{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Q7WIBOGRAOU5TARSU2H6P3GQ43","short_pith_number":"pith:Q7WIBOGR","canonical_record":{"source":{"id":"1809.00116","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-09-01T05:23:55Z","cross_cats_sorted":[],"title_canon_sha256":"230daea63218fab67b9807ed6a7d41774fefc0320aecbb530cf7050aa6f645ec","abstract_canon_sha256":"7c571fb14276e3cfcb9b51bcea35c2e74db944681741b0d773b7d5f9f4b41bd3"},"schema_version":"1.0"},"canonical_sha256":"87ec80b8d103a9d98232a68fe7ecd0e6de0af8efcbbee2817c90a7a5f5eab781","source":{"kind":"arxiv","id":"1809.00116","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00116","created_at":"2026-05-18T00:06:36Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00116v1","created_at":"2026-05-18T00:06:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00116","created_at":"2026-05-18T00:06:36Z"},{"alias_kind":"pith_short_12","alias_value":"Q7WIBOGRAOU5","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q7WIBOGRAOU5TARS","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q7WIBOGR","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Q7WIBOGRAOU5TARSU2H6P3GQ43","target":"record","payload":{"canonical_record":{"source":{"id":"1809.00116","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-09-01T05:23:55Z","cross_cats_sorted":[],"title_canon_sha256":"230daea63218fab67b9807ed6a7d41774fefc0320aecbb530cf7050aa6f645ec","abstract_canon_sha256":"7c571fb14276e3cfcb9b51bcea35c2e74db944681741b0d773b7d5f9f4b41bd3"},"schema_version":"1.0"},"canonical_sha256":"87ec80b8d103a9d98232a68fe7ecd0e6de0af8efcbbee2817c90a7a5f5eab781","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:36.066961Z","signature_b64":"0hyOwbROFopIc3F00spHGJgxQnq1wkq3p4PKqKveSzO+rEVEYrAjd68byjx9cnNPYp/WdsFWMZ0/Dsva0QTSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87ec80b8d103a9d98232a68fe7ecd0e6de0af8efcbbee2817c90a7a5f5eab781","last_reissued_at":"2026-05-18T00:06:36.066504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:36.066504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.00116","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":"2026-05-18T00:06:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZJag9EdXhVEAy4mbJY/3GEZqVZvSae2/1UqtzpOGJAQU8lfTZp41xfVxtfdVZs+s9wM/Qa/U7iO2DRAHU124Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T10:02:21.208529Z"},"content_sha256":"7f0d00a777bcc064defb9a3315e1f6c51c93232dffa762e93dd35a5ddaa02ad4","schema_version":"1.0","event_id":"sha256:7f0d00a777bcc064defb9a3315e1f6c51c93232dffa762e93dd35a5ddaa02ad4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Q7WIBOGRAOU5TARSU2H6P3GQ43","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Triangluar Separation of Bichromatic Point Sets in Polygonal Environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Farnaz Sheikhi, Sharareh Alipour","submitted_at":"2018-09-01T05:23:55Z","abstract_excerpt":"Let $\\mathcal P$ be a simple polygonal environment with $k$ vertices in the plane. Assume that a set $B$ of $b$ blue points and a set $R$ of $r$ red points are distributed in $\\mathcal P$. We study the problem of computing triangles that separate the sets $B$ and $R$, and fall in $\\mathcal P$. We call these triangles \\emph{inscribed triangular separators}. We propose an output-sensitive algorithm to solve this problem in $O(r \\cdot (r+c_B+k)+h_\\triangle)$ time, where $c_B$ is the size of convex hull of $B$, and $h_\\triangle$ is the number of inscribed triangular separators. We also study the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00116","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":"2026-05-18T00:06:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w5jzegSm+Ohe0FfI+1F8rJmVN390k4u7DKo3QuCi6cRRp8u9i2eyngWzChInR3zCS/YnPDML1ppV+cSg8BJADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T10:02:21.208865Z"},"content_sha256":"3846c0199a39da9b9834d53c696e6b6a67e9b69c2f8372748107efd47c213e2c","schema_version":"1.0","event_id":"sha256:3846c0199a39da9b9834d53c696e6b6a67e9b69c2f8372748107efd47c213e2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q7WIBOGRAOU5TARSU2H6P3GQ43/bundle.json","state_url":"https://pith.science