{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QARMC2TI3DDKKBDFTWMBP27FN5","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":"e96b32dbe62a75447a8ffe0f7b903a133c9f339f8c3242179194ed88b97b88fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-21T10:55:21Z","title_canon_sha256":"04ba32fc728a20c91a8d9e4a166041c319853e7fbce26f2c2dce7a1d58e4ff00"},"schema_version":"1.0","source":{"id":"2605.22308","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22308","created_at":"2026-05-22T01:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22308v1","created_at":"2026-05-22T01:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22308","created_at":"2026-05-22T01:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"QARMC2TI3DDK","created_at":"2026-05-22T01:04:37Z"},{"alias_kind":"pith_short_16","alias_value":"QARMC2TI3DDKKBDF","created_at":"2026-05-22T01:04:37Z"},{"alias_kind":"pith_short_8","alias_value":"QARMC2TI","created_at":"2026-05-22T01:04:37Z"}],"graph_snapshots":[{"event_id":"sha256:0dc6d174386ec8c80675c223db4827f0ca4420e403fce1eec96c9b3c4c84887d","target":"graph","created_at":"2026-05-22T01:04:37Z","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/2605.22308/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Anh T. Tran, Takayuki Morifuji","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-21T10:55:21Z","title":"Algebraic properties of twisted Alexander polynomial and Reidemeister torsion of torus knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22308","kind":"arxiv","version":1},"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":"sha256:86bc62451d8b8baf67b265ec2e115c3efb47299e4a10c23a24ecd6826af9658a","target":"record","created_at":"2026-05-22T01:04:37Z","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":"e96b32dbe62a75447a8ffe0f7b903a133c9f339f8c3242179194ed88b97b88fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-21T10:55:21Z","title_canon_sha256":"04ba32fc728a20c91a8d9e4a166041c319853e7fbce26f2c2dce7a1d58e4ff00"},"schema_version":"1.0","source":{"id":"2605.22308","kind":"arxiv","version":1}},"canonical_sha256":"8022c16a68d8c6a504659d9817ebe56f73dbfdebe5e3f469e14a7d41af460a8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8022c16a68d8c6a504659d9817ebe56f73dbfdebe5e3f469e14a7d41af460a8a","first_computed_at":"2026-05-22T01:04:37.113878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:37.113878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BrLgGkSuli3c/q8Om0JosLOvOp0OJ7noETG+HaiaEmrBYEEi35SFP57Rlrf47pTWssoOhiA0ZTR0lGR70BJYDw==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:37.114582Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22308","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86bc62451d8b8baf67b265ec2e115c3efb47299e4a10c23a24ecd6826af9658a","sha256:0dc6d174386ec8c80675c223db4827f0ca4420e403fce1eec96c9b3c4c84887d"],"state_sha256":"d77b22461ecad32b4c3c750ffd09185e04ba298edba122b0a411ad00a44cbad2"}