{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CW4RAIPPGCC5QBPRXDF2SOMTOL","short_pith_number":"pith:CW4RAIPP","canonical_record":{"source":{"id":"1805.07373","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CG","submitted_at":"2018-05-18T18:09:19Z","cross_cats_sorted":[],"title_canon_sha256":"e5d379edecb19f58ddfe2d6f0ad8e2dfce4d3cd200d7b151f8261067e0b54689","abstract_canon_sha256":"0450594e5f6710d4b846efaf28540745b75342eabb06a7fc6ffff3196f75773e"},"schema_version":"1.0"},"canonical_sha256":"15b91021ef3085d805f1b8cba9399372edbab9b6375a77a4e0dc62bc188f60f1","source":{"kind":"arxiv","id":"1805.07373","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07373","created_at":"2026-05-18T00:15:35Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07373v1","created_at":"2026-05-18T00:15:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07373","created_at":"2026-05-18T00:15:35Z"},{"alias_kind":"pith_short_12","alias_value":"CW4RAIPPGCC5","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"CW4RAIPPGCC5QBPR","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"CW4RAIPP","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CW4RAIPPGCC5QBPRXDF2SOMTOL","target":"record","payload":{"canonical_record":{"source":{"id":"1805.07373","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CG","submitted_at":"2018-05-18T18:09:19Z","cross_cats_sorted":[],"title_canon_sha256":"e5d379edecb19f58ddfe2d6f0ad8e2dfce4d3cd200d7b151f8261067e0b54689","abstract_canon_sha256":"0450594e5f6710d4b846efaf28540745b75342eabb06a7fc6ffff3196f75773e"},"schema_version":"1.0"},"canonical_sha256":"15b91021ef3085d805f1b8cba9399372edbab9b6375a77a4e0dc62bc188f60f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:35.906550Z","signature_b64":"0f3eYccIiGLnBlJEBEzrNiFrSoSwypEzwiMKgaWOKuylxJGjUl+0YMlYPKa3r5AeqP4kWQbszA/TjwPoZW9/BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15b91021ef3085d805f1b8cba9399372edbab9b6375a77a4e0dc62bc188f60f1","last_reissued_at":"2026-05-18T00:15:35.905792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:35.905792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.07373","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":"2026-05-18T00:15:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SrvvklTyJpsjAX64xRSwNglDh/JNiTM6IGAVeG1vGMDRIh1ZaBzRUnnpXG5/6WVsZJ1oXG4XLSxLd2K/sKvtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:39:06.626275Z"},"content_sha256":"5a99d770f61b93bdaa439bf00af6aca2f6407beb2af381aa83ea6a7b6bbe9ef0","schema_version":"1.0","event_id":"sha256:5a99d770f61b93bdaa439bf00af6aca2f6407beb2af381aa83ea6a7b6bbe9ef0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CW4RAIPPGCC5QBPRXDF2SOMTOL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate Data Depth Revisited","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"David Bremner, Rasoul Shahsavarifar","submitted_at":"2018-05-18T18:09:19Z","abstract_excerpt":"Halfspace depth and $\\beta$-skeleton depth are two types of depth functions in nonparametric data analysis. The halfspace depth of a query point $q\\in \\mathbb{R}^d$ with respect to $S\\subset\\mathbb{R}^d$ is the minimum portion of the elements of $S$ which are contained in a halfspace which passes through $q$. For $\\beta \\geq 1$, the $\\beta$-skeleton depth of $q$ with respect to $S$ is defined to be the total number of \\emph{$\\beta$-skeleton influence regions} that contain $q$, where each of these influence regions is the intersection of two hyperballs obtained from a pair of points in $S$. