{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SFA2JCKBXF6QFCXIV43GWFMFSN","short_pith_number":"pith:SFA2JCKB","canonical_record":{"source":{"id":"1211.0729","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-11-04T22:38:11Z","cross_cats_sorted":["cs.CG","cs.GR"],"title_canon_sha256":"38d7f5aa607d45a9bb861a8a4716c65256c8790ab587a198fe6bfdebaf493fa9","abstract_canon_sha256":"0d24a46726fcd044a513b9c9933dd844070fd7d68393feefd866d6c8f154b77d"},"schema_version":"1.0"},"canonical_sha256":"9141a48941b97d028ae8af366b158593426b7e9434a8358dfa1a50c34caaac62","source":{"kind":"arxiv","id":"1211.0729","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0729","created_at":"2026-05-18T00:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0729v8","created_at":"2026-05-18T00:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0729","created_at":"2026-05-18T00:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"SFA2JCKBXF6Q","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SFA2JCKBXF6QFCXI","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SFA2JCKB","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SFA2JCKBXF6QFCXIV43GWFMFSN","target":"record","payload":{"canonical_record":{"source":{"id":"1211.0729","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-11-04T22:38:11Z","cross_cats_sorted":["cs.CG","cs.GR"],"title_canon_sha256":"38d7f5aa607d45a9bb861a8a4716c65256c8790ab587a198fe6bfdebaf493fa9","abstract_canon_sha256":"0d24a46726fcd044a513b9c9933dd844070fd7d68393feefd866d6c8f154b77d"},"schema_version":"1.0"},"canonical_sha256":"9141a48941b97d028ae8af366b158593426b7e9434a8358dfa1a50c34caaac62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:51.272671Z","signature_b64":"Ik8MBrgC2BY0Qyk+/TU5X1f7HBinBr8319sBJlR2SneptpLW1W/cIL3JtbrCnqJ73/7aurW/qqJ/bLFmw9z5DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9141a48941b97d028ae8af366b158593426b7e9434a8358dfa1a50c34caaac62","last_reissued_at":"2026-05-18T00:11:51.271996Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:51.271996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.0729","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KACEz9Ul+InDnyMv8+Nl0Sx7v5kqk01cVWMnpc5J93A70KyNiR2HifI/AJflYvGCmZCWM6wmQYC3+wlGLV+yDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:27:06.794833Z"},"content_sha256":"e101b0e973d15e4295bbf38a1cb7ef40039076c3888feac4742bf5da6ba00b80","schema_version":"1.0","event_id":"sha256:e101b0e973d15e4295bbf38a1cb7ef40039076c3888feac4742bf5da6ba00b80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SFA2JCKBXF6QFCXIV43GWFMFSN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Simple Algorithm for Computing BOCP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.GR"],"primary_cat":"cs.DS","authors_text":"Jack Wang","submitted_at":"2012-11-04T22:38:11Z","abstract_excerpt":"In this article, we devise a concise algorithm for computing BOCP. Our method is simple, easy-to-implement but without loss of efficiency. Given two circular-arc polygons with $m$ and $n$ edges respectively, our method runs in $O(m+n+(l+k)\\log l)$ time, using $O(m+n+k)$ space, where $k$ is the number of intersections, and $l$ is the number of {edge}s. Our algorithm has the power to approximate to linear complexity when $k$ and $l$ are small. The superiority of the proposed algorithm is also validated through empirical study."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0729","kind":"arxiv","version":8},"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":"2026-05-18T00:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RaV7dEq8eeKiQ8zAmy87VfGTVlkek+W+A26TjEC+X2BeriZRN3y/MlZYLOPsCjFqRe6OYjm54AVs7YqYs02lCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:27:06.795175Z"},"content_sha256":"dea1a68bb7294c3a057d463d31bc4230ca6b35d09930039c586995aa99142073","schema_version":"1.0","event_id":"sha256:dea1a68bb7294c3a057d463d31bc4230ca6b35d09930039c586995aa99142073"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SFA2JCKBXF6QFCXIV43GWFMFSN/bundle.json","state_url":"https://pith.science/pith/SFA2JCKBXF6QFCXIV43GWFMFSN