{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:Z7NSEBRT7CLD6KSQHB7Q4APDFB","short_pith_number":"pith:Z7NSEBRT","schema_version":"1.0","canonical_sha256":"cfdb220633f8963f2a50387f0e01e32844478f596138277fef8b66f8e0fe3346","source":{"kind":"arxiv","id":"2606.24009","version":1},"attestation_state":"computed","paper":{"title":"Morse-Novikov theory for links","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"A. Pajitnov, H. Endo, L. Chen","submitted_at":"2026-06-22T23:30:42Z","abstract_excerpt":"For a compact 3-manifold W. Thurston introduced a norm on the first cohomology group of the manifold. The unit ball $B$ of this norm is a polyhedron and the set of cohomology classes that are representable by fibrations over a circle is a union of cones on some of the open faces of $B$. In the present paper we study the fibred faces of the Thurston polyhedra of exteriors of links in $S^3$. Our approach is based on the non-abelian Novikov homology associated with the universal covering of the exterior of the link. We prove in particular that for a 2-component 2-bridge link $L$ a cohomology clas"},"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":"2606.24009","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2026-06-22T23:30:42Z","cross_cats_sorted":[],"title_canon_sha256":"242695eead219e7b4f805bbd15c06a3e988327c06c96bcf6a81cf6738c47b206","abstract_canon_sha256":"930e1e02b2a56e60d3468fc16f901e8c4f20174ef6b6ae8928719f8a1c9f4cb1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:14:38.043495Z","signature_b64":"j52WvseMQz+CpSZBMSnWJTc+nhhQNPh+kp/AVdtM36KSclUYodJ3qUGPVbKeyNC5Wr514Nc0k+E59B6wpLF7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfdb220633f8963f2a50387f0e01e32844478f596138277fef8b66f8e0fe3346","last_reissued_at":"2026-06-24T01:14:38.042987Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:14:38.042987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Morse-Novikov theory for links","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"A. Pajitnov, H. Endo, L. Chen","submitted_at":"2026-06-22T23:30:42Z","abstract_excerpt":"For a compact 3-manifold W. Thurston introduced a norm on the first cohomology group of the manifold. The unit ball $B$ of this norm is a polyhedron and the set of cohomology classes that are representable by fibrations over a circle is a union of cones on some of the open faces of $B$. In the present paper we study the fibred faces of the Thurston polyhedra of exteriors of links in $S^3$. Our approach is based on the non-abelian Novikov homology associated with the universal covering of the exterior of the link. We prove in particular that for a 2-component 2-bridge link $L$ a cohomology clas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24009","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/2606.24009/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":"2606.24009","created_at":"2026-06-24T01:14:38.043044+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.24009v1","created_at":"2026-06-24T01:14:38.043044+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24009","created_at":"2026-06-24T01:14:38.043044+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z7NSEBRT7CLD","created_at":"2026-06-24T01:14:38.043044+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z7NSEBRT7CLD6KSQ","created_at":"2026-06-24T01:14:38.043044+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z7NSEBRT","created_at":"2026-06-24T01:14:38.043044+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z7NSEBRT7CLD6KSQHB7Q4APDFB","json":"https://pith.science/pith/Z7NSEBRT7CLD6KSQHB7Q4APDFB.json","graph_json":"https://pith.science/api/pith-number/Z7NSEBRT7CLD6KSQHB7Q4APDFB/graph.json","events_json":"https://pith.science/api/pith-number/Z7NSEBRT7CLD6KSQHB7Q4APDFB/events.json","paper":"https://pith.science/paper/Z7NSEBRT"},"agent_actions":{"view_html":"https://pith.science/pith/Z7NSEBRT7CLD6KSQHB7Q4APDFB","download_json":"https://pith.science/pith/Z7NSEBRT7CLD6KSQHB7Q4APDFB.json","view_paper":"https://pith.science/paper/Z7NSEBRT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.24009&json=true","fetch_graph":"https://pith.science/api/pith-number/Z7NSEBRT7CLD6KSQHB7Q4APDFB/graph.json","fetch_events":"https://pith.science/api/pith-number/Z7NSEBRT7CLD6KSQHB7Q4APDFB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z7NSEBRT7CLD6KSQHB7Q4APDFB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z7NSEBRT7CLD6KSQHB7Q4APDFB/action/storage_attestation","attest_author":"https://pith.science/pith/Z7NSEBRT7CLD6KSQHB7Q4APDFB/action/author_attestation","sign_citation":"https://pith.science/pith/Z7NSEBRT7CLD6KSQHB7Q4APDFB/action/citation_signature","submit_replication":"https://pith.science/pith/Z7NSEBRT7CLD6KSQHB7Q4APDFB/action/replication_record"}},"created_at":"2026-06-24T01:14:38.043044+00:00","updated_at":"2026-06-24T01:14:38.043044+00:00"}