{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GWLICXVP3LUQUURLF7SOWMXTZ6","short_pith_number":"pith:GWLICXVP","canonical_record":{"source":{"id":"1802.01515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-02-05T17:13:16Z","cross_cats_sorted":[],"title_canon_sha256":"bf96354289c1015ae6b38a70534d1a67e8e2d6c2e30a10a50c98e7492f0bbbc3","abstract_canon_sha256":"85b6f8b8e5ecfd69ec5aadaecb76c3446165e43b34878ab98a36961ad3db61b8"},"schema_version":"1.0"},"canonical_sha256":"3596815eafdae90a522b2fe4eb32f3cfbb994a3a1f68e301a75e813dcefb0d9c","source":{"kind":"arxiv","id":"1802.01515","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.01515","created_at":"2026-05-18T00:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"1802.01515v2","created_at":"2026-05-18T00:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01515","created_at":"2026-05-18T00:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"GWLICXVP3LUQ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GWLICXVP3LUQUURL","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GWLICXVP","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GWLICXVP3LUQUURLF7SOWMXTZ6","target":"record","payload":{"canonical_record":{"source":{"id":"1802.01515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-02-05T17:13:16Z","cross_cats_sorted":[],"title_canon_sha256":"bf96354289c1015ae6b38a70534d1a67e8e2d6c2e30a10a50c98e7492f0bbbc3","abstract_canon_sha256":"85b6f8b8e5ecfd69ec5aadaecb76c3446165e43b34878ab98a36961ad3db61b8"},"schema_version":"1.0"},"canonical_sha256":"3596815eafdae90a522b2fe4eb32f3cfbb994a3a1f68e301a75e813dcefb0d9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:59.576524Z","signature_b64":"+Pdp/FGfhURObt1LNs9jIinPm/WK9L1ls3iFWJ7WpkmGqBzBybE4nq6DJxmqBMUvPe+ffhuWaCxZOyaC/9k/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3596815eafdae90a522b2fe4eb32f3cfbb994a3a1f68e301a75e813dcefb0d9c","last_reissued_at":"2026-05-18T00:04:59.575868Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:59.575868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.01515","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"woMYl+V/ryUURaSRrCAS2pTJkpeBn/3lC/us1Qc24ectBrv97XrjnZ1emVKSdaHWTuDU6Heceed5rzU27Fz1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:48:41.642715Z"},"content_sha256":"b6e8563820ce34e09dd3d2366eb387295a2e632ddc788e83b72397d02bebf7b2","schema_version":"1.0","event_id":"sha256:b6e8563820ce34e09dd3d2366eb387295a2e632ddc788e83b72397d02bebf7b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GWLICXVP3LUQUURLF7SOWMXTZ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Robust Vertex Enumeration for Convex Hulls in High Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Bahman Kalantari, Pranjal Awasthi, Yikai Zhang","submitted_at":"2018-02-05T17:13:16Z","abstract_excerpt":"Computation of the vertices of the convex hull of a set $S$ of $n$ points in $\\mathbb{R} ^m$ is a fundamental problem in computational geometry, optimization, machine learning and more. We present \"All Vertex Triangle Algorithm\" (AVTA), a robust and efficient algorithm for computing the subset $\\overline S$ of all $K$ vertices of $conv(S)$, the convex hull of $S$. If $\\Gamma_*$ is the minimum of the distances from each vertex to the convex hull of the remaining vertices, given any $\\gamma \\leq \\gamma_* = \\Gamma_*/R$, $R$ the diameter of $S$, $AVTA$ computes $\\overline S$ in $O(nK(m+ \\gamma^{-2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01515","kind":"arxiv","version":2},"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":"2026-05-18T00:04:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MLHE40/llyqKaZCw9KwIb3kl7VlAj0fLDIeWhbvnUcZ9jJdMFnWSxns4qpCuGa7+j+gAYBikfGK/G/BeTLfIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:48:41.643359Z"},"content_sha256":"bad80783981ba2516b85335c21aa73e68b401d81df024faed2fd05f7c0ccabce","schema_version":"1.0","event_id":"sha256:bad80783981ba2516b85335c21aa73e68b401d81df024faed2fd05f7c0ccabce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GWLICXVP3LUQUURLF7SOWMXTZ6/bundle.json","state_url":"https://pith.science/pith/GWLICXVP3LUQUURLF7SOWMXTZ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GWLICXVP3LUQUURLF7SOWMXTZ6/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":"2026-05-30T16:48:41Z","links":{"resolver":"https://pith.science/pith/GWLICXVP3LUQUURLF7SOWMXTZ6","bundle":"https://pith.science/pith/GWLICXVP3LUQUURLF7SOWMXTZ6/bundle.json","state":"https://pith.science/pith/GWLICXVP3LUQUURLF7SOWMXTZ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GWLICXVP3LUQUURLF7SOWMXTZ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GWLICXVP3LUQUURLF7SOWMXTZ6","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":"85b6f8b8e5ecfd69ec5aadaecb76c3446165e43b34878ab98a36961ad3db61b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-02-05T17:13:16Z","title_canon_sha256":"bf96354289c1015ae6b38a70534d1a67e8e2d6c2e30a10a50c98e7492f0bbbc3"},"schema_version":"1.0","source":{"id":"1802.01515","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.01515","created_at":"2026-05-18T00:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"1802.01515v2","created_at":"2026-05-18T00:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01515","created_at":"2026-05-18T00:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"GWLICXVP3LUQ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GWLICXVP3LUQUURL","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GWLICXVP","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:bad80783981ba2516b85335c21aa73e68b401d81df024faed2fd05f7c0ccabce","target":"graph","created_at":"2026-05-18T00:04:59Z","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":"Computation of the vertices of the convex hull of a set $S$ of $n$ points in $\\mathbb{R} ^m$ is a fundamental problem in computational geometry, optimization, machine learning and more. We present \"All Vertex Triangle Algorithm\" (AVTA), a robust and efficient algorithm for computing the subset $\\overline S$ of all $K$ vertices of $conv(S)$, the convex hull of $S$. If $\\Gamma_*$ is the minimum of the distances from each vertex to the convex hull of the remaining vertices, given any $\\gamma \\leq \\gamma_* = \\Gamma_*/R$, $R$ the diameter of $S$, $AVTA$ computes $\\overline S$ in $O(nK(m+ \\gamma^{-2","authors_text":"Bahman Kalantari, Pranjal Awasthi, Yikai Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-02-05T17:13:16Z","title":"Robust Vertex Enumeration for Convex Hulls in High Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01515","kind":"arxiv","version":2},"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:b6e8563820ce34e09dd3d2366eb387295a2e632ddc788e83b72397d02bebf7b2","target":"record","created_at":"2026-05-18T00:04:59Z","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":"85b6f8b8e5ecfd69ec5aadaecb76c3446165e43b34878ab98a36961ad3db61b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-02-05T17:13:16Z","title_canon_sha256":"bf96354289c1015ae6b38a70534d1a67e8e2d6c2e30a10a50c98e7492f0bbbc3"},"schema_version":"1.0","source":{"id":"1802.01515","kind":"arxiv","version":2}},"canonical_sha256":"3596815eafdae90a522b2fe4eb32f3cfbb994a3a1f68e301a75e813dcefb0d9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3596815eafdae90a522b2fe4eb32f3cfbb994a3a1f68e301a75e813dcefb0d9c","first_computed_at":"2026-05-18T00:04:59.575868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:59.575868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+Pdp/FGfhURObt1LNs9jIinPm/WK9L1ls3iFWJ7WpkmGqBzBybE4nq6DJxmqBMUvPe+ffhuWaCxZOyaC/9k/BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:59.576524Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.01515","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6e8563820ce34e09dd3d2366eb387295a2e632ddc788e83b72397d02bebf7b2","sha256:bad80783981ba2516b85335c21aa73e68b401d81df024faed2fd05f7c0ccabce"],"state_sha256":"c1d12ad791940259a3c8643303c1783e653e10dcf1f8abd57d9d857f119677f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7d/ozeioLMPm8MoPRAAFl2DvkBUDdezRtbtkKQ1B8JETP9eIf8UgBM3qWR6HtonfrwQPtFJWjwX6p0cq1JsfDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:48:41.647120Z","bundle_sha256":"fca09f63ea864a75097090317108c49600a7c71f5c56987b4bb1d30a832ee86a"}}