{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4JPZC5ZXLANSUOZJEBOGGQPHSB","short_pith_number":"pith:4JPZC5ZX","canonical_record":{"source":{"id":"1312.1001","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-04T01:42:40Z","cross_cats_sorted":[],"title_canon_sha256":"bbb1a871ef69da62e8f01026a3e3bab09565ace1ef80eea1cbeccc680cb3f421","abstract_canon_sha256":"6ea8f96c01339400c874945ee6c19797704a34dc7f9e448bbac390553adc60a1"},"schema_version":"1.0"},"canonical_sha256":"e25f917737581b2a3b29205c6341e7907501c0ccf701df4e12996fb1ee52e9f3","source":{"kind":"arxiv","id":"1312.1001","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1001","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1001v4","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1001","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"4JPZC5ZXLANS","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4JPZC5ZXLANSUOZJ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4JPZC5ZX","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4JPZC5ZXLANSUOZJEBOGGQPHSB","target":"record","payload":{"canonical_record":{"source":{"id":"1312.1001","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-04T01:42:40Z","cross_cats_sorted":[],"title_canon_sha256":"bbb1a871ef69da62e8f01026a3e3bab09565ace1ef80eea1cbeccc680cb3f421","abstract_canon_sha256":"6ea8f96c01339400c874945ee6c19797704a34dc7f9e448bbac390553adc60a1"},"schema_version":"1.0"},"canonical_sha256":"e25f917737581b2a3b29205c6341e7907501c0ccf701df4e12996fb1ee52e9f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:09.895757Z","signature_b64":"rGatkKUT26mcYUzkKwsUkkvdEQXVxt6ZStOL3lgAwEAVRAFO486xfghJJWSYEXbfY5NDFlIhcYcU2jcdfoDDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e25f917737581b2a3b29205c6341e7907501c0ccf701df4e12996fb1ee52e9f3","last_reissued_at":"2026-05-18T00:23:09.895078Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:09.895078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.1001","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qrqRdvyVL018oDh6gn0YZArQbO19vLQoAyPJCKflWdmqiWJinqbJ0xFqtrVhWrjAjsfKJ14XtS+LcD4rc3epCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:26:40.217347Z"},"content_sha256":"f18b7d628f16b6177465115b4a2a99590d7c33c0234de43119da1d2d49d26d58","schema_version":"1.0","event_id":"sha256:f18b7d628f16b6177465115b4a2a99590d7c33c0234de43119da1d2d49d26d58"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4JPZC5ZXLANSUOZJEBOGGQPHSB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal detection of intersections between convex polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Luis Barba, Stefan Langerman","submitted_at":"2013-12-04T01:42:40Z","abstract_excerpt":"For a polyhedron $P$ in $\\mathbb{R}^d$, denote by $|P|$ its combinatorial complexity, i.e., the number of faces of all dimensions of the polyhedra. In this paper, we revisit the classic problem of preprocessing polyhedra independently so that given two preprocessed polyhedra $P$ and $Q$ in $\\mathbb{R}^d$, each translated and rotated, their intersection can be tested rapidly.\n  For $d=3$ we show how to perform such a test in $O(\\log |P| + \\log |Q|)$ time after linear preprocessing time and space. This running time is the best possible and improves upon the last best known query time of $O(\\log|"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1001","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ym3hMAO1i9lHZd9ulPv8c8JPHjgSuWvgY3xrVOln3G2EZ3YanlAygu6xJHRHR+AUvNCX4byfb4JJzERaxoOrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:26:40.217973Z"},"content_sha256":"ced733708ad0cdf6f72a28cf7b012eb9567173f2ab0f8b2ab2eee5720ec6f47c","schema_version":"1.0","event_id":"sha256:ced733708ad0cdf6f72a28cf7b012eb9567173f2ab0f8b2ab2eee5720ec6f47c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4JPZC5ZXLANSUOZJEBOGGQPHSB/bundle.json","state_url":"https://pith.science/pith/4JPZC5ZXLANSUOZJEBOGGQPHSB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4