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We prove that, for any two distinct $BR$-matchings $M$ and $M'$, there exists a sequence of $BR$-matchings $M = M_1, ..., M_k = M'$ such that $M_{i-1} $ is compatible with $M_i$. This implies the connectivity of the compatible bichromatic matching graph containing one node for each bichromatic matching and an edge joining each pair of compat"},"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":"1207.2375","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-07-10T14:39:41Z","cross_cats_sorted":[],"title_canon_sha256":"b0f569f6a5713c51914031f1dd6df4b4480306bbfd32c14bd3405bedb5f4d384","abstract_canon_sha256":"a245ad639d7b29f17a653106a0625f1dcf34cda794bafabc22dd7a728ef4e8f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:13.752654Z","signature_b64":"7qUvngdKoVzRkK7ZJ/9r3AEDhO05X0p0ad9Yez/GqPIop7fcFZkHjB/KVpkjFxGMP5bKTXYXcN0FyUlCsQ/6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"630d6b52ed7324827d11b7bb25fb6c025adc60423117ca6d6b4b4a8f1f76a59c","last_reissued_at":"2026-05-18T03:06:13.752238Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:13.752238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bichromatic compatible matchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Diane L. Souvaine, Greg Aloupis, Luis Barba, Stefan Langerman","submitted_at":"2012-07-10T14:39:41Z","abstract_excerpt":"For a set $R$ of $n$ red points and a set $B$ of $n$ blue points, a $BR$-matching is a non-crossing geometric perfect matching where each segment has one endpoint in $B$ and one in $R$. Two $BR$-matchings are compatible if their union is also non-crossing. We prove that, for any two distinct $BR$-matchings $M$ and $M'$, there exists a sequence of $BR$-matchings $M = M_1, ..., M_k = M'$ such that $M_{i-1} $ is compatible with $M_i$. This implies the connectivity of the compatible bichromatic matching graph containing one node for each bichromatic matching and an edge joining each pair of compat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2375","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":"1207.2375","created_at":"2026-05-18T03:06:13.752299+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.2375v3","created_at":"2026-05-18T03:06:13.752299+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2375","created_at":"2026-05-18T03:06:13.752299+00:00"},{"alias_kind":"pith_short_12","alias_value":"MMGWWUXNOMSI","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MMGWWUXNOMSIE7IR","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MMGWWUXN","created_at":"2026-05-18T12:27:14.488303+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/MMGWWUXNOMSIE7IRW65SL63MAJ","json":"https://pith.science/pith/MMGWWUXNOMSIE7IRW65SL63MAJ.json","graph_json":"https://pith.science/api/pith-number/MMGWWUXNOMSIE7IRW65SL63MAJ/graph.json","events_json":"https://pith.science/api/pith-number/MMGWWUXNOMSIE7IRW65SL63MAJ/events.json","paper":"https://pith.science/paper/MMGWWUXN"},"agent_actions":{"view_html":"https://pith.science/pith/MMGWWUXNOMSIE7IRW65SL63MAJ","download_json":"https://pith.science/pith/MMGWWUXNOMSIE7IRW65SL63MAJ.json","view_paper":"https://pith.science/paper/MMGWWUXN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.2375&json=true","fetch_graph":"https://pith.science/api/pith-number/MMGWWUXNOMSIE7IRW65SL63MAJ/graph.json","fetch_events":"https://pith.science/api/pith-number/MMGWWUXNOMSIE7IRW65SL63MAJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MMGWWUXNOMSIE7IRW65SL63MAJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MMGWWUXNOMSIE7IRW65SL63MAJ/action/storage_attestation","attest_author":"https://pith.science/pith/MMGWWUXNOMSIE7IRW65SL63MAJ/action/author_attestation","sign_citation":"https://pith.science/pith/MMGWWUXNOMSIE7IRW65SL63MAJ/action/citation_signature","submit_replication":"https://pith.science/pith/MMGWWUXNOMSIE7IRW65SL63MAJ/action/replication_record"}},"created_at":"2026-05-18T03:06:13.752299+00:00","updated_at":"2026-05-18T03:06:13.752299+00:00"}