{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HNNBSTWZF5OWPGAHQQSZTW6RRU","short_pith_number":"pith:HNNBSTWZ","canonical_record":{"source":{"id":"1412.3347","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-12-10T15:57:52Z","cross_cats_sorted":[],"title_canon_sha256":"ccd23fad2c901e828d85092fde358099d526ed8673ae969f06bdfaa87daa6cef","abstract_canon_sha256":"5f31a877dcd97a26f19eccae80ef56e1e9ec834d5ce4f51e15bb8a1d7860796a"},"schema_version":"1.0"},"canonical_sha256":"3b5a194ed92f5d679807842599dbd18d19ed9519d78111ff514fa1c4407337ff","source":{"kind":"arxiv","id":"1412.3347","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3347","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3347v2","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3347","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"pith_short_12","alias_value":"HNNBSTWZF5OW","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HNNBSTWZF5OWPGAH","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HNNBSTWZ","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HNNBSTWZF5OWPGAHQQSZTW6RRU","target":"record","payload":{"canonical_record":{"source":{"id":"1412.3347","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-12-10T15:57:52Z","cross_cats_sorted":[],"title_canon_sha256":"ccd23fad2c901e828d85092fde358099d526ed8673ae969f06bdfaa87daa6cef","abstract_canon_sha256":"5f31a877dcd97a26f19eccae80ef56e1e9ec834d5ce4f51e15bb8a1d7860796a"},"schema_version":"1.0"},"canonical_sha256":"3b5a194ed92f5d679807842599dbd18d19ed9519d78111ff514fa1c4407337ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:51.712882Z","signature_b64":"bbPfEAbKJZ6hQfdcHQftHu/43QJ0crmS4UULF7Sed+KvfB+nCW7jh/b0KgmoUD3YFYW/ayLgRKs6LxhS9fBNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b5a194ed92f5d679807842599dbd18d19ed9519d78111ff514fa1c4407337ff","last_reissued_at":"2026-05-18T00:06:51.712191Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:51.712191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.3347","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QJALMJbLVo4hkDYuoUwSJs6w3Z0AhwxRsYDaaIe9f1eRM9tjBPAaYMOQMvdxfsu1hqDH30gbUOnAf77XXLMPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:43:47.854934Z"},"content_sha256":"19dfaac80c968d9cd3f8f50801e0d6f94381d5711c46b599c7e695892699646a","schema_version":"1.0","event_id":"sha256:19dfaac80c968d9cd3f8f50801e0d6f94381d5711c46b599c7e695892699646a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HNNBSTWZF5OWPGAHQQSZTW6RRU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computational Aspects of the Colorful Carath\\'eodory Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Wolfgang Mulzer, Yannik Stein","submitted_at":"2014-12-10T15:57:52Z","abstract_excerpt":"Let $C_1,\\dots,C_{d+1}\\subset \\mathbb{R}^d$ be $d+1$ point sets, each containing the origin in its convex hull. We call these sets color classes, and we call a sequence $p_1, \\dots, p_{d+1}$ with $p_i \\in C_i$, for $i = 1, \\dots, d+1$, a colorful choice. The colorful Carath\\'eodory theorem guarantees the existence of a colorful choice that also contains the origin in its convex hull. The computational complexity of finding such a colorful choice (CCP) is unknown. This is particularly interesting in the light of polynomial-time reductions from several related problems, such as computing centerp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3347","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3cae7ooUm6NOfLhJirl6UV6PWRnC0UdfG5tAGrI/qTRp3at3AZN27F6Zb9kxD4KiNfZ27shh9mY+FWcCXLvBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:43:47.855667Z"},"content_sha256":"6579db4e82c54c030af4855cc95f9ae9cd81ecbf86218423a2317652cdd94234","schema_version":"1.0","event_id":"sha256:6579db4e82c54c030af4855cc95f9ae9cd81ecbf86218423a2317652cdd94234"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNNBSTWZF5OWPGAHQQSZTW6RRU/bundle.json","state_url":"https://pith.science/pith/HNNBSTWZF5OWPGAHQQSZTW6RRU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNNBSTWZF5OWPGAHQQSZTW6RRU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T16:43:47Z","links":{"resolver":"https://pith.science/pith/HNNBSTWZF5OWPGAHQQSZTW6RRU","bundle":"https://pith.science/pith/HNNBSTWZF5OWPGAHQQSZTW6RRU/bundle.json","state":"https://pith.science/pith/HNNBSTWZF5OWPGAHQQSZTW6RRU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNNBSTWZF5OWPGAHQQSZTW6RRU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HNNBSTWZF5OWPGAHQQSZTW6RRU","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":"5f31a877dcd97a26f19eccae80ef56e1e9ec834d5ce4f51e15bb8a1d7860796a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-12-10T15:57:52Z","title_canon_sha256":"ccd23fad2c901e828d85092fde358099d526ed8673ae969f06bdfaa87daa6cef"},"schema_version":"1.0","source":{"id":"1412.3347","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3347","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3347v2","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3347","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"pith_short_12","alias_value":"HNNBSTWZF5OW","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HNNBSTWZF5OWPGAH","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HNNBSTWZ","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:6579db4e82c54c030af4855cc95f9ae9cd81ecbf86218423a2317652cdd94234","target":"graph","created_at":"2026-05-18T00:06:51Z","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":"Let $C_1,\\dots,C_{d+1}\\subset \\mathbb{R}^d$ be $d+1$ point sets, each containing the origin in its convex hull. We call these sets color classes, and we call a sequence $p_1, \\dots, p_{d+1}$ with $p_i \\in C_i$, for $i = 1, \\dots, d+1$, a colorful choice. The colorful Carath\\'eodory theorem guarantees the existence of a colorful choice that also contains the origin in its convex hull. The computational complexity of finding such a colorful choice (CCP) is unknown. This is particularly interesting in the light of polynomial-time reductions from several related problems, such as computing centerp","authors_text":"Wolfgang Mulzer, Yannik Stein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-12-10T15:57:52Z","title":"Computational Aspects of the Colorful Carath\\'eodory Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3347","kind":"arxiv","version":2},"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":"sha256:19dfaac80c968d9cd3f8f50801e0d6f94381d5711c46b599c7e695892699646a","target":"record","created_at":"2026-05-18T00:06:51Z","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":"5f31a877dcd97a26f19eccae80ef56e1e9ec834d5ce4f51e15bb8a1d7860796a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-12-10T15:57:52Z","title_canon_sha256":"ccd23fad2c901e828d85092fde358099d526ed8673ae969f06bdfaa87daa6cef"},"schema_version":"1.0","source":{"id":"1412.3347","kind":"arxiv","version":2}},"canonical_sha256":"3b5a194ed92f5d679807842599dbd18d19ed9519d78111ff514fa1c4407337ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b5a194ed92f5d679807842599dbd18d19ed9519d78111ff514fa1c4407337ff","first_computed_at":"2026-05-18T00:06:51.712191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:51.712191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bbPfEAbKJZ6hQfdcHQftHu/43QJ0crmS4UULF7Sed+KvfB+nCW7jh/b0KgmoUD3YFYW/ayLgRKs6LxhS9fBNDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:51.712882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3347","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19dfaac80c968d9cd3f8f50801e0d6f94381d5711c46b599c7e695892699646a","sha256:6579db4e82c54c030af4855cc95f9ae9cd81ecbf86218423a2317652cdd94234"],"state_sha256":"2b30f0731bbe4ceae993ad3ae7301f687d6f033f9d3b9b78811cdf3cf49b25d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"owt9GWQ+Ug3584zz1SGBYVeq4zWiewQhuXdLKgUQ4aQPKwF9k3C6WltW0g7u6/JeYE/gUgk6WDvjRdpS94F5DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:43:47.859449Z","bundle_sha256":"2065c178f30008e3cf15623b385c411bc4ad2a4daf50fe6fd285b5a00c41ab18"}}