{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:I6GT257A2QGUKXRBAJOOG4KHMR","short_pith_number":"pith:I6GT257A","schema_version":"1.0","canonical_sha256":"478d3d77e0d40d455e21025ce371476443e3f256d21798934b8ab25d7109ff63","source":{"kind":"arxiv","id":"1407.4091","version":4},"attestation_state":"computed","paper":{"title":"Cutting convex curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Andreas F. Holmsen, Edgardo Rold\\'an-Pensado, J\\'anos Kincses","submitted_at":"2014-07-15T18:45:23Z","abstract_excerpt":"We show that for any two convex curves $C_1$ and $C_2$ in $\\mathbb R^d$ parametrized by $[0,1]$ with opposite orientations, there exists a hyperplane $H$ with the following property: For any $t\\in [0,1]$ the points $C_1(t)$ and $C_2(t)$ are never in the same open halfspace bounded by $H$. This will be deduced from a more general result on equipartitions of ordered point sets by hyperplanes."},"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":"1407.4091","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-07-15T18:45:23Z","cross_cats_sorted":[],"title_canon_sha256":"30682bfdf283722ad23ef0882134347cb66c5626e2514efee0296dc69e8a1dba","abstract_canon_sha256":"1e0679e0b92f365f1bdaea353b60c07174a24effdf377107e04d737f6d92ff31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:10.324771Z","signature_b64":"4IZcIYiq0lrmnAtJwTJzRHzO7nEsfs+IDRSwMnTeL1WTM0TTO7QISL2j5iQ/tGFVXFvDSm6sBduXngrS5fBXAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"478d3d77e0d40d455e21025ce371476443e3f256d21798934b8ab25d7109ff63","last_reissued_at":"2026-05-18T01:18:10.324291Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:10.324291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cutting convex curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Andreas F. Holmsen, Edgardo Rold\\'an-Pensado, J\\'anos Kincses","submitted_at":"2014-07-15T18:45:23Z","abstract_excerpt":"We show that for any two convex curves $C_1$ and $C_2$ in $\\mathbb R^d$ parametrized by $[0,1]$ with opposite orientations, there exists a hyperplane $H$ with the following property: For any $t\\in [0,1]$ the points $C_1(t)$ and $C_2(t)$ are never in the same open halfspace bounded by $H$. This will be deduced from a more general result on equipartitions of ordered point sets by hyperplanes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4091","kind":"arxiv","version":4},"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":"1407.4091","created_at":"2026-05-18T01:18:10.324370+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.4091v4","created_at":"2026-05-18T01:18:10.324370+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4091","created_at":"2026-05-18T01:18:10.324370+00:00"},{"alias_kind":"pith_short_12","alias_value":"I6GT257A2QGU","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"I6GT257A2QGUKXRB","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"I6GT257A","created_at":"2026-05-18T12:28:33.132498+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/I6GT257A2QGUKXRBAJOOG4KHMR","json":"https://pith.science/pith/I6GT257A2QGUKXRBAJOOG4KHMR.json","graph_json":"https://pith.science/api/pith-number/I6GT257A2QGUKXRBAJOOG4KHMR/graph.json","events_json":"https://pith.science/api/pith-number/I6GT257A2QGUKXRBAJOOG4KHMR/events.json","paper":"https://pith.science/paper/I6GT257A"},"agent_actions":{"view_html":"https://pith.science/pith/I6GT257A2QGUKXRBAJOOG4KHMR","download_json":"https://pith.science/pith/I6GT257A2QGUKXRBAJOOG4KHMR.json","view_paper":"https://pith.science/paper/I6GT257A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.4091&json=true","fetch_graph":"https://pith.science/api/pith-number/I6GT257A2QGUKXRBAJOOG4KHMR/graph.json","fetch_events":"https://pith.science/api/pith-number/I6GT257A2QGUKXRBAJOOG4KHMR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I6GT257A2QGUKXRBAJOOG4KHMR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I6GT257A2QGUKXRBAJOOG4KHMR/action/storage_attestation","attest_author":"https://pith.science/pith/I6GT257A2QGUKXRBAJOOG4KHMR/action/author_attestation","sign_citation":"https://pith.science/pith/I6GT257A2QGUKXRBAJOOG4KHMR/action/citation_signature","submit_replication":"https://pith.science/pith/I6GT257A2QGUKXRBAJOOG4KHMR/action/replication_record"}},"created_at":"2026-05-18T01:18:10.324370+00:00","updated_at":"2026-05-18T01:18:10.324370+00:00"}