/pith/Q7WIBOGRAOU5TARSU2H6P3GQ43/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q7WIBOGRAOU5TARSU2H6P3GQ43/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":"2026-06-08T10:02:21Z","links":{"resolver":"https://pith.science/pith/Q7WIBOGRAOU5TARSU2H6P3GQ43","bundle":"https://pith.science/pith/Q7WIBOGRAOU5TARSU2H6P3GQ43/bundle.json","state":"https://pith.science/pith/Q7WIBOGRAOU5TARSU2H6P3GQ43/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q7WIBOGRAOU5TARSU2H6P3GQ43/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Q7WIBOGRAOU5TARSU2H6P3GQ43","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":"7c571fb14276e3cfcb9b51bcea35c2e74db944681741b0d773b7d5f9f4b41bd3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-09-01T05:23:55Z","title_canon_sha256":"230daea63218fab67b9807ed6a7d41774fefc0320aecbb530cf7050aa6f645ec"},"schema_version":"1.0","source":{"id":"1809.00116","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00116","created_at":"2026-05-18T00:06:36Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00116v1","created_at":"2026-05-18T00:06:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00116","created_at":"2026-05-18T00:06:36Z"},{"alias_kind":"pith_short_12","alias_value":"Q7WIBOGRAOU5","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q7WIBOGRAOU5TARS","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q7WIBOGR","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:3846c0199a39da9b9834d53c696e6b6a67e9b69c2f8372748107efd47c213e2c","target":"graph","created_at":"2026-05-18T00:06:36Z","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 $\\mathcal P$ be a simple polygonal environment with $k$ vertices in the plane. Assume that a set $B$ of $b$ blue points and a set $R$ of $r$ red points are distributed in $\\mathcal P$. We study the problem of computing triangles that separate the sets $B$ and $R$, and fall in $\\mathcal P$. We call these triangles \\emph{inscribed triangular separators}. We propose an output-sensitive algorithm to solve this problem in $O(r \\cdot (r+c_B+k)+h_\\triangle)$ time, where $c_B$ is the size of convex hull of $B$, and $h_\\triangle$ is the number of inscribed triangular separators. We also study the c","authors_text":"Farnaz Sheikhi, Sharareh Alipour","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-09-01T05:23:55Z","title":"On Triangluar Separation of Bichromatic Point Sets in Polygonal Environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00116","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":"sha256:7f0d00a777bcc064defb9a3315e1f6c51c93232dffa762e93dd35a5ddaa02ad4","target":"record","created_at":"2026-05-18T00:06:36Z","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":"7c571fb14276e3cfcb9b51bcea35c2e74db944681741b0d773b7d5f9f4b41bd3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-09-01T05:23:55Z","title_canon_sha256":"230daea63218fab67b9807ed6a7d41774fefc0320aecbb530cf7050aa6f645ec"},"schema_version":"1.0","source":{"id":"1809.00116","kind":"arxiv","version":1}},"canonical_sha256":"87ec80b8d103a9d98232a68fe7ecd0e6de0af8efcbbee2817c90a7a5f5eab781","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87ec80b8d103a9d98232a68fe7ecd0e6de0af8efcbbee2817c90a7a5f5eab781","first_computed_at":"2026-05-18T00:06:36.066504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:36.066504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0hyOwbROFopIc3F00spHGJgxQnq1wkq3p4PKqKveSzO+rEVEYrAjd68byjx9cnNPYp/WdsFWMZ0/Dsva0QTSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:36.066961Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.00116","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f0d00a777bcc064defb9a3315e1f6c51c93232dffa762e93dd35a5ddaa02ad4","sha256:3846c0199a39da9b9834d53c696e6b6a67e9b69c2f8372748107efd47c213e2c"],"state_sha256":"22161f40c328fd07f741f05c0a80a67196005b8405efcce909f4df0e145738d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w5hu6avEhYZpAEdRkeA0rUqR55rFyJAMw/I1o4PQDD6jcaa8YBJ2Vum7f0jKN4sT6nuc/3M7SL7mlbo6DxvMBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T10:02:21.210782Z","bundle_sha256":"ebf6cac140bade3085af54602d65bdfa6a8dd1a29a5e7857a16028e072a47992"}}