OSGIY4F6SKIXHMPH3ER2ECICSF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OSGIY4F6SKIXHMPH3ER2ECICSF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OSGIY4F6SKIXHMPH3ER2ECICSF","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":"f3cd605215fa3f5c690958508be74bcfa15681c67270f936ca36945d47ca0383","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-08-27T08:53:18Z","title_canon_sha256":"3b8feacaf4d09bbfb73a11eb2295d42898b10eab4ce6dcffb2bba6969e3efb69"},"schema_version":"1.0","source":{"id":"1808.08737","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08737","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08737v3","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08737","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"pith_short_12","alias_value":"OSGIY4F6SKIX","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OSGIY4F6SKIXHMPH","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OSGIY4F6","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:125d95bbf50471039aa4cd1a53b694ae89687890aaf282f557c272d4d320bccf","target":"graph","created_at":"2026-05-17T23:55:38Z","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 a lower bound on the number of maximally broken trajectories of the negative gradient flow of a Morse-Smale function on a closed aspherical manifold in terms of integral (torsion) homology.","authors_text":"Caterina Campagnolo, Roman Sauer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-08-27T08:53:18Z","title":"Counting maximally broken Morse trajectories on aspherical manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08737","kind":"arxiv","version":3},"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":"sha256:523bdf410dd68fda92e2d73556821096cbb0a5ff01147b12af8e28616f934167","target":"record","created_at":"2026-05-17T23:55:38Z","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":"f3cd605215fa3f5c690958508be74bcfa15681c67270f936ca36945d47ca0383","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-08-27T08:53:18Z","title_canon_sha256":"3b8feacaf4d09bbfb73a11eb2295d42898b10eab4ce6dcffb2bba6969e3efb69"},"schema_version":"1.0","source":{"id":"1808.08737","kind":"arxiv","version":3}},"canonical_sha256":"748c8c70be929173b1e7d923a209029158b9898e365d214f5adc72ed0993a983","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"748c8c70be929173b1e7d923a209029158b9898e365d214f5adc72ed0993a983","first_computed_at":"2026-05-17T23:55:38.407163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:38.407163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CK9FKsDIgcl07uC6V7A5NrIn5TTJFcAQLaNFATHy0m37DljUe+wrGqa6cnNb1s8qJTVQPYa6hcAj6fqfQynWAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:38.407556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.08737","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:523bdf410dd68fda92e2d73556821096cbb0a5ff01147b12af8e28616f934167","sha256:125d95bbf50471039aa4cd1a53b694ae89687890aaf282f557c272d4d320bccf"],"state_sha256":"a6a9748c68f96053deee85c04a6f2ab913e5ab93d83c702188605c8da1988005"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z1EcRqBtAdXFlFV3Lqi6AQr8OO4+FxHriANjBntvhOl+Ez1Pbu8SDBubTiqNOj2lfGUAeQ5nDe98eMcttV90BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:29:46.323582Z","bundle_sha256":"cbc22d7028229b2ef923b3042bf1a505c54f610c12a85948257c542c0be319e7"}}