JPZC5ZXLANSUOZJEBOGGQPHSB/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":"2026-05-27T01:26:40Z","links":{"resolver":"https://pith.science/pith/4JPZC5ZXLANSUOZJEBOGGQPHSB","bundle":"https://pith.science/pith/4JPZC5ZXLANSUOZJEBOGGQPHSB/bundle.json","state":"https://pith.science/pith/4JPZC5ZXLANSUOZJEBOGGQPHSB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4JPZC5ZXLANSUOZJEBOGGQPHSB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4JPZC5ZXLANSUOZJEBOGGQPHSB","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":"6ea8f96c01339400c874945ee6c19797704a34dc7f9e448bbac390553adc60a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-04T01:42:40Z","title_canon_sha256":"bbb1a871ef69da62e8f01026a3e3bab09565ace1ef80eea1cbeccc680cb3f421"},"schema_version":"1.0","source":{"id":"1312.1001","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1001","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1001v4","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1001","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"4JPZC5ZXLANS","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4JPZC5ZXLANSUOZJ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4JPZC5ZX","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:ced733708ad0cdf6f72a28cf7b012eb9567173f2ab0f8b2ab2eee5720ec6f47c","target":"graph","created_at":"2026-05-18T00:23:09Z","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":"For a polyhedron $P$ in $\\mathbb{R}^d$, denote by $|P|$ its combinatorial complexity, i.e., the number of faces of all dimensions of the polyhedra. In this paper, we revisit the classic problem of preprocessing polyhedra independently so that given two preprocessed polyhedra $P$ and $Q$ in $\\mathbb{R}^d$, each translated and rotated, their intersection can be tested rapidly.\n  For $d=3$ we show how to perform such a test in $O(\\log |P| + \\log |Q|)$ time after linear preprocessing time and space. This running time is the best possible and improves upon the last best known query time of $O(\\log|","authors_text":"Luis Barba, Stefan Langerman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-04T01:42:40Z","title":"Optimal detection of intersections between convex polyhedra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1001","kind":"arxiv","version":4},"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:f18b7d628f16b6177465115b4a2a99590d7c33c0234de43119da1d2d49d26d58","target":"record","created_at":"2026-05-18T00:23:09Z","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":"6ea8f96c01339400c874945ee6c19797704a34dc7f9e448bbac390553adc60a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-04T01:42:40Z","title_canon_sha256":"bbb1a871ef69da62e8f01026a3e3bab09565ace1ef80eea1cbeccc680cb3f421"},"schema_version":"1.0","source":{"id":"1312.1001","kind":"arxiv","version":4}},"canonical_sha256":"e25f917737581b2a3b29205c6341e7907501c0ccf701df4e12996fb1ee52e9f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e25f917737581b2a3b29205c6341e7907501c0ccf701df4e12996fb1ee52e9f3","first_computed_at":"2026-05-18T00:23:09.895078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:09.895078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rGatkKUT26mcYUzkKwsUkkvdEQXVxt6ZStOL3lgAwEAVRAFO486xfghJJWSYEXbfY5NDFlIhcYcU2jcdfoDDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:09.895757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1001","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f18b7d628f16b6177465115b4a2a99590d7c33c0234de43119da1d2d49d26d58","sha256:ced733708ad0cdf6f72a28cf7b012eb9567173f2ab0f8b2ab2eee5720ec6f47c"],"state_sha256":"cbb59fd7670435d8d2897aad0366f9717bdd0603ffc9b1667ffefe7b037f73ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vHXR9kUAQu+2bycABZWkAroQERPiaxtmmzr/RLVIMTWpdSTP04HlwF20RNMsJrHZJgWH67Dp0fl1GjMsXbFzBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T01:26:40.220974Z","bundle_sha256":"cc22a5ea7933cc4407818964e1d64e20b63674567107004cf1cea8b32134d525"}}