{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OCD73KG7DFB4WQMK76XEMKP6ZL","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":"4e900aacc55f48e2fba501c2f621e7fd9222d58c7a7d46e252210a5e4c748a85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-04-09T01:09:59Z","title_canon_sha256":"4d799c47c2211fa336d41f29f083737cc5924ddedf77fbf53c7a258547b42a48"},"schema_version":"1.0","source":{"id":"1704.02550","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02550","created_at":"2026-05-18T00:12:00Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02550v2","created_at":"2026-05-18T00:12:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02550","created_at":"2026-05-18T00:12:00Z"},{"alias_kind":"pith_short_12","alias_value":"OCD73KG7DFB4","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OCD73KG7DFB4WQMK","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OCD73KG7","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:07a4743a182d1e4b9f3e579d89d2d48a76636378a6c41bee10c914daec861835","target":"graph","created_at":"2026-05-18T00:12:00Z","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 $f,g:X\\to Y$ be maps from a compact infra-nilmanifold $X$ to a compact nilmanifold $Y$ with $\\dim X\\ge \\dim Y$. In this note, we show that a certain Wecken type property holds, i.e., if the Nielsen number $N(f,g)$ vanishes then $f$ and $g$ are deformable to be coincidence free. We also show that if $X$ is a connected finite complex $X$ and the Reidemeister coincidence number $R(f,g)=\\infty$ then $f\\sim f'$ so that $C(f',g)=\\{x\\in X \\mid f'(x)=g(x)\\}$ is empty.","authors_text":"Daciberg Gon\\c{c}alves, Peter Wong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-04-09T01:09:59Z","title":"Coincidence Wecken property for nilmanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02550","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":"sha256:2dc5496bed61aa93fbccef554c34ddcced28affc2536b156b4588d49c3eb8130","target":"record","created_at":"2026-05-18T00:12:00Z","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":"4e900aacc55f48e2fba501c2f621e7fd9222d58c7a7d46e252210a5e4c748a85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-04-09T01:09:59Z","title_canon_sha256":"4d799c47c2211fa336d41f29f083737cc5924ddedf77fbf53c7a258547b42a48"},"schema_version":"1.0","source":{"id":"1704.02550","kind":"arxiv","version":2}},"canonical_sha256":"7087fda8df1943cb418affae4629fecae598095310be8971f732c9f5f122540a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7087fda8df1943cb418affae4629fecae598095310be8971f732c9f5f122540a","first_computed_at":"2026-05-18T00:12:00.537222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:00.537222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dFoU8c/wfafo7P7lZj/op0mwWHsT6tKCWNzggfTdYScu/ASZ2s4zh1qzMDwz+RKwJZ/jmv9UYC0QWmXAvfjSBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:00.537739Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.02550","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2dc5496bed61aa93fbccef554c34ddcced28affc2536b156b4588d49c3eb8130","sha256:07a4743a182d1e4b9f3e579d89d2d48a76636378a6c41bee10c914daec861835"],"state_sha256":"124ab000c2068fb07f26fbc66618231ade57be4844f8c8cf8375baa5921b8eee"}