{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QVSO5GISFPRXBGYNI4TZ5WDHPS","short_pith_number":"pith:QVSO5GIS","canonical_record":{"source":{"id":"1607.06244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-07-21T09:25:31Z","cross_cats_sorted":["math.AT","math.SG"],"title_canon_sha256":"33697ecbc77490b2b5db14493dbe81b204e83f75e055ba0bc875c9d63f620fc7","abstract_canon_sha256":"78e1aa09667593c3bcab911cbbab573b280aab18ab5e68b718c1c063f6bb5fd0"},"schema_version":"1.0"},"canonical_sha256":"8564ee99122be3709b0d47279ed8677c80d606fcff4451ad465d171fae4c39c0","source":{"kind":"arxiv","id":"1607.06244","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06244","created_at":"2026-05-18T01:10:42Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06244v1","created_at":"2026-05-18T01:10:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06244","created_at":"2026-05-18T01:10:42Z"},{"alias_kind":"pith_short_12","alias_value":"QVSO5GISFPRX","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QVSO5GISFPRXBGYN","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QVSO5GIS","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QVSO5GISFPRXBGYNI4TZ5WDHPS","target":"record","payload":{"canonical_record":{"source":{"id":"1607.06244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-07-21T09:25:31Z","cross_cats_sorted":["math.AT","math.SG"],"title_canon_sha256":"33697ecbc77490b2b5db14493dbe81b204e83f75e055ba0bc875c9d63f620fc7","abstract_canon_sha256":"78e1aa09667593c3bcab911cbbab573b280aab18ab5e68b718c1c063f6bb5fd0"},"schema_version":"1.0"},"canonical_sha256":"8564ee99122be3709b0d47279ed8677c80d606fcff4451ad465d171fae4c39c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:42.174398Z","signature_b64":"s3+/f1Q/bs78LuWXGZsggRp3PysApWtHOEB6x17DrFiQgg2XkB4m8lwe5APDOLsQsFHxE9N3X/YT+1Fl0ezyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8564ee99122be3709b0d47279ed8677c80d606fcff4451ad465d171fae4c39c0","last_reissued_at":"2026-05-18T01:10:42.173829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:42.173829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.06244","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":"2026-05-18T01:10:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SIl+gPoBNtqmMOIlNsUCPu44f9MyElW7j1YG8kcXNswye9Hv52PmLxFaleZTRUpRFn2o5U8LgXJWaGAY/mRuDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:27:37.645032Z"},"content_sha256":"038e91fd3f769f9dcd805703733b5f1d031c0d325a8db0002eb89d2ba1af913e","schema_version":"1.0","event_id":"sha256:038e91fd3f769f9dcd805703733b5f1d031c0d325a8db0002eb89d2ba1af913e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QVSO5GISFPRXBGYNI4TZ5WDHPS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Morse-Bott inequalities, orientations, and the Thom isomorphism in Morse homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.SG"],"primary_cat":"math.GT","authors_text":"Thomas O. Rot","submitted_at":"2016-07-21T09:25:31Z","abstract_excerpt":"The Morse-Bott inequalities relate the topology of a closed manifold to the topology of the critical point set of a Morse-Bott function defined on it. The Morse-Bott inequalities are sometimes stated under incorrect orientation assumptions. We show that these assumptions are insufficient with an explicit counterexample and clarify the origin of the mistake."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06244","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":"2026-05-18T01:10:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5kSvNOvJqGlJZm4nmJ9D4I58QW88sjuboqHjOZxAezv0sIWCT/MVJxXqjOR8305KT/gDVK8HiYjy4lEZCrPaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:27:37.645395Z"},"content_sha256":"f690dc103f32c5c9716b3781a6a06ae7410845e79bf63b30548974ea75e62651","schema_version":"1.0","event_id":"sha256:f690dc103f32c5c9716b3781a6a06ae7410845e79bf63b30548974ea75e62651"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVSO5GISFPRXBGYNI4TZ5WDHPS/bundle.json","state_url