{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LHPOM34WFHXTLNU3XYJXXYZ5OW","short_pith_number":"pith:LHPOM34W","schema_version":"1.0","canonical_sha256":"59dee66f9629ef35b69bbe137be33d759bddf69c4f750d7ecb14059ce0955584","source":{"kind":"arxiv","id":"1208.6339","version":5},"attestation_state":"computed","paper":{"title":"The universal character ring of some families of one-relator groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Anh T. Tran","submitted_at":"2012-08-31T00:45:12Z","abstract_excerpt":"We study the universal character ring of some families of one-relator groups. As an application, we calculate the universal character ring of two-generator one-relator groups whose relators are palindrome, and, in particular, of the (-2,2m+1,2n+1)-pretzel knot for all integers m and n. For the (-2,3,2n+1)-pretzel knot, we give a less technical proof of a result in [LT1] on its universal character ring, and an elementary proof of a result in [Ma] on the number of irreducible components of its character variety."},"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":"1208.6339","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-08-31T00:45:12Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"fc28804411f35064a7e8ec2becf323fde70e04328eedabeba45f85340fd0e9e7","abstract_canon_sha256":"6c3fb5154f224778cb3319d3cf2cc71be8ae4d3ed291dafde34d01da8921d50f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:26.307465Z","signature_b64":"R59lqrkZWElx/0/5QtH1RG/o94xQNYlTcPSuguCUlyW5kZSCXzvImfUXZpK+bH2Y/f9HObDxesN7f0Ruh5C3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59dee66f9629ef35b69bbe137be33d759bddf69c4f750d7ecb14059ce0955584","last_reissued_at":"2026-05-18T01:22:26.306778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:26.306778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The universal character ring of some families of one-relator groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Anh T. Tran","submitted_at":"2012-08-31T00:45:12Z","abstract_excerpt":"We study the universal character ring of some families of one-relator groups. As an application, we calculate the universal character ring of two-generator one-relator groups whose relators are palindrome, and, in particular, of the (-2,2m+1,2n+1)-pretzel knot for all integers m and n. For the (-2,3,2n+1)-pretzel knot, we give a less technical proof of a result in [LT1] on its universal character ring, and an elementary proof of a result in [Ma] on the number of irreducible components of its character variety."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6339","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1208.6339","created_at":"2026-05-18T01:22:26.306869+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.6339v5","created_at":"2026-05-18T01:22:26.306869+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6339","created_at":"2026-05-18T01:22:26.306869+00:00"},{"alias_kind":"pith_short_12","alias_value":"LHPOM34WFHXT","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LHPOM34WFHXTLNU3","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LHPOM34W","created_at":"2026-05-18T12:27:14.488303+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/LHPOM34WFHXTLNU3XYJXXYZ5OW","json":"https://pith.science/pith/LHPOM34WFHXTLNU3XYJXXYZ5OW.json","graph_json":"https://pith.science/api/pith-number/LHPOM34WFHXTLNU3XYJXXYZ5OW/graph.json","events_json":"https://pith.science/api/pith-number/LHPOM34WFHXTLNU3XYJXXYZ5OW/events.json","paper":"https://pith.science/paper/LHPOM34W"},"agent_actions":{"view_html":"https://pith.science/pith/LHPOM34WFHXTLNU3XYJXXYZ5OW","download_json":"https://pith.science/pith/LHPOM34WFHXTLNU3XYJXXYZ5OW.json","view_paper":"https://pith.science/paper/LHPOM34W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.6339&json=true","fetch_graph":"https://pith.science/api/pith-number/LHPOM34WFHXTLNU3XYJXXYZ5OW/graph.json","fetch_events":"https://pith.science/api/pith-number/LHPOM34WFHXTLNU3XYJXXYZ5OW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LHPOM34WFHXTLNU3XYJXXYZ5OW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LHPOM34WFHXTLNU3XYJXXYZ5OW/action/storage_attestation","attest_author":"https://pith.science/pith/LHPOM34WFHXTLNU3XYJXXYZ5OW/action/author_attestation","sign_citation":"https://pith.science/pith/LHPOM34WFHXTLNU3XYJXXYZ5OW/action/citation_signature","submit_replication":"https://pith.science/pith/LHPOM34WFHXTLNU3XYJXXYZ5OW/action/replication_record"}},"created_at":"2026-05-18T01:22:26.306869+00:00","updated_at":"2026-05-18T01:22:26.306869+00:00"}