{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:37ETCIVMMZ2QKNYHN2XZYPE7FK","short_pith_number":"pith:37ETCIVM","schema_version":"1.0","canonical_sha256":"dfc93122ac66750537076eaf9c3c9f2aa0774141d0a16c2b05bd3902bf86ef8d","source":{"kind":"arxiv","id":"2406.08662","version":1},"attestation_state":"computed","paper":{"title":"On Fox's trapezoidal conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Andr\\'as Juh\\'asz, Soheil Azarpendar, Tam\\'as K\\'alm\\'an","submitted_at":"2024-06-12T21:47:33Z","abstract_excerpt":"We investigate Fox's trapezoidal conjecture for alternating links. We show that it holds for diagrammatic Murasugi sums of special alternating links, where all sums involved have length less than three (which includes diagrammatic plumbing). It also holds for links containing a large twist region, which we call twist-concentrated. Furthermore, we show some weaker inequalities between consecutive coefficients of the Alexander polynomial of an alternating 3-braid closure, and extend this to arbitrary alternating links. We then study an extension of the trapezoidal conjecture due to Hirasawa and "},"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":"2406.08662","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-06-12T21:47:33Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"abad3699fd73abacb47666c2b57d8d319049a107161cb0d3b5decbd7aacde1f5","abstract_canon_sha256":"975c3c24897da029648961fe4786bf266cd54fee31e7945462f135b9929125b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:31:20.982324Z","signature_b64":"ilHs2Acs5p+Ig7pYaQxpCe4dfGz+GY6oVV7cL9v3Q3aQ2nZoRzgQEVwZblb5BrIqJV4vp08NmNm65ii1PSV6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfc93122ac66750537076eaf9c3c9f2aa0774141d0a16c2b05bd3902bf86ef8d","last_reissued_at":"2026-07-05T08:31:20.981834Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:31:20.981834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Fox's trapezoidal conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Andr\\'as Juh\\'asz, Soheil Azarpendar, Tam\\'as K\\'alm\\'an","submitted_at":"2024-06-12T21:47:33Z","abstract_excerpt":"We investigate Fox's trapezoidal conjecture for alternating links. We show that it holds for diagrammatic Murasugi sums of special alternating links, where all sums involved have length less than three (which includes diagrammatic plumbing). It also holds for links containing a large twist region, which we call twist-concentrated. Furthermore, we show some weaker inequalities between consecutive coefficients of the Alexander polynomial of an alternating 3-braid closure, and extend this to arbitrary alternating links. We then study an extension of the trapezoidal conjecture due to Hirasawa and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.08662","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/2406.08662/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":"2406.08662","created_at":"2026-07-05T08:31:20.981893+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.08662v1","created_at":"2026-07-05T08:31:20.981893+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.08662","created_at":"2026-07-05T08:31:20.981893+00:00"},{"alias_kind":"pith_short_12","alias_value":"37ETCIVMMZ2Q","created_at":"2026-07-05T08:31:20.981893+00:00"},{"alias_kind":"pith_short_16","alias_value":"37ETCIVMMZ2QKNYH","created_at":"2026-07-05T08:31:20.981893+00:00"},{"alias_kind":"pith_short_8","alias_value":"37ETCIVM","created_at":"2026-07-05T08:31:20.981893+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.11301","citing_title":"Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/37ETCIVMMZ2QKNYHN2XZYPE7FK","json":"https://pith.science/pith/37ETCIVMMZ2QKNYHN2XZYPE7FK.json","graph_json":"https://pith.science/api/pith-number/37ETCIVMMZ2QKNYHN2XZYPE7FK/graph.json","events_json":"https://pith.science/api/pith-number/37ETCIVMMZ2QKNYHN2XZYPE7FK/events.json","paper":"https://pith.science/paper/37ETCIVM"},"agent_actions":{"view_html":"https://pith.science/pith/37ETCIVMMZ2QKNYHN2XZYPE7FK","download_json":"https://pith.science/pith/37ETCIVMMZ2QKNYHN2XZYPE7FK.json","view_paper":"https://pith.science/paper/37ETCIVM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.08662&json=true","fetch_graph":"https://pith.science/api/pith-number/37ETCIVMMZ2QKNYHN2XZYPE7FK/graph.json","fetch_events":"https://pith.science/api/pith-number/37ETCIVMMZ2QKNYHN2XZYPE7FK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/37ETCIVMMZ2QKNYHN2XZYPE7FK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/37ETCIVMMZ2QKNYHN2XZYPE7FK/action/storage_attestation","attest_author":"https://pith.science/pith/37ETCIVMMZ2QKNYHN2XZYPE7FK/action/author_attestation","sign_citation":"https://pith.science/pith/37ETCIVMMZ2QKNYHN2XZYPE7FK/action/citation_signature","submit_replication":"https://pith.science/pith/37ETCIVMMZ2QKNYHN2XZYPE7FK/action/replication_record"}},"created_at":"2026-07-05T08:31:20.981893+00:00","updated_at":"2026-07-05T08:31:20.981893+00:00"}