{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:U4J3ISFLRP7BR6NTL3DOGWC5SJ","short_pith_number":"pith:U4J3ISFL","canonical_record":{"source":{"id":"1804.11295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-04-30T16:16:06Z","cross_cats_sorted":[],"title_canon_sha256":"3222ecd818ba5e7ea2b338600e4c291cbaf1347066787409747e8b91d7910260","abstract_canon_sha256":"cb97f77e673de96c009098835ff88c8c5b3bccc9ecc7a5aef9383e7427aa3d0c"},"schema_version":"1.0"},"canonical_sha256":"a713b448ab8bfe18f9b35ec6e3585d927f8cca810c7df525a94a64286284a646","source":{"kind":"arxiv","id":"1804.11295","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.11295","created_at":"2026-05-18T00:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"1804.11295v1","created_at":"2026-05-18T00:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.11295","created_at":"2026-05-18T00:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"U4J3ISFLRP7B","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U4J3ISFLRP7BR6NT","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U4J3ISFL","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:U4J3ISFLRP7BR6NTL3DOGWC5SJ","target":"record","payload":{"canonical_record":{"source":{"id":"1804.11295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-04-30T16:16:06Z","cross_cats_sorted":[],"title_canon_sha256":"3222ecd818ba5e7ea2b338600e4c291cbaf1347066787409747e8b91d7910260","abstract_canon_sha256":"cb97f77e673de96c009098835ff88c8c5b3bccc9ecc7a5aef9383e7427aa3d0c"},"schema_version":"1.0"},"canonical_sha256":"a713b448ab8bfe18f9b35ec6e3585d927f8cca810c7df525a94a64286284a646","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:14.044740Z","signature_b64":"qK6K5Sv81EZUonRJ4F3jOveGjNuHDhLDBtGL6x+bCMJzbBFuj0jtdDslL+cVKqpSvmwYpSJd3Hgiqtx3rebMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a713b448ab8bfe18f9b35ec6e3585d927f8cca810c7df525a94a64286284a646","last_reissued_at":"2026-05-18T00:17:14.044210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:14.044210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.11295","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":"2026-05-18T00:17:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g9Wqkexe5baxqwmykgF17HBSxI80Ag3dt5nQaSkTnENYqwIBAfjaxSu0wkhgTqqsSdL+0Sp6jwTRV3TeCdgnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:44:38.262172Z"},"content_sha256":"d9ed17d322f950f300db4222cfd0639296b5a0950df8b8999e24baf95259df7a","schema_version":"1.0","event_id":"sha256:d9ed17d322f950f300db4222cfd0639296b5a0950df8b8999e24baf95259df7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:U4J3ISFLRP7BR6NTL3DOGWC5SJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algorithms for Deciding Membership in Polytopes of General Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Evangelos Anagnostopoulos, Ioannis Z. Emiris, Vissarion Fisikopoulos","submitted_at":"2018-04-30T16:16:06Z","abstract_excerpt":"We study the fundamental problem of polytope membership aiming at large convex polytopes, i.e. in high dimension and with many facets, given as an intersection of halfspaces. Standard data-structures as well as brute force methods cannot scale, due to the curse of dimen- sionality. We design an efficient algorithm, by reduction to the approx- imate Nearest Neighbor (ANN) problem based on the construction of a Voronoi diagram with the polytope being one bounded cell. We thus trade exactness for efficiency so as to obtain complexity bounds polyno- mial in the dimension, by exploiting recent prog"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11295","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":"2026-05-18T00:17:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SATs3eqmuMh+IctQ249A25YukS5m9A6f/gzAaBXhfNWfpF19kfZPGaJPRKsmf2xoLy4fYoPCOsKCXE15SSR7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:44:38.262781Z"},"content_sha256":"5ec3618db422f287d1cd34981a77f0605dfb0a106c59ac5804f8748eed16df76","schema_version":"1.0","event_id":"sha256:5ec3618db422f287d1cd34981a77f0605dfb0a106c59ac5804f8748eed16df76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4J3ISFLRP7BR6NTL3DOGWC5SJ/bundle.json","state_url":"https://pith.science/pith/U4J3ISFLRP7BR6NTL3DOGWC5SJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4J3ISFLRP7BR6NTL3DOGWC5SJ/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":"2026-06-11T01:44:38Z","links":{"resolver":"https://pith.science/pith/U4J3ISFLRP7BR6NTL3DOGWC5SJ","bundle":"https://pith.science/pith/U4J3ISFLRP7BR6NTL3DOGWC5SJ/bundle.json","state":"https://pith.science/pith/U4J3ISFLRP7BR6NTL3DOGWC5SJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4J3ISFLRP7BR6NTL3DOGWC5SJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U4J3ISFLRP7BR6NTL3DOGWC5SJ","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":"cb97f77e673de96c009098835ff88c8c5b3bccc9ecc7a5aef9383e7427aa3d0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-04-30T16:16:06Z","title_canon_sha256":"3222ecd818ba5e7ea2b338600e4c291cbaf1347066787409747e8b91d7910260"},"schema_version":"1.0","source":{"id":"1804.11295","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.11295","created_at":"2026-05-18T00:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"1804.11295v1","created_at":"2026-05-18T00:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.11295","created_at":"2026-05-18T00:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"U4J3ISFLRP7B","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U4J3ISFLRP7BR6NT","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U4J3ISFL","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:5ec3618db422f287d1cd34981a77f0605dfb0a106c59ac5804f8748eed16df76","target":"graph","created_at":"2026-05-18T00:17:14Z","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 fundamental problem of polytope membership aiming at large convex polytopes, i.e. in high dimension and with many facets, given as an intersection of halfspaces. Standard data-structures as well as brute force methods cannot scale, due to the curse of dimen- sionality. We design an efficient algorithm, by reduction to the approx- imate Nearest Neighbor (ANN) problem based on the construction of a Voronoi diagram with the polytope being one bounded cell. We thus trade exactness for efficiency so as to obtain complexity bounds polyno- mial in the dimension, by exploiting recent prog","authors_text":"Evangelos Anagnostopoulos, Ioannis Z. Emiris, Vissarion Fisikopoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-04-30T16:16:06Z","title":"Algorithms for Deciding Membership in Polytopes of General Dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11295","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:d9ed17d322f950f300db4222cfd0639296b5a0950df8b8999e24baf95259df7a","target":"record","created_at":"2026-05-18T00:17:14Z","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":"cb97f77e673de96c009098835ff88c8c5b3bccc9ecc7a5aef9383e7427aa3d0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-04-30T16:16:06Z","title_canon_sha256":"3222ecd818ba5e7ea2b338600e4c291cbaf1347066787409747e8b91d7910260"},"schema_version":"1.0","source":{"id":"1804.11295","kind":"arxiv","version":1}},"canonical_sha256":"a713b448ab8bfe18f9b35ec6e3585d927f8cca810c7df525a94a64286284a646","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a713b448ab8bfe18f9b35ec6e3585d927f8cca810c7df525a94a64286284a646","first_computed_at":"2026-05-18T00:17:14.044210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:14.044210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qK6K5Sv81EZUonRJ4F3jOveGjNuHDhLDBtGL6x+bCMJzbBFuj0jtdDslL+cVKqpSvmwYpSJd3Hgiqtx3rebMBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:14.044740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.11295","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9ed17d322f950f300db4222cfd0639296b5a0950df8b8999e24baf95259df7a","sha256:5ec3618db422f287d1cd34981a77f0605dfb0a106c59ac5804f8748eed16df76"],"state_sha256":"f7bc3ff1d2a9f24c905a752ae965d3ccb9e4a71112ef786199d5bd11b479ca8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vo1RcbXN2nuYkw6VQE8JmlzgoGKUdKzKhHLBJF1r+Q6ZgeVsNAfH1mfoZ0lNz0N9fISuTC7viGgAgc62Tvk0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T01:44:38.266290Z","bundle_sha256":"d2c969e42d900e771e5e6423bf0308045346e0262126c2d951580c7761639c8a"}}