{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SO2UIFHBZBQPSLMAMYJI7DB7Q7","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":"30e1a9f6b42d122f6d9002d2652e49c42ed905eb9fb9a6957cc04c69e119b5cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-22T04:52:05Z","title_canon_sha256":"11078e499dccb8f07110f31cf648a47121cebd4754d62627f2c43454e1a981b4"},"schema_version":"1.0","source":{"id":"1010.4613","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4613","created_at":"2026-05-18T04:38:57Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4613v1","created_at":"2026-05-18T04:38:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4613","created_at":"2026-05-18T04:38:57Z"},{"alias_kind":"pith_short_12","alias_value":"SO2UIFHBZBQP","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SO2UIFHBZBQPSLMA","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SO2UIFHB","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:5732157cd45fd856fc48fdceeb5524552925418b13a91fd64f7144ff18aee17b","target":"graph","created_at":"2026-05-18T04:38:57Z","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"},"paper":{"abstract_excerpt":"We give new bounds on the Erdos-Szekeres theorems for convex bodies of Bisztriczky and Fejes Toth and of Pach and Toth. We derive them from a combinatorial characterization of convex position of a family of planar convex bodies. This characterization confirms that the concept of Order Type for points can be extended to noncrossing families of convex bodies in a geometrically meaningful way.","authors_text":"Alfredo Hubard, Andrew Suk, Emiliano Mora, Luis Montejano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-22T04:52:05Z","title":"Order Types of convex bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4613","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":"sha256:82396ffe5262b9248b5680b42a3586e20767ce0f0ea48755112751fa998505b6","target":"record","created_at":"2026-05-18T04:38:57Z","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":"30e1a9f6b42d122f6d9002d2652e49c42ed905eb9fb9a6957cc04c69e119b5cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-22T04:52:05Z","title_canon_sha256":"11078e499dccb8f07110f31cf648a47121cebd4754d62627f2c43454e1a981b4"},"schema_version":"1.0","source":{"id":"1010.4613","kind":"arxiv","version":1}},"canonical_sha256":"93b54414e1c860f92d8066128f8c3f87edf94483c6e9bb5b8462548f3ac6c096","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93b54414e1c860f92d8066128f8c3f87edf94483c6e9bb5b8462548f3ac6c096","first_computed_at":"2026-05-18T04:38:57.835670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:57.835670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WZSYnUoqA5GZZtqWdOVr5PvppWwfpHqdV34g51qOkV62WODCLWqA+qIUrRRvjP6bxim0fsVPu6bhQWLWErjgCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:57.836281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.4613","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82396ffe5262b9248b5680b42a3586e20767ce0f0ea48755112751fa998505b6","sha256:5732157cd45fd856fc48fdceeb5524552925418b13a91fd64f7144ff18aee17b"],"state_sha256":"f0ab9306db4f3b1a03df613caef4d396acf6b5e13f63ace38dbcfb996ff2a6f9"}