{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:KC5ZLLS6I5D5PXID6AUGDQTCRL","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":"3cdae7cf7dd91e5607534c98346d6e9e8ee8a2c9735315798715860a86dd1fb9","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-10-30T19:54:07Z","title_canon_sha256":"a13f47701ee2d2490908b6650549718b4873a91235f18050fec67a186f1bef44"},"schema_version":"1.0","source":{"id":"2310.19979","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.19979","created_at":"2026-07-05T10:19:20Z"},{"alias_kind":"arxiv_version","alias_value":"2310.19979v2","created_at":"2026-07-05T10:19:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.19979","created_at":"2026-07-05T10:19:20Z"},{"alias_kind":"pith_short_12","alias_value":"KC5ZLLS6I5D5","created_at":"2026-07-05T10:19:20Z"},{"alias_kind":"pith_short_16","alias_value":"KC5ZLLS6I5D5PXID","created_at":"2026-07-05T10:19:20Z"},{"alias_kind":"pith_short_8","alias_value":"KC5ZLLS6","created_at":"2026-07-05T10:19:20Z"}],"graph_snapshots":[{"event_id":"sha256:5328ed8e8a640454c7ccfe93607c59a97970bd67b5109ad4993ccaa2af303dac","target":"graph","created_at":"2026-07-05T10:19:20Z","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/2310.19979/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we compute the Reduced Fox Coloring Group of the diagrams of Wheel Graphs which can also be represented at the closure of the braids $(\\sigma_1 \\sigma_2^{-1})^n$. In doing so, we utilize Fibonacci numbers and their properties.\n  Following this, we generalize our result to compute the Alexander-Burau-Fox Module over the ring $\\mathbb{Z}[t^{\\pm 1}]$ for the same class of links. In our computation, Chebyshev polynomials function as a generalization of Fibonacci Numbers.","authors_text":"Anthony Christiana, Huizheng Guo, Jozef H. Przytycki","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-10-30T19:54:07Z","title":"Using Fibonacci Numbers and Chebyshev Polynomials to Express Fox Coloring Groups and Alexander-Burau-Fox Modules of Diagrams of Wheel Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.19979","kind":"arxiv","version":2},"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:d1c65d28f09d99f9f8b2c2d8d4511415780a3fbe84ff4644cc3e226e6a80e8dc","target":"record","created_at":"2026-07-05T10:19:20Z","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":"3cdae7cf7dd91e5607534c98346d6e9e8ee8a2c9735315798715860a86dd1fb9","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-10-30T19:54:07Z","title_canon_sha256":"a13f47701ee2d2490908b6650549718b4873a91235f18050fec67a186f1bef44"},"schema_version":"1.0","source":{"id":"2310.19979","kind":"arxiv","version":2}},"canonical_sha256":"50bb95ae5e4747d7dd03f02861c2628af9095c1f1dd26226676a215126a119d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50bb95ae5e4747d7dd03f02861c2628af9095c1f1dd26226676a215126a119d8","first_computed_at":"2026-07-05T10:19:20.601533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:19:20.601533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"To8MCea3Qn6M/DliYKvn0jl64duD0X8gl59it3ncA00u+wYnTHQOtdouigwjmuzN5UtRpPsa9NnX2bO+yHkSAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:19:20.602093Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.19979","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1c65d28f09d99f9f8b2c2d8d4511415780a3fbe84ff4644cc3e226e6a80e8dc","sha256:5328ed8e8a640454c7ccfe93607c59a97970bd67b5109ad4993ccaa2af303dac"],"state_sha256":"661c826a575234fb9aaf45ec0d7815ce46039c736eb3d620ad48726ae47f6c8e"}