{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:UEXI6G6M4VBYMWOABWWQG5I6D5","short_pith_number":"pith:UEXI6G6M","canonical_record":{"source":{"id":"1902.08841","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-02-23T19:55:38Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"5b57ee4b1af60a17ca6001243f489b1f9798c9b76a1936c65564e4cb95d9d386","abstract_canon_sha256":"88ca4e50e035c92469066cc0bf7a5b3a9a72df182c33330184c6d50d145f021c"},"schema_version":"1.0"},"canonical_sha256":"a12e8f1bcce5438659c00dad03751e1f5093210ea1af0add0b057449632cca99","source":{"kind":"arxiv","id":"1902.08841","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08841","created_at":"2026-07-05T03:00:43Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08841v5","created_at":"2026-07-05T03:00:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08841","created_at":"2026-07-05T03:00:43Z"},{"alias_kind":"pith_short_12","alias_value":"UEXI6G6M4VBY","created_at":"2026-07-05T03:00:43Z"},{"alias_kind":"pith_short_16","alias_value":"UEXI6G6M4VBYMWOA","created_at":"2026-07-05T03:00:43Z"},{"alias_kind":"pith_short_8","alias_value":"UEXI6G6M","created_at":"2026-07-05T03:00:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:UEXI6G6M4VBYMWOABWWQG5I6D5","target":"record","payload":{"canonical_record":{"source":{"id":"1902.08841","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-02-23T19:55:38Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"5b57ee4b1af60a17ca6001243f489b1f9798c9b76a1936c65564e4cb95d9d386","abstract_canon_sha256":"88ca4e50e035c92469066cc0bf7a5b3a9a72df182c33330184c6d50d145f021c"},"schema_version":"1.0"},"canonical_sha256":"a12e8f1bcce5438659c00dad03751e1f5093210ea1af0add0b057449632cca99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:00:43.833823Z","signature_b64":"jQwd0arRzmhz/VIMbIucU/wvzZRTX/D1ED139j4vWjDjVM1r/NjW5YOT01P2KSXXi+f3wK+DLzkxN4S4GdMDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a12e8f1bcce5438659c00dad03751e1f5093210ea1af0add0b057449632cca99","last_reissued_at":"2026-07-05T03:00:43.833372Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:00:43.833372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.08841","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:00:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FWLtArsusl9OyTHgjc2HYkuyHXYGt0mWc1Vf91UQj3bLVs46TJMrYYrfvZizY8ttALTDcAAqSvL72A7DvrxGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:22:03.669113Z"},"content_sha256":"f0d1424ace9c65c7c43950e44c6ca8ff0676ba245c430b5dbfcbc13b6b6c2a07","schema_version":"1.0","event_id":"sha256:f0d1424ace9c65c7c43950e44c6ca8ff0676ba245c430b5dbfcbc13b6b6c2a07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:UEXI6G6M4VBYMWOABWWQG5I6D5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GT","authors_text":"Naoki Kitazawa","submitted_at":"2019-02-23T19:55:38Z","abstract_excerpt":"The Reeb graph of a function on a smooth manifold is the graph obtained as the space of all connected components of level sets such that the set of all vertices coincides with the set of all connected components of level sets including singular points. Reeb graphs are fundamental and important in the algebraic and differential topological theory of Morse functions and their generalizations.\n  In this paper, as a related fundamental and important study, for given graphs, we construct certain smooth functions inducing the graphs as the Reeb graphs. Such works have been demonstrated by Masumoto, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08841","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1902.08841/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:00:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LHnEA1ygrCBHyxA2RAuByslMYGRvZr2jK7k3pcDvdqzMXnYxyybmDxhddIMXUdMs7VHclklI23XwFSHpB+vJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:22:03.669831Z"},"content_sha256":"b68b123a56757628049176729d58fb1a7c45914aec0e39cfd2ef282e03f2851b","schema_version":"1.0","event_id":"sha256:b68b123a56757628049176729d58fb1a7c45914aec0e39cfd2ef282e03f2851b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UEXI6G6M4VBYMWOABWWQG5I6D5/bundle.json","state_url":"https://pith.science/pith/UEXI6G6M4VBYMWOABWWQG5I6D