{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:U7EBWPCNCPBP67BBSPIDCXYF5Z","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":"decfdb492dbbb9d6e74533c1a2ee558f692e0ab8fbbdb588a845b5574702354c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-03-28T16:19:16Z","title_canon_sha256":"a18de76dd263cc3b62055ecb928a0f24704f0ed67bf45cee5af3eba745c3514f"},"schema_version":"1.0","source":{"id":"2503.22571","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.22571","created_at":"2026-07-05T10:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"2503.22571v1","created_at":"2026-07-05T10:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.22571","created_at":"2026-07-05T10:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"U7EBWPCNCPBP","created_at":"2026-07-05T10:41:06Z"},{"alias_kind":"pith_short_16","alias_value":"U7EBWPCNCPBP67BB","created_at":"2026-07-05T10:41:06Z"},{"alias_kind":"pith_short_8","alias_value":"U7EBWPCN","created_at":"2026-07-05T10:41:06Z"}],"graph_snapshots":[{"event_id":"sha256:1584ec870985e716d27974a40148031e9a83fad67d32e4d6e609423bdabd6209","target":"graph","created_at":"2026-07-05T10:41:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.22571/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a unified approach to prove Helly-type theorems for monotone properties of boxes, such as having large volume or containing points from a given set. As a corollary, we obtain new proofs for several earlier results regarding specific monotone properties. Our results generalise to $H$-convex sets as well.","authors_text":"Attila Jung, N\\'ora Frankl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-03-28T16:19:16Z","title":"Helly-type theorems for monotone properties of boxes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.22571","kind":"arxiv","version":1},"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":"sha256:3f0e712520567d5528b327741819ade14f55dc1862cec595b2b516da3eba3cb5","target":"record","created_at":"2026-07-05T10:41:06Z","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":"decfdb492dbbb9d6e74533c1a2ee558f692e0ab8fbbdb588a845b5574702354c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-03-28T16:19:16Z","title_canon_sha256":"a18de76dd263cc3b62055ecb928a0f24704f0ed67bf45cee5af3eba745c3514f"},"schema_version":"1.0","source":{"id":"2503.22571","kind":"arxiv","version":1}},"canonical_sha256":"a7c81b3c4d13c2ff7c2193d0315f05ee7fc3920256e4fb516c4ee6f6865a79a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7c81b3c4d13c2ff7c2193d0315f05ee7fc3920256e4fb516c4ee6f6865a79a2","first_computed_at":"2026-07-05T10:41:06.901055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:41:06.901055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pnsj1X95R8xa08BneZCtl7wGIqLEqh7hqOxdDLuUgrvw8qM0yhQsl07o++KTtsVZ0TyLf6+y1R1LnYs4yLFIAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:41:06.901543Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.22571","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f0e712520567d5528b327741819ade14f55dc1862cec595b2b516da3eba3cb5","sha256:1584ec870985e716d27974a40148031e9a83fad67d32e4d6e609423bdabd6209"],"state_sha256":"c98e6329d4fb54504f1767ad052bd307a8c04bb83aa4090df399b8f604759a52"}