{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HHGIIUSCGZFFGA7OM6HQ5KP5DJ","short_pith_number":"pith:HHGIIUSC","canonical_record":{"source":{"id":"1802.03415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-02-09T19:09:52Z","cross_cats_sorted":[],"title_canon_sha256":"f2f8fdd41c3169d4a92ddb831fecd91cdac23b3c29c0d35424999ecc9f89ecc2","abstract_canon_sha256":"cef727c49afc7124cecc47d3ec9524e23688df409073738b81704ef331eab47f"},"schema_version":"1.0"},"canonical_sha256":"39cc845242364a5303ee678f0ea9fd1a4df570a09ef9843be8ba7f321daf8ccc","source":{"kind":"arxiv","id":"1802.03415","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03415","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03415v1","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03415","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"pith_short_12","alias_value":"HHGIIUSCGZFF","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HHGIIUSCGZFFGA7O","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HHGIIUSC","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HHGIIUSCGZFFGA7OM6HQ5KP5DJ","target":"record","payload":{"canonical_record":{"source":{"id":"1802.03415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-02-09T19:09:52Z","cross_cats_sorted":[],"title_canon_sha256":"f2f8fdd41c3169d4a92ddb831fecd91cdac23b3c29c0d35424999ecc9f89ecc2","abstract_canon_sha256":"cef727c49afc7124cecc47d3ec9524e23688df409073738b81704ef331eab47f"},"schema_version":"1.0"},"canonical_sha256":"39cc845242364a5303ee678f0ea9fd1a4df570a09ef9843be8ba7f321daf8ccc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:51.756007Z","signature_b64":"9ksyYgeL+NIDj4Y84d/1N2InrxEkgRlknApPV4gslFPUZZQuv9J28JaQfTCvr1y2JVdzTFYulgWEMAXi46hNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39cc845242364a5303ee678f0ea9fd1a4df570a09ef9843be8ba7f321daf8ccc","last_reissued_at":"2026-05-18T00:23:51.755470Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:51.755470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.03415","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G5DeAUeRkqkSYu6CLG6SVjK/C5VHeGOQODvj+IvS4QQleyLvEaXc1j7fwOhh0V5PjB5sIl/5sHozS2ywHw+4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:10:55.128542Z"},"content_sha256":"276b374fbd60fc051e980654fe9969fe3b9e101ee6a249a5516d646c43fa4468","schema_version":"1.0","event_id":"sha256:276b374fbd60fc051e980654fe9969fe3b9e101ee6a249a5516d646c43fa4468"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HHGIIUSCGZFFGA7OM6HQ5KP5DJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Colored ray configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Alfredo Garc\\'ia, Ferran Hurtado, Javier Tejel, Jorge Urrutia, Maria Saumell, Pablo P\\'erez-Lantero, Rafel Jaume, Rodrigo I. Silveira, Ruy Fabila-Monroy","submitted_at":"2018-02-09T19:09:52Z","abstract_excerpt":"We study the cyclic color sequences induced at infinity by colored rays with apices being a given balanced finite bichromatic point set. We first study the case in which the rays are required to be pairwise disjoint. We derive a lower bound on the number of color sequences that can be realized from any such fixed point set and examine color sequences that can be realized regardless of the point set, exhibiting negative examples as well. We also provide a tight upper bound on the number of configurations that can be realized from a point set, and point sets for which there are asymptotically le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03415","kind":"arxiv","version":1},"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":"2026-05-18T00:23:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rnYOJUV8PnRP8x52GYVaV2mn/OjallKEUYjkUq5T+eXoGr12g2mW+X9pYITNgPPmdN4KTkQV4/zXz5PgpCSJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:10:55.129174Z"},"content_sha256":"89e64d479f0937e44e32737eb98ad3015a4141af78a409750dee77ae1f4bd043","schema_version":"1.0","event_id":"sha256:89e64d479f0937e44e32737eb98ad3015a4141af78a409750dee77ae1f4bd043"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HHGIIUSCGZFFGA7OM6HQ5KP5DJ/bundle.json","state_url":"https://pith.science/pith/HHGIIUSCGZFFGA7OM6HQ5KP5DJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HHGIIUSCGZFFGA7OM6HQ5KP5DJ/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":"2026-05-26T22:10:55Z","links":{"resolver":"https://pith.science/pith/HHGIIUSCGZFFGA7OM6HQ5KP5DJ","bundle":"https://pith.science/pith/HHGIIUSCGZFFGA7OM6HQ5KP5DJ/bundle.json","state":"https://pith.science/pith/HHGIIUSCGZFFGA7OM6HQ5KP5DJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HHGIIUSCGZFFGA7OM6HQ5KP5DJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HHGIIUSCGZFFGA7OM6HQ5KP5DJ","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":"cef727c49afc7124cecc47d3ec9524e23688df409073738b81704ef331eab47f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-02-09T19:09:52Z","title_canon_sha256":"f2f8fdd41c3169d4a92ddb831fecd91cdac23b3c29c0d35424999ecc9f89ecc2"},"schema_version":"1.0","source":{"id":"1802.03415","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03415","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03415v1","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03415","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"pith_short_12","alias_value":"HHGIIUSCGZFF","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HHGIIUSCGZFFGA7O","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HHGIIUSC","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:89e64d479f0937e44e32737eb98ad3015a4141af78a409750dee77ae1f4bd043","target":"graph","created_at":"2026-05-18T00:23:51Z","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":"We study the cyclic color sequences induced at infinity by colored rays with apices being a given balanced finite bichromatic point set. We first study the case in which the rays are required to be pairwise disjoint. We derive a lower bound on the number of color sequences that can be realized from any such fixed point set and examine color sequences that can be realized regardless of the point set, exhibiting negative examples as well. We also provide a tight upper bound on the number of configurations that can be realized from a point set, and point sets for which there are asymptotically le","authors_text":"Alfredo Garc\\'ia, Ferran Hurtado, Javier Tejel, Jorge Urrutia, Maria Saumell, Pablo P\\'erez-Lantero, Rafel Jaume, Rodrigo I. Silveira, Ruy Fabila-Monroy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-02-09T19:09:52Z","title":"Colored ray configurations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03415","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":"sha256:276b374fbd60fc051e980654fe9969fe3b9e101ee6a249a5516d646c43fa4468","target":"record","created_at":"2026-05-18T00:23:51Z","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":"cef727c49afc7124cecc47d3ec9524e23688df409073738b81704ef331eab47f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-02-09T19:09:52Z","title_canon_sha256":"f2f8fdd41c3169d4a92ddb831fecd91cdac23b3c29c0d35424999ecc9f89ecc2"},"schema_version":"1.0","source":{"id":"1802.03415","kind":"arxiv","version":1}},"canonical_sha256":"39cc845242364a5303ee678f0ea9fd1a4df570a09ef9843be8ba7f321daf8ccc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39cc845242364a5303ee678f0ea9fd1a4df570a09ef9843be8ba7f321daf8ccc","first_computed_at":"2026-05-18T00:23:51.755470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:51.755470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ksyYgeL+NIDj4Y84d/1N2InrxEkgRlknApPV4gslFPUZZQuv9J28JaQfTCvr1y2JVdzTFYulgWEMAXi46hNAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:51.756007Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.03415","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:276b374fbd60fc051e980654fe9969fe3b9e101ee6a249a5516d646c43fa4468","sha256:89e64d479f0937e44e32737eb98ad3015a4141af78a409750dee77ae1f4bd043"],"state_sha256":"61dddbea584c5d4a2fb2bde43d22e9cef7a6e8255deb1122f8d3223d19c4fcd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7nBmzKnU4O/XpxohTWoeSFVFDoESRcC4zbB1ySFYHqv8fHrvCflbPl3wQG6tugbwRpaR2ytjXBh7I0Kf4mBdAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:10:55.132440Z","bundle_sha256":"8a4e56d3d9a348a59f5bb402b6d8fd277719e6e0cbc62e58b572210e98741577"}}