{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IH377NH5JMIA3GXMYO5QSL63FU","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":"3dc448917da5cad309251ddd9f2eeb9f3db701c16312fa5d0318d71d90d40e68","cross_cats_sorted":["math.DS","math.OA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-04-28T17:17:51Z","title_canon_sha256":"a7510bf9990f04bc2790cd72232c1352365aae0b0c4559e4891eefe151500670"},"schema_version":"1.0","source":{"id":"1704.09013","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.09013","created_at":"2026-05-18T00:19:30Z"},{"alias_kind":"arxiv_version","alias_value":"1704.09013v2","created_at":"2026-05-18T00:19:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.09013","created_at":"2026-05-18T00:19:30Z"},{"alias_kind":"pith_short_12","alias_value":"IH377NH5JMIA","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IH377NH5JMIA3GXM","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IH377NH5","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:966882b4f5550178eb9ab9999397a9214c2edfa5cfe79fb1eb4f549a5238bf29","target":"graph","created_at":"2026-05-18T00:19:30Z","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"},"paper":{"abstract_excerpt":"Let $R(\\phi)$ be the number of $\\phi$-conjugacy (or Reidemeister) classes of an endomorphism $\\phi$ of a group $G$. We prove for several classes of groups (including polycyclic) that the number $R(\\phi)$ is equal to the number of fixed points of the induced map of an appropriate subspace of the unitary dual space $\\widehat G$, when $R(\\phi)<\\infty$. Applying the result to iterations of $\\phi$ we obtain Gauss congruences for Reidemeister numbers.\n  In contrast with the case of automorphisms, studied previously, we have a plenty of examples having the above finiteness condition, even among group","authors_text":"Alexander Fel'shtyn, Evgenij Troitsky","cross_cats":["math.DS","math.OA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-04-28T17:17:51Z","title":"Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.09013","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:e7d5cb7510f9c448cc5df2e63c3cf96b4cc5a8d9c85ebf6ea565a3d36807d55e","target":"record","created_at":"2026-05-18T00:19:30Z","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":"3dc448917da5cad309251ddd9f2eeb9f3db701c16312fa5d0318d71d90d40e68","cross_cats_sorted":["math.DS","math.OA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-04-28T17:17:51Z","title_canon_sha256":"a7510bf9990f04bc2790cd72232c1352365aae0b0c4559e4891eefe151500670"},"schema_version":"1.0","source":{"id":"1704.09013","kind":"arxiv","version":2}},"canonical_sha256":"41f7ffb4fd4b100d9aecc3bb092fdb2d1020afd0a30a898826aaf0a9d9640b9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41f7ffb4fd4b100d9aecc3bb092fdb2d1020afd0a30a898826aaf0a9d9640b9b","first_computed_at":"2026-05-18T00:19:30.639444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:30.639444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h5/a+qwFWcwGqyf5fUkRqecsfcYED5UU7SLcCnr4zWMV7j2Hp0DRoVImVox85owxkqY2fDTLCUn2nFUg1oG2AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:30.639949Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.09013","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7d5cb7510f9c448cc5df2e63c3cf96b4cc5a8d9c85ebf6ea565a3d36807d55e","sha256:966882b4f5550178eb9ab9999397a9214c2edfa5cfe79fb1eb4f549a5238bf29"],"state_sha256":"e9835c665487bddaab6f2942df0131479d1f8bd8ae57bc89fbebb30720ea4e88"}