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SFA2JCKBXF6QFCXIV43GWFMFSN/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":"2026-06-25T10:27:06Z","links":{"resolver":"https://pith.science/pith/SFA2JCKBXF6QFCXIV43GWFMFSN","bundle":"https://pith.science/pith/SFA2JCKBXF6QFCXIV43GWFMFSN/bundle.json","state":"https://pith.science/pith/SFA2JCKBXF6QFCXIV43GWFMFSN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SFA2JCKBXF6QFCXIV43GWFMFSN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SFA2JCKBXF6QFCXIV43GWFMFSN","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":"0d24a46726fcd044a513b9c9933dd844070fd7d68393feefd866d6c8f154b77d","cross_cats_sorted":["cs.CG","cs.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-11-04T22:38:11Z","title_canon_sha256":"38d7f5aa607d45a9bb861a8a4716c65256c8790ab587a198fe6bfdebaf493fa9"},"schema_version":"1.0","source":{"id":"1211.0729","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0729","created_at":"2026-05-18T00:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0729v8","created_at":"2026-05-18T00:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0729","created_at":"2026-05-18T00:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"SFA2JCKBXF6Q","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SFA2JCKBXF6QFCXI","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SFA2JCKB","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:dea1a68bb7294c3a057d463d31bc4230ca6b35d09930039c586995aa99142073","target":"graph","created_at":"2026-05-18T00:11:51Z","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":"In this article, we devise a concise algorithm for computing BOCP. Our method is simple, easy-to-implement but without loss of efficiency. Given two circular-arc polygons with $m$ and $n$ edges respectively, our method runs in $O(m+n+(l+k)\\log l)$ time, using $O(m+n+k)$ space, where $k$ is the number of intersections, and $l$ is the number of {edge}s. Our algorithm has the power to approximate to linear complexity when $k$ and $l$ are small. The superiority of the proposed algorithm is also validated through empirical study.","authors_text":"Jack Wang","cross_cats":["cs.CG","cs.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-11-04T22:38:11Z","title":"A Simple Algorithm for Computing BOCP"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0729","kind":"arxiv","version":8},"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:e101b0e973d15e4295bbf38a1cb7ef40039076c3888feac4742bf5da6ba00b80","target":"record","created_at":"2026-05-18T00:11:51Z","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":"0d24a46726fcd044a513b9c9933dd844070fd7d68393feefd866d6c8f154b77d","cross_cats_sorted":["cs.CG","cs.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-11-04T22:38:11Z","title_canon_sha256":"38d7f5aa607d45a9bb861a8a4716c65256c8790ab587a198fe6bfdebaf493fa9"},"schema_version":"1.0","source":{"id":"1211.0729","kind":"arxiv","version":8}},"canonical_sha256":"9141a48941b97d028ae8af366b158593426b7e9434a8358dfa1a50c34caaac62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9141a48941b97d028ae8af366b158593426b7e9434a8358dfa1a50c34caaac62","first_computed_at":"2026-05-18T00:11:51.271996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:51.271996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ik8MBrgC2BY0Qyk+/TU5X1f7HBinBr8319sBJlR2SneptpLW1W/cIL3JtbrCnqJ73/7aurW/qqJ/bLFmw9z5DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:51.272671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0729","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e101b0e973d15e4295bbf38a1cb7ef40039076c3888feac4742bf5da6ba00b80","sha256:dea1a68bb7294c3a057d463d31bc4230ca6b35d09930039c586995aa99142073"],"state_sha256":"abccc17c24b546e1b4a4f676ca0769121ef2d1c6333e79bf4a8704d5f94e1506"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4GdqAGBOVUjxBL7ma8Rj8OUTCCl1PVhcD1tY+9gmE/1DtR6E1tn59IzShCxEsTXMJGK7jMVX5wQqz9+WF96TAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T10:27:06.797130Z","bundle_sha256":"a5751575b31e79260e931ed4c03b0abad09c26148250e7d7f14f3a04dfde57b7"}}