{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5HN6XAZJ5CUQM44L7TIUYAPFWF","short_pith_number":"pith:5HN6XAZJ","canonical_record":{"source":{"id":"1802.04677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-02-13T15:18:26Z","cross_cats_sorted":["math.DS","q-bio.QM"],"title_canon_sha256":"62c07928dfa405e9dc384c22ec457ebc50dd8498b02a028be9d7253d094c7aec","abstract_canon_sha256":"71ae98cf00cb82d199a607ae11f9c0a16a17e5c96511cd1eecb63523e2dafa7a"},"schema_version":"1.0"},"canonical_sha256":"e9dbeb8329e8a906738bfcd14c01e5b1733ed7d12ecdf21bf3ccae68d287c76f","source":{"kind":"arxiv","id":"1802.04677","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04677","created_at":"2026-05-18T00:23:41Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04677v1","created_at":"2026-05-18T00:23:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04677","created_at":"2026-05-18T00:23:41Z"},{"alias_kind":"pith_short_12","alias_value":"5HN6XAZJ5CUQ","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5HN6XAZJ5CUQM44L","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5HN6XAZJ","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5HN6XAZJ5CUQM44L7TIUYAPFWF","target":"record","payload":{"canonical_record":{"source":{"id":"1802.04677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-02-13T15:18:26Z","cross_cats_sorted":["math.DS","q-bio.QM"],"title_canon_sha256":"62c07928dfa405e9dc384c22ec457ebc50dd8498b02a028be9d7253d094c7aec","abstract_canon_sha256":"71ae98cf00cb82d199a607ae11f9c0a16a17e5c96511cd1eecb63523e2dafa7a"},"schema_version":"1.0"},"canonical_sha256":"e9dbeb8329e8a906738bfcd14c01e5b1733ed7d12ecdf21bf3ccae68d287c76f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:41.757136Z","signature_b64":"Arsagb/d+0TajFEwlRWAPzi+8MY1KDxtSt9KrpMSoGkexD/jq0ltp54HKr01IaqlCTrKho17IN9v/lzHUnzeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9dbeb8329e8a906738bfcd14c01e5b1733ed7d12ecdf21bf3ccae68d287c76f","last_reissued_at":"2026-05-18T00:23:41.756430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:41.756430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.04677","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":"2026-05-18T00:23:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pBvls+yg104+dpID6hDqjdf/AHAzIix9f8AmJ4NgCEYMiAVZxZXv7xRi4035whzX/LVWZcsO3MJKeE5Cg012BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:21:12.963043Z"},"content_sha256":"d88cec78092ddd8d61e045918f59f52e67f296ad09df1692136356b90ba4c36c","schema_version":"1.0","event_id":"sha256:d88cec78092ddd8d61e045918f59f52e67f296ad09df1692136356b90ba4c36c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5HN6XAZJ5CUQM44L7TIUYAPFWF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evolutionary homology on coupled dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","q-bio.QM"],"primary_cat":"math.AT","authors_text":"Elizabeth Munch, Guo-Wei Wei, Zixuan Cang","submitted_at":"2018-02-13T15:18:26Z","abstract_excerpt":"Time dependence is a universal phenomenon in nature, and a variety of mathematical models in terms of dynamical systems have been developed to understand the time-dependent behavior of real-world problems. Originally constructed to analyze the topological persistence over spatial scales, persistent homology has rarely been devised for time evolution. We propose the use of a new filtration function for persistent homology which takes as input the adjacent oscillator trajectories of a dynamical system. We also regulate the dynamical system by a weighted graph Laplacian matrix derived from the ne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04677","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":"2026-05-18T00:23:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zZ19hz0eiLDjZ0ACjWJFBTs2FapN4sopOM32iwpdOHBX1lQx4U3Nio9GGk0pff+DX8hg473E4OMsF4NepYjPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:21:12.963587Z"},"content_sha256":"e0a6b4b46801b47c690f012a29a3b242fa1fe28cbd91e5f52ab63bd88579346d","schema_version":"1.0","event_id":"sha256:e0a6b4b46801b47c690f012a29a3b242fa1fe28cbd91e5f52ab63bd88579346d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5HN6XAZJ5CUQM44L7TIUYAPFWF/bundle.json","state_url":"https://pith.science/pith