{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TY5VAUZKLQNCUFXLT3BDDFNEG5","short_pith_number":"pith:TY5VAUZK","schema_version":"1.0","canonical_sha256":"9e3b50532a5c1a2a16eb9ec23195a4377cc87f3c6347038168ec2835c7cde74d","source":{"kind":"arxiv","id":"1801.00324","version":1},"attestation_state":"computed","paper":{"title":"Blockers for Triangulations of a Convex Polygon and a Geometric Maker-Breaker Game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chaya Keller, Yael Stein","submitted_at":"2017-12-31T17:34:24Z","abstract_excerpt":"Let $G$ be a complete convex geometric graph whose vertex set $P$ forms a convex polygon $C$, and let $F$ be a family of subgraphs of $G$. A blocker for $F$ is a set of edges, of smallest possible size, that contains a common edge with every element of $F$. Previous works determined the blockers for various families $F$ of non-crossing subgraphs, including the families of all perfect matchings, all spanning trees, all Hamiltonian paths, etc.\n  In this paper we present a complete characterization of the family $B$ of blockers for the family $T$ of triangulations of $C$. In particular, we show t"},"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":"1801.00324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-31T17:34:24Z","cross_cats_sorted":[],"title_canon_sha256":"89e0a4967ef67e4c4d60b1b0c0749a61947a068da51164e0844458f015ad52f4","abstract_canon_sha256":"2d30e94f64d3443f564bfa69849d25055b0aa99312924fd8200541eec2d1b679"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:58.697453Z","signature_b64":"KZo4ROSHeSroqB4LdzONG3jW6GodIL2JzEQ9xPoqN9GcCsPD7irF2w1jyfPHqGBDD+RRgUEYxdGciBwAMCeYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e3b50532a5c1a2a16eb9ec23195a4377cc87f3c6347038168ec2835c7cde74d","last_reissued_at":"2026-05-18T00:26:58.696804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:58.696804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Blockers for Triangulations of a Convex Polygon and a Geometric Maker-Breaker Game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chaya Keller, Yael Stein","submitted_at":"2017-12-31T17:34:24Z","abstract_excerpt":"Let $G$ be a complete convex geometric graph whose vertex set $P$ forms a convex polygon $C$, and let $F$ be a family of subgraphs of $G$. A blocker for $F$ is a set of edges, of smallest possible size, that contains a common edge with every element of $F$. Previous works determined the blockers for various families $F$ of non-crossing subgraphs, including the families of all perfect matchings, all spanning trees, all Hamiltonian paths, etc.\n  In this paper we present a complete characterization of the family $B$ of blockers for the family $T$ of triangulations of $C$. In particular, we show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00324","kind":"arxiv","version":1},"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":"1801.00324","created_at":"2026-05-18T00:26:58.696893+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.00324v1","created_at":"2026-05-18T00:26:58.696893+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00324","created_at":"2026-05-18T00:26:58.696893+00:00"},{"alias_kind":"pith_short_12","alias_value":"TY5VAUZKLQNC","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"TY5VAUZKLQNCUFXL","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"TY5VAUZK","created_at":"2026-05-18T12:31:46.661854+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/TY5VAUZKLQNCUFXLT3BDDFNEG5","json":"https://pith.science/pith/TY5VAUZKLQNCUFXLT3BDDFNEG5.json","graph_json":"https://pith.science/api/pith-number/TY5VAUZKLQNCUFXLT3BDDFNEG5/graph.json","events_json":"https://pith.science/api/pith-number/TY5VAUZKLQNCUFXLT3BDDFNEG5/events.json","paper":"https://pith.science/paper/TY5VAUZK"},"agent_actions":{"view_html":"https://pith.science/pith/TY5VAUZKLQNCUFXLT3BDDFNEG5","download_json":"https://pith.science/pith/TY5VAUZKLQNCUFXLT3BDDFNEG5.json","view_paper":"https://pith.science/paper/TY5VAUZK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.00324&json=true","fetch_graph":"https://pith.science/api/pith-number/TY5VAUZKLQNCUFXLT3BDDFNEG5/graph.json","fetch_events":"https://pith.science/api/pith-number/TY5VAUZKLQNCUFXLT3BDDFNEG5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TY5VAUZKLQNCUFXLT3BDDFNEG5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TY5VAUZKLQNCUFXLT3BDDFNEG5/action/storage_attestation","attest_author":"https://pith.science/pith/TY5VAUZKLQNCUFXLT3BDDFNEG5/action/author_attestation","sign_citation":"https://pith.science/pith/TY5VAUZKLQNCUFXLT3BDDFNEG5/action/citation_signature","submit_replication":"https://pith.science/pith/TY5VAUZKLQNCUFXLT3BDDFNEG5/action/replication_record"}},"created_at":"2026-05-18T00:26:58.696893+00:00","updated_at":"2026-05-18T00:26:58.696893+00:00"}