{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2P5K44R2HQUIG2KD3X2DPJG4LJ","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":"12e0606607eb82c38c60ffe3555ecd6f773a147e7d60f8dfeee3151a2b0d6126","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-10-27T23:38:20Z","title_canon_sha256":"fdb11f71ea60237a4383857ba0136110ff39bb37771b63c149541dbdb14f6072"},"schema_version":"1.0","source":{"id":"1610.09035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09035","created_at":"2026-05-18T01:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09035v1","created_at":"2026-05-18T01:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09035","created_at":"2026-05-18T01:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"2P5K44R2HQUI","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2P5K44R2HQUIG2KD","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2P5K44R2","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:765bd48fd21315df3d293e0343922d45620d9e93ff9f4361b8dabb01082a57a9","target":"graph","created_at":"2026-05-18T01:00:59Z","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":"In the setting of continuous maps between compact orientable manifolds of the same dimension, there is a well known averaging formula for the coincidence Lefschetz number in terms of the Lefschetz numbers of lifts to some finite covering space. We state and prove an analogous averaging formula for the coincidence Reidemeister trace. This generalizes a recent formula in fixed point theory by Liu and Zhao.\n  We give two separate and independent proofs of our main result: one using methods developed by Kim and the first author for averaging Nielsen numbers, and one using an axiomatic approach for","authors_text":"Jong Bum Lee, P. Christopher Staecker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-10-27T23:38:20Z","title":"An averaging formula for the coincidence Reidemeister trace"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09035","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":"sha256:8b6618b4fb183b2ad81b712c16ea9509cc4dc32cc414410a3293d6e351dfda83","target":"record","created_at":"2026-05-18T01:00:59Z","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":"12e0606607eb82c38c60ffe3555ecd6f773a147e7d60f8dfeee3151a2b0d6126","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-10-27T23:38:20Z","title_canon_sha256":"fdb11f71ea60237a4383857ba0136110ff39bb37771b63c149541dbdb14f6072"},"schema_version":"1.0","source":{"id":"1610.09035","kind":"arxiv","version":1}},"canonical_sha256":"d3faae723a3c28836943ddf437a4dc5a7259239fc4bb7e7b645adfcc867126dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3faae723a3c28836943ddf437a4dc5a7259239fc4bb7e7b645adfcc867126dc","first_computed_at":"2026-05-18T01:00:59.367539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:59.367539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5UEfoWhpvnMoXHneDUE9fs6ed3cF4ds2481HyryAcCpt1bKkVxGTnZwuy3/epGJDryg65FqNTUke8m7jVn5iAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:59.368382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b6618b4fb183b2ad81b712c16ea9509cc4dc32cc414410a3293d6e351dfda83","sha256:765bd48fd21315df3d293e0343922d45620d9e93ff9f4361b8dabb01082a57a9"],"state_sha256":"4cafe00a91bfff2c6845e1ed1b7d531c8b72cb055fd847298fc6905347968b0f"}