5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UEXI6G6M4VBYMWOABWWQG5I6D5/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":"2026-08-13T08:22:03Z","links":{"resolver":"https://pith.science/pith/UEXI6G6M4VBYMWOABWWQG5I6D5","bundle":"https://pith.science/pith/UEXI6G6M4VBYMWOABWWQG5I6D5/bundle.json","state":"https://pith.science/pith/UEXI6G6M4VBYMWOABWWQG5I6D5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UEXI6G6M4VBYMWOABWWQG5I6D5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UEXI6G6M4VBYMWOABWWQG5I6D5","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":"88ca4e50e035c92469066cc0bf7a5b3a9a72df182c33330184c6d50d145f021c","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-02-23T19:55:38Z","title_canon_sha256":"5b57ee4b1af60a17ca6001243f489b1f9798c9b76a1936c65564e4cb95d9d386"},"schema_version":"1.0","source":{"id":"1902.08841","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08841","created_at":"2026-07-05T03:00:43Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08841v5","created_at":"2026-07-05T03:00:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08841","created_at":"2026-07-05T03:00:43Z"},{"alias_kind":"pith_short_12","alias_value":"UEXI6G6M4VBY","created_at":"2026-07-05T03:00:43Z"},{"alias_kind":"pith_short_16","alias_value":"UEXI6G6M4VBYMWOA","created_at":"2026-07-05T03:00:43Z"},{"alias_kind":"pith_short_8","alias_value":"UEXI6G6M","created_at":"2026-07-05T03:00:43Z"}],"graph_snapshots":[{"event_id":"sha256:b68b123a56757628049176729d58fb1a7c45914aec0e39cfd2ef282e03f2851b","target":"graph","created_at":"2026-07-05T03:00:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1902.08841/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Reeb graph of a function on a smooth manifold is the graph obtained as the space of all connected components of level sets such that the set of all vertices coincides with the set of all connected components of level sets including singular points. Reeb graphs are fundamental and important in the algebraic and differential topological theory of Morse functions and their generalizations.\n  In this paper, as a related fundamental and important study, for given graphs, we construct certain smooth functions inducing the graphs as the Reeb graphs. Such works have been demonstrated by Masumoto, ","authors_text":"Naoki Kitazawa","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-02-23T19:55:38Z","title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08841","kind":"arxiv","version":5},"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:f0d1424ace9c65c7c43950e44c6ca8ff0676ba245c430b5dbfcbc13b6b6c2a07","target":"record","created_at":"2026-07-05T03:00:43Z","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":"88ca4e50e035c92469066cc0bf7a5b3a9a72df182c33330184c6d50d145f021c","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-02-23T19:55:38Z","title_canon_sha256":"5b57ee4b1af60a17ca6001243f489b1f9798c9b76a1936c65564e4cb95d9d386"},"schema_version":"1.0","source":{"id":"1902.08841","kind":"arxiv","version":5}},"canonical_sha256":"a12e8f1bcce5438659c00dad03751e1f5093210ea1af0add0b057449632cca99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a12e8f1bcce5438659c00dad03751e1f5093210ea1af0add0b057449632cca99","first_computed_at":"2026-07-05T03:00:43.833372Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:00:43.833372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jQwd0arRzmhz/VIMbIucU/wvzZRTX/D1ED139j4vWjDjVM1r/NjW5YOT01P2KSXXi+f3wK+DLzkxN4S4GdMDCg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:00:43.833823Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.08841","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0d1424ace9c65c7c43950e44c6ca8ff0676ba245c430b5dbfcbc13b6b6c2a07","sha256:b68b123a56757628049176729d58fb1a7c45914aec0e39cfd2ef282e03f2851b"],"state_sha256":"f8f1e00f67d39c74f3a98b9f5c35d3945a161df4661e0c2a8023b04bc3da1a8c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tm53yNhhDb5lUVm+zEILghA/nb8bJfqvv2v/QyV1j91NUO+X2yxMLCbCeoYzNOJ5Srnuty+1ipSBtkx4EjQbDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T08:22:03.676844Z","bundle_sha256":"2c3b5268e456e2adbd3a8b05c8f787663bddadc3ea2ad23954df82f65d4440a1"}}