/5HN6XAZJ5CUQM44L7TIUYAPFWF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5HN6XAZJ5CUQM44L7TIUYAPFWF/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":"2026-06-08T13:21:12Z","links":{"resolver":"https://pith.science/pith/5HN6XAZJ5CUQM44L7TIUYAPFWF","bundle":"https://pith.science/pith/5HN6XAZJ5CUQM44L7TIUYAPFWF/bundle.json","state":"https://pith.science/pith/5HN6XAZJ5CUQM44L7TIUYAPFWF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5HN6XAZJ5CUQM44L7TIUYAPFWF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5HN6XAZJ5CUQM44L7TIUYAPFWF","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":"71ae98cf00cb82d199a607ae11f9c0a16a17e5c96511cd1eecb63523e2dafa7a","cross_cats_sorted":["math.DS","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-02-13T15:18:26Z","title_canon_sha256":"62c07928dfa405e9dc384c22ec457ebc50dd8498b02a028be9d7253d094c7aec"},"schema_version":"1.0","source":{"id":"1802.04677","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04677","created_at":"2026-05-18T00:23:41Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04677v1","created_at":"2026-05-18T00:23:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04677","created_at":"2026-05-18T00:23:41Z"},{"alias_kind":"pith_short_12","alias_value":"5HN6XAZJ5CUQ","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5HN6XAZJ5CUQM44L","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5HN6XAZJ","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:e0a6b4b46801b47c690f012a29a3b242fa1fe28cbd91e5f52ab63bd88579346d","target":"graph","created_at":"2026-05-18T00:23:41Z","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":"Time dependence is a universal phenomenon in nature, and a variety of mathematical models in terms of dynamical systems have been developed to understand the time-dependent behavior of real-world problems. Originally constructed to analyze the topological persistence over spatial scales, persistent homology has rarely been devised for time evolution. We propose the use of a new filtration function for persistent homology which takes as input the adjacent oscillator trajectories of a dynamical system. We also regulate the dynamical system by a weighted graph Laplacian matrix derived from the ne","authors_text":"Elizabeth Munch, Guo-Wei Wei, Zixuan Cang","cross_cats":["math.DS","q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-02-13T15:18:26Z","title":"Evolutionary homology on coupled dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04677","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:d88cec78092ddd8d61e045918f59f52e67f296ad09df1692136356b90ba4c36c","target":"record","created_at":"2026-05-18T00:23:41Z","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":"71ae98cf00cb82d199a607ae11f9c0a16a17e5c96511cd1eecb63523e2dafa7a","cross_cats_sorted":["math.DS","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-02-13T15:18:26Z","title_canon_sha256":"62c07928dfa405e9dc384c22ec457ebc50dd8498b02a028be9d7253d094c7aec"},"schema_version":"1.0","source":{"id":"1802.04677","kind":"arxiv","version":1}},"canonical_sha256":"e9dbeb8329e8a906738bfcd14c01e5b1733ed7d12ecdf21bf3ccae68d287c76f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9dbeb8329e8a906738bfcd14c01e5b1733ed7d12ecdf21bf3ccae68d287c76f","first_computed_at":"2026-05-18T00:23:41.756430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:41.756430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Arsagb/d+0TajFEwlRWAPzi+8MY1KDxtSt9KrpMSoGkexD/jq0ltp54HKr01IaqlCTrKho17IN9v/lzHUnzeAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:41.757136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04677","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d88cec78092ddd8d61e045918f59f52e67f296ad09df1692136356b90ba4c36c","sha256:e0a6b4b46801b47c690f012a29a3b242fa1fe28cbd91e5f52ab63bd88579346d"],"state_sha256":"e51d23e8ef468bdf69535c3cc7a65b6ffaedbe000f92eb0395139e5b101fa895"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ltl/3ehipYlTQJsN9idMG/2i2mLQ5Ln208fKuWHCMhAj2hVfWeVDzKDKL8xVHYQiYDeea1vh/1QY0oHm5+VZAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T13:21:12.966335Z","bundle_sha256":"80d2f7952b89a0e34af90b6af929c5fedea5b53f0af13a2eeff5151704774aa8"}}