{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DOQPYLAMOYBEMS42KT2KWJW6YX","short_pith_number":"pith:DOQPYLAM","canonical_record":{"source":{"id":"1805.12567","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2018-05-31T17:18:17Z","cross_cats_sorted":[],"title_canon_sha256":"7dc60157cc07a5785a278c767abfe1dcee741774e2f471cd00abd0be77b70d9f","abstract_canon_sha256":"8db3a68c426735d1156e11a9a12f2b180794772028ff1dd3417b041989e8bbcb"},"schema_version":"1.0"},"canonical_sha256":"1ba0fc2c0c7602464b9a54f4ab26dec5f6ab931fb2d40380d06363434751235f","source":{"kind":"arxiv","id":"1805.12567","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.12567","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1805.12567v1","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.12567","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"DOQPYLAMOYBE","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DOQPYLAMOYBEMS42","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DOQPYLAM","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DOQPYLAMOYBEMS42KT2KWJW6YX","target":"record","payload":{"canonical_record":{"source":{"id":"1805.12567","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2018-05-31T17:18:17Z","cross_cats_sorted":[],"title_canon_sha256":"7dc60157cc07a5785a278c767abfe1dcee741774e2f471cd00abd0be77b70d9f","abstract_canon_sha256":"8db3a68c426735d1156e11a9a12f2b180794772028ff1dd3417b041989e8bbcb"},"schema_version":"1.0"},"canonical_sha256":"1ba0fc2c0c7602464b9a54f4ab26dec5f6ab931fb2d40380d06363434751235f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:29.902876Z","signature_b64":"NGDlTSu3nKiy2PIANmCulPpN+riyEbZ9LQ7EUnrkWvVjB/d+qf1rXZKOwEZAH39w4jZJomG/czXPMKgTdAJdDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ba0fc2c0c7602464b9a54f4ab26dec5f6ab931fb2d40380d06363434751235f","last_reissued_at":"2026-05-18T00:14:29.902346Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:29.902346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.12567","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":"2026-05-18T00:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5GErNmYKkJyFd9MKvMfuX/Yx7L9zZP6TKs6u5SX6wfOU9iEPQ44s+0HVySomzibacv1urd2NVLq84NyYoZ/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:09:04.865514Z"},"content_sha256":"09908052ba341381fb7fd62be3bde45d9a545ad0cb9ecbb9d77f78991c936e06","schema_version":"1.0","event_id":"sha256:09908052ba341381fb7fd62be3bde45d9a545ad0cb9ecbb9d77f78991c936e06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DOQPYLAMOYBEMS42KT2KWJW6YX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Barcodes in level and sub level persistence and Morse-Novikov theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dan Burghelea","submitted_at":"2018-05-31T17:18:17Z","abstract_excerpt":"In this note we recall the relations between the barcodes in level and sub-level persistence and make precise their relation with the Morse-Novikov complex of a Morse real- or angle-valued map. The results in this papers are implicit in my previous work(w.collaborators), but apparently not well known even to experts."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.12567","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":"2026-05-18T00:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KGMRE1bByTV4ZSI0OFG6ew79CrcShqQ9N49cIhcqQvTUqCFOHaEwYM4Ifoteey0xW/MvJccUTFYf28iKBNcFDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:09:04.865987Z"},"content_sha256":"bdc0505f20dfb195602611faffc1562c9bd64e4dcdaa3d9e1b01e96fefd9a6d2","schema_version":"1.0","event_id":"sha256:bdc0505f20dfb195602611faffc1562c9bd64e4dcdaa3d9e1b01e96fefd9a6d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DOQPYLAMOYBEMS42KT2KWJW6YX/bundle.json","state_url":"https://pith.science/pith/DOQPYLAMOYBEMS42KT2KWJW6YX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DOQPYLAMOYBEMS42KT2KWJW6YX/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":"2026-06-25T08:09:04Z","links":{"resolver":"https://pith.science/pith/DOQPYLAMOYBEMS42KT2KWJW6YX","bundle":"https://pith.science/pith/DOQPYLAMOYBEMS42KT2KWJW6YX/bundle.json","state":"https://pith.science/pith/DOQPYLAMOYBEMS42KT2KWJW6YX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DOQPYLAMOYBEMS42KT2KWJW6YX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DOQPYLAMOYBEMS42KT2KWJW6YX","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":"8db3a68c426735d1156e11a9a12f2b180794772028ff1dd3417b041989e8bbcb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2018-05-31T17:18:17Z","title_canon_sha256":"7dc60157cc07a5785a278c767abfe1dcee741774e2f471cd00abd0be77b70d9f"},"schema_version":"1.0","source":{"id":"1805.12567","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.12567","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1805.12567v1","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.12567","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"DOQPYLAMOYBE","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DOQPYLAMOYBEMS42","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DOQPYLAM","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:bdc0505f20dfb195602611faffc1562c9bd64e4dcdaa3d9e1b01e96fefd9a6d2","target":"graph","created_at":"2026-05-18T00:14:29Z","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":"In this note we recall the relations between the barcodes in level and sub-level persistence and make precise their relation with the Morse-Novikov complex of a Morse real- or angle-valued map. The results in this papers are implicit in my previous work(w.collaborators), but apparently not well known even to experts.","authors_text":"Dan Burghelea","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2018-05-31T17:18:17Z","title":"Barcodes in level and sub level persistence and Morse-Novikov theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.12567","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":"sha256:09908052ba341381fb7fd62be3bde45d9a545ad0cb9ecbb9d77f78991c936e06","target":"record","created_at":"2026-05-18T00:14:29Z","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":"8db3a68c426735d1156e11a9a12f2b180794772028ff1dd3417b041989e8bbcb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2018-05-31T17:18:17Z","title_canon_sha256":"7dc60157cc07a5785a278c767abfe1dcee741774e2f471cd00abd0be77b70d9f"},"schema_version":"1.0","source":{"id":"1805.12567","kind":"arxiv","version":1}},"canonical_sha256":"1ba0fc2c0c7602464b9a54f4ab26dec5f6ab931fb2d40380d06363434751235f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ba0fc2c0c7602464b9a54f4ab26dec5f6ab931fb2d40380d06363434751235f","first_computed_at":"2026-05-18T00:14:29.902346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:29.902346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NGDlTSu3nKiy2PIANmCulPpN+riyEbZ9LQ7EUnrkWvVjB/d+qf1rXZKOwEZAH39w4jZJomG/czXPMKgTdAJdDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:29.902876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.12567","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09908052ba341381fb7fd62be3bde45d9a545ad0cb9ecbb9d77f78991c936e06","sha256:bdc0505f20dfb195602611faffc1562c9bd64e4dcdaa3d9e1b01e96fefd9a6d2"],"state_sha256":"3a5c0abf2a08688a4b56cb877e5e4c62fa50f0aab97eb70b0eb74ad8fa98e0c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XHUaTvyxDmDasrHkFQ2oeJg6ldfBuCWayKPvFVgqqQa/GqVECIw3z9eTwDJ70WUUpDE66TI1i7r6MD6QQupSAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:09:04.867791Z","bundle_sha256":"38d1a7319f794a71566ccd6ce2c8dd852b429996c4125cdda2e403100ec68f4a"}}