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07373","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":"2026-05-18T00:15:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S+e3y31ahqtWYepYRYHKyb+rTgrfp8piX+PPJpVcq58WsqUYy6P9PqIv1UuC6FTKckDhsK/PQdRP3knGUxxMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:39:06.626920Z"},"content_sha256":"b100f49c84267b11513744a3c3f8e432a13911355c7459ee5812ff67195a08fc","schema_version":"1.0","event_id":"sha256:b100f49c84267b11513744a3c3f8e432a13911355c7459ee5812ff67195a08fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL/bundle.json","state_url":"https://pith.science/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL/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":"2026-06-06T06:39:06Z","links":{"resolver":"https://pith.science/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL","bundle":"https://pith.science/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL/bundle.json","state":"https://pith.science/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CW4RAIPPGCC5QBPRXDF2SOMTOL","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":"0450594e5f6710d4b846efaf28540745b75342eabb06a7fc6ffff3196f75773e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CG","submitted_at":"2018-05-18T18:09:19Z","title_canon_sha256":"e5d379edecb19f58ddfe2d6f0ad8e2dfce4d3cd200d7b151f8261067e0b54689"},"schema_version":"1.0","source":{"id":"1805.07373","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07373","created_at":"2026-05-18T00:15:35Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07373v1","created_at":"2026-05-18T00:15:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07373","created_at":"2026-05-18T00:15:35Z"},{"alias_kind":"pith_short_12","alias_value":"CW4RAIPPGCC5","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"CW4RAIPPGCC5QBPR","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"CW4RAIPP","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:b100f49c84267b11513744a3c3f8e432a13911355c7459ee5812ff67195a08fc","target":"graph","created_at":"2026-05-18T00:15:35Z","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":"Halfspace depth and $\\beta$-skeleton depth are two types of depth functions in nonparametric data analysis. The halfspace depth of a query point $q\\in \\mathbb{R}^d$ with respect to $S\\subset\\mathbb{R}^d$ is the minimum portion of the elements of $S$ which are contained in a halfspace which passes through $q$. For $\\beta \\geq 1$, the $\\beta$-skeleton depth of $q$ with respect to $S$ is defined to be the total number of \\emph{$\\beta$-skeleton influence regions} that contain $q$, where each of these influence regions is the intersection of two hyperballs obtained from a pair of points in $S$. The","authors_text":"David Bremner, Rasoul Shahsavarifar","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CG","submitted_at":"2018-05-18T18:09:19Z","title":"Approximate Data Depth Revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07373","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":"sha256:5a99d770f61b93bdaa439bf00af6aca2f6407beb2af381aa83ea6a7b6bbe9ef0","target":"record","created_at":"2026-05-18T00:15:35Z","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":"0450594e5f6710d4b846efaf28540745b75342eabb06a7fc6ffff3196f75773e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CG","submitted_at":"2018-05-18T18:09:19Z","title_canon_sha256":"e5d379edecb19f58ddfe2d6f0ad8e2dfce4d3cd200d7b151f8261067e0b54689"},"schema_version":"1.0","source":{"id":"1805.07373","kind":"arxiv","version":1}},"canonical_sha256":"15b91021ef3085d805f1b8cba9399372edbab9b6375a77a4e0dc62bc188f60f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15b91021ef3085d805f1b8cba9399372edbab9b6375a77a4e0dc62bc188f60f1","first_computed_at":"2026-05-18T00:15:35.905792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:35.905792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0f3eYccIiGLnBlJEBEzrNiFrSoSwypEzwiMKgaWOKuylxJGjUl+0YMlYPKa3r5AeqP4kWQbszA/TjwPoZW9/BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:35.906550Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07373","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a99d770f61b93bdaa439bf00af6aca2f6407beb2af381aa83ea6a7b6bbe9ef0","sha256:b100f49c84267b11513744a3c3f8e432a13911355c7459ee5812ff67195a08fc"],"state_sha256":"a4a54068540b10a67bb4ef24911cf2e9be5656e1f342b70eb15e22412b9fbbd4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aQs6WGjXGv3wVhbqIgBUql8Wd68B9RqqMDx62HCFk0HGiA5cUgArl+BzQC6h6LMmh8iCoDWYGg3hAgkc+bfBDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T06:39:06.629894Z","bundle_sha256":"518f7ad9e3b27e7c0a0e6f016232662e8480f5d627397bb9382b2ebcde1c83d3"}}