{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4QP6SS6QU5SE6MKULHFTGAPRPJ","short_pith_number":"pith:4QP6SS6Q","schema_version":"1.0","canonical_sha256":"e41fe94bd0a7644f315459cb3301f17a5065e65994058c4c154d1315fd830207","source":{"kind":"arxiv","id":"1705.00089","version":2},"attestation_state":"computed","paper":{"title":"Piercing axis-parallel boxes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maria Chudnovsky, Shira Zerbib, Sophie Spirkl","submitted_at":"2017-04-28T22:34:04Z","abstract_excerpt":"Let $\\F$ be a finite family of axis-parallel boxes in $\\R^d$ such that $\\F$ contains no $k+1$ pairwise disjoint boxes. We prove that if $\\F$ contains a subfamily $\\M$ of $k$ pairwise disjoint boxes with the property that for every $F\\in \\F$ and $M\\in \\M$ with $F \\cap M \\neq \\emptyset$, either $F$ contains a corner of $M$ or $M$ contains $2^{d-1}$ corners of $F$, then $\\F$ can be pierced by $O(k)$ points. One consequence of this result is that if $d=2$ and the ratio between any of the side lengths of any box is bounded by a constant, then $\\F$ can be pierced by $O(k)$ points. We further show th"},"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":"1705.00089","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-28T22:34:04Z","cross_cats_sorted":[],"title_canon_sha256":"e11f86085ab7567eb48de1aa6c7ec65b6cf294cfac7199c52e8caed3c97636c1","abstract_canon_sha256":"b6ad83ac0146dc5d07d8d3d67a9e9c9da848069d5d6ee2c8ea0f2fad8f3f0947"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:12.283512Z","signature_b64":"3pv+8kfET8MlWWhrPd2Ng5wnByX10jjR6Ic49RKOmwnDzwAXDZ+tsM124tL44B/9xH6f5u8S4pSdChkYqTPXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e41fe94bd0a7644f315459cb3301f17a5065e65994058c4c154d1315fd830207","last_reissued_at":"2026-05-18T00:39:12.282751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:12.282751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Piercing axis-parallel boxes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maria Chudnovsky, Shira Zerbib, Sophie Spirkl","submitted_at":"2017-04-28T22:34:04Z","abstract_excerpt":"Let $\\F$ be a finite family of axis-parallel boxes in $\\R^d$ such that $\\F$ contains no $k+1$ pairwise disjoint boxes. We prove that if $\\F$ contains a subfamily $\\M$ of $k$ pairwise disjoint boxes with the property that for every $F\\in \\F$ and $M\\in \\M$ with $F \\cap M \\neq \\emptyset$, either $F$ contains a corner of $M$ or $M$ contains $2^{d-1}$ corners of $F$, then $\\F$ can be pierced by $O(k)$ points. One consequence of this result is that if $d=2$ and the ratio between any of the side lengths of any box is bounded by a constant, then $\\F$ can be pierced by $O(k)$ points. We further show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00089","kind":"arxiv","version":2},"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":"1705.00089","created_at":"2026-05-18T00:39:12.282886+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.00089v2","created_at":"2026-05-18T00:39:12.282886+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00089","created_at":"2026-05-18T00:39:12.282886+00:00"},{"alias_kind":"pith_short_12","alias_value":"4QP6SS6QU5SE","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"4QP6SS6QU5SE6MKU","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"4QP6SS6Q","created_at":"2026-05-18T12:31:00.734936+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/4QP6SS6QU5SE6MKULHFTGAPRPJ","json":"https://pith.science/pith/4QP6SS6QU5SE6MKULHFTGAPRPJ.json","graph_json":"https://pith.science/api/pith-number/4QP6SS6QU5SE6MKULHFTGAPRPJ/graph.json","events_json":"https://pith.science/api/pith-number/4QP6SS6QU5SE6MKULHFTGAPRPJ/events.json","paper":"https://pith.science/paper/4QP6SS6Q"},"agent_actions":{"view_html":"https://pith.science/pith/4QP6SS6QU5SE6MKULHFTGAPRPJ","download_json":"https://pith.science/pith/4QP6SS6QU5SE6MKULHFTGAPRPJ.json","view_paper":"https://pith.science/paper/4QP6SS6Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.00089&json=true","fetch_graph":"https://pith.science/api/pith-number/4QP6SS6QU5SE6MKULHFTGAPRPJ/graph.json","fetch_events":"https://pith.science/api/pith-number/4QP6SS6QU5SE6MKULHFTGAPRPJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4QP6SS6QU5SE6MKULHFTGAPRPJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4QP6SS6QU5SE6MKULHFTGAPRPJ/action/storage_attestation","attest_author":"https://pith.science/pith/4QP6SS6QU5SE6MKULHFTGAPRPJ/action/author_attestation","sign_citation":"https://pith.science/pith/4QP6SS6QU5SE6MKULHFTGAPRPJ/action/citation_signature","submit_replication":"https://pith.science/pith/4QP6SS6QU5SE6MKULHFTGAPRPJ/action/replication_record"}},"created_at":"2026-05-18T00:39:12.282886+00:00","updated_at":"2026-05-18T00:39:12.282886+00:00"}