{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:QARMC2TI3DDKKBDFTWMBP27FN5","short_pith_number":"pith:QARMC2TI","schema_version":"1.0","canonical_sha256":"8022c16a68d8c6a504659d9817ebe56f73dbfdebe5e3f469e14a7d41af460a8a","source":{"kind":"arxiv","id":"2605.22308","version":1},"attestation_state":"computed","paper":{"title":"Algebraic properties of twisted Alexander polynomial and Reidemeister torsion of torus knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Anh T. Tran, Takayuki Morifuji","submitted_at":"2026-05-21T10:55:21Z","abstract_excerpt":"In this paper we prove that every coefficient of twisted Alexander polynomials of torus knots associated with irreducible $\\mathrm{SL}_n(\\Bbb C)$-representations is an $\\Bbb A$-valued locally constant function on the $\\mathrm{SL}_n(\\Bbb C)$-character variety, where $\\Bbb A$ is the ring of all algebraic integers over $\\Bbb C$. Moreover, as a generalization of a recent result of Kitano and Nozaki, we show that $\\mathrm{SL}_n(\\Bbb C)$-Reidemeister torsions are algebraic integers for many Seifert fibered spaces. Also, we discuss the power sums of Reidemeister torsions of torus knots for low-dimens"},"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":"2605.22308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-21T10:55:21Z","cross_cats_sorted":[],"title_canon_sha256":"04ba32fc728a20c91a8d9e4a166041c319853e7fbce26f2c2dce7a1d58e4ff00","abstract_canon_sha256":"e96b32dbe62a75447a8ffe0f7b903a133c9f339f8c3242179194ed88b97b88fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:37.114582Z","signature_b64":"BrLgGkSuli3c/q8Om0JosLOvOp0OJ7noETG+HaiaEmrBYEEi35SFP57Rlrf47pTWssoOhiA0ZTR0lGR70BJYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8022c16a68d8c6a504659d9817ebe56f73dbfdebe5e3f469e14a7d41af460a8a","last_reissued_at":"2026-05-22T01:04:37.113878Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:37.113878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic properties of twisted Alexander polynomial and Reidemeister torsion of torus knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Anh T. Tran, Takayuki Morifuji","submitted_at":"2026-05-21T10:55:21Z","abstract_excerpt":"In this paper we prove that every coefficient of twisted Alexander polynomials of torus knots associated with irreducible $\\mathrm{SL}_n(\\Bbb C)$-representations is an $\\Bbb A$-valued locally constant function on the $\\mathrm{SL}_n(\\Bbb C)$-character variety, where $\\Bbb A$ is the ring of all algebraic integers over $\\Bbb C$. Moreover, as a generalization of a recent result of Kitano and Nozaki, we show that $\\mathrm{SL}_n(\\Bbb C)$-Reidemeister torsions are algebraic integers for many Seifert fibered spaces. Also, we discuss the power sums of Reidemeister torsions of torus knots for low-dimens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22308","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/2605.22308/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":"2605.22308","created_at":"2026-05-22T01:04:37.114001+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.22308v1","created_at":"2026-05-22T01:04:37.114001+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22308","created_at":"2026-05-22T01:04:37.114001+00:00"},{"alias_kind":"pith_short_12","alias_value":"QARMC2TI3DDK","created_at":"2026-05-22T01:04:37.114001+00:00"},{"alias_kind":"pith_short_16","alias_value":"QARMC2TI3DDKKBDF","created_at":"2026-05-22T01:04:37.114001+00:00"},{"alias_kind":"pith_short_8","alias_value":"QARMC2TI","created_at":"2026-05-22T01:04:37.114001+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/QARMC2TI3DDKKBDFTWMBP27FN5","json":"https://pith.science/pith/QARMC2TI3DDKKBDFTWMBP27FN5.json","graph_json":"https://pith.science/api/pith-number/QARMC2TI3DDKKBDFTWMBP27FN5/graph.json","events_json":"https://pith.science/api/pith-number/QARMC2TI3DDKKBDFTWMBP27FN5/events.json","paper":"https://pith.science/paper/QARMC2TI"},"agent_actions":{"view_html":"https://pith.science/pith/QARMC2TI3DDKKBDFTWMBP27FN5","download_json":"https://pith.science/pith/QARMC2TI3DDKKBDFTWMBP27FN5.json","view_paper":"https://pith.science/paper/QARMC2TI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.22308&json=true","fetch_graph":"https://pith.science/api/pith-number/QARMC2TI3DDKKBDFTWMBP27FN5/graph.json","fetch_events":"https://pith.science/api/pith-number/QARMC2TI3DDKKBDFTWMBP27FN5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QARMC2TI3DDKKBDFTWMBP27FN5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QARMC2TI3DDKKBDFTWMBP27FN5/action/storage_attestation","attest_author":"https://pith.science/pith/QARMC2TI3DDKKBDFTWMBP27FN5/action/author_attestation","sign_citation":"https://pith.science/pith/QARMC2TI3DDKKBDFTWMBP27FN5/action/citation_signature","submit_replication":"https://pith.science/pith/QARMC2TI3DDKKBDFTWMBP27FN5/action/replication_record"}},"created_at":"2026-05-22T01:04:37.114001+00:00","updated_at":"2026-05-22T01:04:37.114001+00:00"}