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In this paper, we show that if $L(f,g)=0$ then $N(f,g)=0$; if $L(f,g)\\ne 0$ then $N(f,g)=R(f,g)$ where $L(f,g), N(f,g)$, and $R(f,g)$ denote the Lefschetz, Nielsen, and Reidemeister coincidence numbers of $f$ and $g$, respectively. When $\\dim X> \\dim M$, we give conditions under which $N(f,g)=0$ implies $f$ and $g$ are deformable to be coincidence free."},"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":"math/0701702","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2007-01-24T18:25:40Z","cross_cats_sorted":[],"title_canon_sha256":"2b6bafb82ba48b65b9c0560a17cc2d3eed98a618248b0897d25f497c00914fb3","abstract_canon_sha256":"295696a6bcfdec81d637a279fe59070da3009f428f88fe72456ba0e04b086294"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:30.040720Z","signature_b64":"H+sopuEObf1lQALLo+WsxskxeiA/l4Mc7UIUIrNUPujuw19wKfCiWvZYfzdIV3XtwXs0m8xx2yzRm9nn6l3+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"443ef33b0e17a0583c46caae88d7f32cd2e8703304be1216aa833203245fb7f0","last_reissued_at":"2026-05-18T04:22:30.040199Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:30.040199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Jiang-type theorems for coincidences of maps into homogeneous spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Daniel Vendr\\'uscolo, Peter Wong","submitted_at":"2007-01-24T18:25:40Z","abstract_excerpt":"Let $f,g: X\\to G/K$ be maps from a closed connected orientable manifold $X$ to an orientable coset space $M=G/K$ where $G$ is a compact connected Lie group, $K$ a closed subgroup and $\\dim X=\\dim M$. In this paper, we show that if $L(f,g)=0$ then $N(f,g)=0$; if $L(f,g)\\ne 0$ then $N(f,g)=R(f,g)$ where $L(f,g), N(f,g)$, and $R(f,g)$ denote the Lefschetz, Nielsen, and Reidemeister coincidence numbers of $f$ and $g$, respectively. When $\\dim X> \\dim M$, we give conditions under which $N(f,g)=0$ implies $f$ and $g$ are deformable to be coincidence free."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701702","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"math/0701702","created_at":"2026-05-18T04:22:30.040278+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0701702v3","created_at":"2026-05-18T04:22:30.040278+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701702","created_at":"2026-05-18T04:22:30.040278+00:00"},{"alias_kind":"pith_short_12","alias_value":"IQ7PGOYOC6QF","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"IQ7PGOYOC6QFQPCG","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"IQ7PGOYO","created_at":"2026-05-18T12:25:55.427421+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/IQ7PGOYOC6QFQPCGZKXIRV7TFT","json":"https://pith.science/pith/IQ7PGOYOC6QFQPCGZKXIRV7TFT.json","graph_json":"https://pith.science/api/pith-number/IQ7PGOYOC6QFQPCGZKXIRV7TFT/graph.json","events_json":"https://pith.science/api/pith-number/IQ7PGOYOC6QFQPCGZKXIRV7TFT/events.json","paper":"https://pith.science/paper/IQ7PGOYO"},"agent_actions":{"view_html":"https://pith.science/pith/IQ7PGOYOC6QFQPCGZKXIRV7TFT","download_json":"https://pith.science/pith/IQ7PGOYOC6QFQPCGZKXIRV7TFT.json","view_paper":"https://pith.science/paper/IQ7PGOYO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0701702&json=true","fetch_graph":"https://pith.science/api/pith-number/IQ7PGOYOC6QFQPCGZKXIRV7TFT/graph.json","fetch_events":"https://pith.science/api/pith-number/IQ7PGOYOC6QFQPCGZKXIRV7TFT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IQ7PGOYOC6QFQPCGZKXIRV7TFT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IQ7PGOYOC6QFQPCGZKXIRV7TFT/action/storage_attestation","attest_author":"https://pith.science/pith/IQ7PGOYOC6QFQPCGZKXIRV7TFT/action/author_attestation","sign_citation":"https://pith.science/pith/IQ7PGOYOC6QFQPCGZKXIRV7TFT/action/citation_signature","submit_replication":"https://pith.science/pith/IQ7PGOYOC6QFQPCGZKXIRV7TFT/action/replication_record"}},"created_at":"2026-05-18T04:22:30.040278+00:00","updated_at":"2026-05-18T04:22:30.040278+00:00"}