{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:X4R3GZBZHWCKZ74ZGNGYU2SGQC","short_pith_number":"pith:X4R3GZBZ","canonical_record":{"source":{"id":"2401.14927","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-01-26T15:04:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c6d256b579dfd3d82f1af4f122fd11bd5d09777a5fa3bbd7a6bb2925a837213a","abstract_canon_sha256":"4ee43297d8cb0fe1ebdbb7570fdef1cbbdd9df8a264bb4c26cf9e22a0ac8f66f"},"schema_version":"1.0"},"canonical_sha256":"bf23b364393d84acff99334d8a6a4680bfeeb3bb08839bbb61a0a6cf1ae94643","source":{"kind":"arxiv","id":"2401.14927","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.14927","created_at":"2026-07-05T11:42:20Z"},{"alias_kind":"arxiv_version","alias_value":"2401.14927v3","created_at":"2026-07-05T11:42:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.14927","created_at":"2026-07-05T11:42:20Z"},{"alias_kind":"pith_short_12","alias_value":"X4R3GZBZHWCK","created_at":"2026-07-05T11:42:20Z"},{"alias_kind":"pith_short_16","alias_value":"X4R3GZBZHWCKZ74Z","created_at":"2026-07-05T11:42:20Z"},{"alias_kind":"pith_short_8","alias_value":"X4R3GZBZ","created_at":"2026-07-05T11:42:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:X4R3GZBZHWCKZ74ZGNGYU2SGQC","target":"record","payload":{"canonical_record":{"source":{"id":"2401.14927","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-01-26T15:04:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c6d256b579dfd3d82f1af4f122fd11bd5d09777a5fa3bbd7a6bb2925a837213a","abstract_canon_sha256":"4ee43297d8cb0fe1ebdbb7570fdef1cbbdd9df8a264bb4c26cf9e22a0ac8f66f"},"schema_version":"1.0"},"canonical_sha256":"bf23b364393d84acff99334d8a6a4680bfeeb3bb08839bbb61a0a6cf1ae94643","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:42:20.216518Z","signature_b64":"8BaJ2vtlz7NEUjULMkDKn5z+dtYpcZu0VXKujXPtyZ1u9s+dtwB6pQrCddAv56q/Z5hgOutILYGwD3QTB+/CDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf23b364393d84acff99334d8a6a4680bfeeb3bb08839bbb61a0a6cf1ae94643","last_reissued_at":"2026-07-05T11:42:20.216113Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:42:20.216113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.14927","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:42:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ZSlXT9cOfA/5rxHf20ZC0MKmGBVYy/UYkt4P1E6FDG5wyM0YQ3877WBEiAtsXHHsLc2XEvBW++6HJT82jwKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T02:05:48.938266Z"},"content_sha256":"d70fb66a356417de8ca0ad0f346e1966e33f205ebd1479a0a2e85c1e5e316775","schema_version":"1.0","event_id":"sha256:d70fb66a356417de8ca0ad0f346e1966e33f205ebd1479a0a2e85c1e5e316775"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:X4R3GZBZHWCKZ74ZGNGYU2SGQC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Alexander polynomial of special alternating links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Alexander Vidinas, Elena S. Hafner, Karola M\\'esz\\'aros","submitted_at":"2024-01-26T15:04:17Z","abstract_excerpt":"The Alexander polynomial (1928) is the first polynomial invariant of links devised to help distinguish links up to isotopy. Fox's conjecture (1962) -- stating that the absolute values of the coefficients of the Alexander polynomial for any alternating link are trapezoidal -- was settled for special alternating links by the present authors (2023); K\\'alm\\'an, the second author, and Postnikov gave an alternative proof (2025). The present paper is a study of the special combinatorial and discrete geometric properties that Alexander polynomials of special alternating links possess along with a gen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.14927","kind":"arxiv","version":3},"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/2401.14927/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:42:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gkHbuuLoZKlFG7eGvd5/UtvOvaNVAuwPPbk2tdkYs22Ne2kb4iDvc34esXpp5caQcLfgvKmWrh3CvX6cQMYpCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T02:05:48.938794Z"},"content_sha256":"279c41c941743ba69a28f56d889d6fda4ad27ee675dffe835d95e30b6357cddb","schema_version":"1.0","event_id":"sha256:279c41c941743ba69a28f56d889d6fda4ad27ee675dffe835d95e30b6357cddb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X4R3GZBZHWCKZ74ZGNGYU2SGQC/bundle.json","state_url":"https://pith.science/