":"https://pith.science/pith/QVSO5GISFPRXBGYNI4TZ5WDHPS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVSO5GISFPRXBGYNI4TZ5WDHPS/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":"2026-06-01T01:27:37Z","links":{"resolver":"https://pith.science/pith/QVSO5GISFPRXBGYNI4TZ5WDHPS","bundle":"https://pith.science/pith/QVSO5GISFPRXBGYNI4TZ5WDHPS/bundle.json","state":"https://pith.science/pith/QVSO5GISFPRXBGYNI4TZ5WDHPS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVSO5GISFPRXBGYNI4TZ5WDHPS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QVSO5GISFPRXBGYNI4TZ5WDHPS","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":"78e1aa09667593c3bcab911cbbab573b280aab18ab5e68b718c1c063f6bb5fd0","cross_cats_sorted":["math.AT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-07-21T09:25:31Z","title_canon_sha256":"33697ecbc77490b2b5db14493dbe81b204e83f75e055ba0bc875c9d63f620fc7"},"schema_version":"1.0","source":{"id":"1607.06244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06244","created_at":"2026-05-18T01:10:42Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06244v1","created_at":"2026-05-18T01:10:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06244","created_at":"2026-05-18T01:10:42Z"},{"alias_kind":"pith_short_12","alias_value":"QVSO5GISFPRX","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QVSO5GISFPRXBGYN","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QVSO5GIS","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:f690dc103f32c5c9716b3781a6a06ae7410845e79bf63b30548974ea75e62651","target":"graph","created_at":"2026-05-18T01:10:42Z","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":"The Morse-Bott inequalities relate the topology of a closed manifold to the topology of the critical point set of a Morse-Bott function defined on it. The Morse-Bott inequalities are sometimes stated under incorrect orientation assumptions. We show that these assumptions are insufficient with an explicit counterexample and clarify the origin of the mistake.","authors_text":"Thomas O. Rot","cross_cats":["math.AT","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-07-21T09:25:31Z","title":"The Morse-Bott inequalities, orientations, and the Thom isomorphism in Morse homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06244","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":"sha256:038e91fd3f769f9dcd805703733b5f1d031c0d325a8db0002eb89d2ba1af913e","target":"record","created_at":"2026-05-18T01:10:42Z","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":"78e1aa09667593c3bcab911cbbab573b280aab18ab5e68b718c1c063f6bb5fd0","cross_cats_sorted":["math.AT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-07-21T09:25:31Z","title_canon_sha256":"33697ecbc77490b2b5db14493dbe81b204e83f75e055ba0bc875c9d63f620fc7"},"schema_version":"1.0","source":{"id":"1607.06244","kind":"arxiv","version":1}},"canonical_sha256":"8564ee99122be3709b0d47279ed8677c80d606fcff4451ad465d171fae4c39c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8564ee99122be3709b0d47279ed8677c80d606fcff4451ad465d171fae4c39c0","first_computed_at":"2026-05-18T01:10:42.173829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:42.173829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s3+/f1Q/bs78LuWXGZsggRp3PysApWtHOEB6x17DrFiQgg2XkB4m8lwe5APDOLsQsFHxE9N3X/YT+1Fl0ezyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:42.174398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:038e91fd3f769f9dcd805703733b5f1d031c0d325a8db0002eb89d2ba1af913e","sha256:f690dc103f32c5c9716b3781a6a06ae7410845e79bf63b30548974ea75e62651"],"state_sha256":"f094a158aff7a42b60b894d6dce8fadf5fc59692a500893fc977570959b64363"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0PlXk7v7j6/6kQjlvwS2+IOmkvOJSQr9yTcwIHIkb5TGaz3294XBW3plntj+NJku0KonRFqC/wejjo1ojTFtCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:27:37.647322Z","bundle_sha256":"3e1b4aec04caefe6018fbe2a5138aba95b98d66a4f2949a21c2a2b2548795131"}}