{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:NGNQ5ZDYSH2Y67MMUVW5TXGLBI","short_pith_number":"pith:NGNQ5ZDY","schema_version":"1.0","canonical_sha256":"699b0ee47891f58f7d8ca56dd9dccb0a0a661349c1b31766c02373992e9699b2","source":{"kind":"arxiv","id":"2507.05452","version":1},"attestation_state":"computed","paper":{"title":"Topological Sequence Analysis of Genomes: Delta Complex approaches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"math.AT","authors_text":"Dong Chen, Guo-Wei Wei, Jian Liu, Li Shen","submitted_at":"2025-07-07T20:10:31Z","abstract_excerpt":"Algebraic topology has been widely applied to point cloud data to capture geometric shapes and topological structures. However, its application to genome sequence analysis remains rare. In this work, we propose topological sequence analysis (TSA) techniques by constructing $\\Delta$-complexes and classifying spaces, leading to persistent homology, and persistent path homology on genome sequences. We also develop $\\Delta$-complex-based persistent Laplacians to facilitate the topological spectral analysis of genome sequences. Finally, we demonstrate the utility of the proposed TSA approaches in p"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.05452","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-07-07T20:10:31Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"b23dbc608dfd8cfe6439a5ab0582e937ec1fa4047049a86affffdfc274213a71","abstract_canon_sha256":"f5d198f1ba6690eb52fc2c3632d92d13aed038bf4a9c7868e485f65c03f91180"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:33:30.832812Z","signature_b64":"KNGRUknO0NqA8ZNTD8CbOwd0j827f2HxTGGC6YB6gdbdIhdR3XLppuvwFs0WQTv2t+KCy8ORYb32sV964tCdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"699b0ee47891f58f7d8ca56dd9dccb0a0a661349c1b31766c02373992e9699b2","last_reissued_at":"2026-07-05T11:33:30.832334Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:33:30.832334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological Sequence Analysis of Genomes: Delta Complex approaches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"math.AT","authors_text":"Dong Chen, Guo-Wei Wei, Jian Liu, Li Shen","submitted_at":"2025-07-07T20:10:31Z","abstract_excerpt":"Algebraic topology has been widely applied to point cloud data to capture geometric shapes and topological structures. However, its application to genome sequence analysis remains rare. In this work, we propose topological sequence analysis (TSA) techniques by constructing $\\Delta$-complexes and classifying spaces, leading to persistent homology, and persistent path homology on genome sequences. We also develop $\\Delta$-complex-based persistent Laplacians to facilitate the topological spectral analysis of genome sequences. Finally, we demonstrate the utility of the proposed TSA approaches in p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05452","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.05452/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.05452","created_at":"2026-07-05T11:33:30.832394+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.05452v1","created_at":"2026-07-05T11:33:30.832394+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.05452","created_at":"2026-07-05T11:33:30.832394+00:00"},{"alias_kind":"pith_short_12","alias_value":"NGNQ5ZDYSH2Y","created_at":"2026-07-05T11:33:30.832394+00:00"},{"alias_kind":"pith_short_16","alias_value":"NGNQ5ZDYSH2Y67MM","created_at":"2026-07-05T11:33:30.832394+00:00"},{"alias_kind":"pith_short_8","alias_value":"NGNQ5ZDY","created_at":"2026-07-05T11:33:30.832394+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.19504","citing_title":"Topological Data Analysis and Topological Deep Learning Beyond Persistent Homology -- A Review","ref_index":198,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NGNQ5ZDYSH2Y67MMUVW5TXGLBI","json":"https://pith.science/pith/NGNQ5ZDYSH2Y67MMUVW5TXGLBI.json","graph_json":"https://pith.science/api/pith-number/NGNQ5ZDYSH2Y67MMUVW5TXGLBI/graph.json","events_json":"https://pith.science/api/pith-number/NGNQ5ZDYSH2Y67MMUVW5TXGLBI/events.json","paper":"https://pith.science/paper/NGNQ5ZDY"},"agent_actions":{"view_html":"https://pith.science/pith/NGNQ5ZDYSH2Y67MMUVW5TXGLBI","download_json":"https://pith.science/pith/NGNQ5ZDYSH2Y67MMUVW5TXGLBI.json","view_paper":"https://pith.science/paper/NGNQ5ZDY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.05452&json=true","fetch_graph":"https://pith.science/api/pith-number/NGNQ5ZDYSH2Y67MMUVW5TXGLBI/graph.json","fetch_events":"https://pith.science/api/pith-number/NGNQ5ZDYSH2Y67MMUVW5TXGLBI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NGNQ5ZDYSH2Y67MMUVW5TXGLBI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NGNQ5ZDYSH2Y67MMUVW5TXGLBI/action/storage_attestation","attest_author":"https://pith.science/pith/NGNQ5ZDYSH2Y67MMUVW5TXGLBI/action/author_attestation","sign_citation":"https://pith.science/pith/NGNQ5ZDYSH2Y67MMUVW5TXGLBI/action/citation_signature","submit_replication":"https://pith.science/pith/NGNQ5ZDYSH2Y67MMUVW5TXGLBI/action/replication_record"}},"created_at":"2026-07-05T11:33:30.832394+00:00","updated_at":"2026-07-05T11:33:30.832394+00:00"}