pith/X4R3GZBZHWCKZ74ZGNGYU2SGQC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X4R3GZBZHWCKZ74ZGNGYU2SGQC/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":"2026-08-17T02:05:48Z","links":{"resolver":"https://pith.science/pith/X4R3GZBZHWCKZ74ZGNGYU2SGQC","bundle":"https://pith.science/pith/X4R3GZBZHWCKZ74ZGNGYU2SGQC/bundle.json","state":"https://pith.science/pith/X4R3GZBZHWCKZ74ZGNGYU2SGQC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X4R3GZBZHWCKZ74ZGNGYU2SGQC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:X4R3GZBZHWCKZ74ZGNGYU2SGQC","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":"4ee43297d8cb0fe1ebdbb7570fdef1cbbdd9df8a264bb4c26cf9e22a0ac8f66f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-01-26T15:04:17Z","title_canon_sha256":"c6d256b579dfd3d82f1af4f122fd11bd5d09777a5fa3bbd7a6bb2925a837213a"},"schema_version":"1.0","source":{"id":"2401.14927","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.14927","created_at":"2026-07-05T11:42:20Z"},{"alias_kind":"arxiv_version","alias_value":"2401.14927v3","created_at":"2026-07-05T11:42:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.14927","created_at":"2026-07-05T11:42:20Z"},{"alias_kind":"pith_short_12","alias_value":"X4R3GZBZHWCK","created_at":"2026-07-05T11:42:20Z"},{"alias_kind":"pith_short_16","alias_value":"X4R3GZBZHWCKZ74Z","created_at":"2026-07-05T11:42:20Z"},{"alias_kind":"pith_short_8","alias_value":"X4R3GZBZ","created_at":"2026-07-05T11:42:20Z"}],"graph_snapshots":[{"event_id":"sha256:279c41c941743ba69a28f56d889d6fda4ad27ee675dffe835d95e30b6357cddb","target":"graph","created_at":"2026-07-05T11:42:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2401.14927/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Alexander polynomial (1928) is the first polynomial invariant of links devised to help distinguish links up to isotopy. Fox's conjecture (1962) -- stating that the absolute values of the coefficients of the Alexander polynomial for any alternating link are trapezoidal -- was settled for special alternating links by the present authors (2023); K\\'alm\\'an, the second author, and Postnikov gave an alternative proof (2025). The present paper is a study of the special combinatorial and discrete geometric properties that Alexander polynomials of special alternating links possess along with a gen","authors_text":"Alexander Vidinas, Elena S. Hafner, Karola M\\'esz\\'aros","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-01-26T15:04:17Z","title":"On the Alexander polynomial of special alternating links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.14927","kind":"arxiv","version":3},"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:d70fb66a356417de8ca0ad0f346e1966e33f205ebd1479a0a2e85c1e5e316775","target":"record","created_at":"2026-07-05T11:42:20Z","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":"4ee43297d8cb0fe1ebdbb7570fdef1cbbdd9df8a264bb4c26cf9e22a0ac8f66f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-01-26T15:04:17Z","title_canon_sha256":"c6d256b579dfd3d82f1af4f122fd11bd5d09777a5fa3bbd7a6bb2925a837213a"},"schema_version":"1.0","source":{"id":"2401.14927","kind":"arxiv","version":3}},"canonical_sha256":"bf23b364393d84acff99334d8a6a4680bfeeb3bb08839bbb61a0a6cf1ae94643","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf23b364393d84acff99334d8a6a4680bfeeb3bb08839bbb61a0a6cf1ae94643","first_computed_at":"2026-07-05T11:42:20.216113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:42:20.216113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8BaJ2vtlz7NEUjULMkDKn5z+dtYpcZu0VXKujXPtyZ1u9s+dtwB6pQrCddAv56q/Z5hgOutILYGwD3QTB+/CDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:42:20.216518Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.14927","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d70fb66a356417de8ca0ad0f346e1966e33f205ebd1479a0a2e85c1e5e316775","sha256:279c41c941743ba69a28f56d889d6fda4ad27ee675dffe835d95e30b6357cddb"],"state_sha256":"59f9dc96f7daa5fc360b61e50be7eb96788b6694bc112db336c9d25e87411dd6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sjxyWFl4fMEnq38T3lcnifYStImP8PIsyRolXrEM4cBOBj/cK+l1v+zjUyjkPchRYsGTi6/YwHHZWVyYoZOeDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T02:05:48.943236Z","bundle_sha256":"babd17cbea18e0758aad4db00de1657d44aa16dc6d97f0ef41812c622578d092"}}