{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FIBAEKNUB2D3UOSYC7C5UJRQ47","short_pith_number":"pith:FIBAEKNU","canonical_record":{"source":{"id":"1511.00628","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2015-11-02T18:54:49Z","cross_cats_sorted":["cs.CG","cs.DS"],"title_canon_sha256":"ba7db9c058ce23d33048509df775a078f2851611b42b18af03726de7a3d39ac3","abstract_canon_sha256":"bad9f45d92ca46f42130d64ea43349c2d7d0ea7bd3b99664aaa3647e3b13685c"},"schema_version":"1.0"},"canonical_sha256":"2a020229b40e87ba3a5817c5da2630e7f24c7a516f4454c42ee1299a83396882","source":{"kind":"arxiv","id":"1511.00628","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00628","created_at":"2026-05-18T01:28:11Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00628v1","created_at":"2026-05-18T01:28:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00628","created_at":"2026-05-18T01:28:11Z"},{"alias_kind":"pith_short_12","alias_value":"FIBAEKNUB2D3","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FIBAEKNUB2D3UOSY","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FIBAEKNU","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FIBAEKNUB2D3UOSYC7C5UJRQ47","target":"record","payload":{"canonical_record":{"source":{"id":"1511.00628","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2015-11-02T18:54:49Z","cross_cats_sorted":["cs.CG","cs.DS"],"title_canon_sha256":"ba7db9c058ce23d33048509df775a078f2851611b42b18af03726de7a3d39ac3","abstract_canon_sha256":"bad9f45d92ca46f42130d64ea43349c2d7d0ea7bd3b99664aaa3647e3b13685c"},"schema_version":"1.0"},"canonical_sha256":"2a020229b40e87ba3a5817c5da2630e7f24c7a516f4454c42ee1299a83396882","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:11.780263Z","signature_b64":"Tv9sn+hvS5lCrHtIthc6PyFSRd3IDmzLU1ZuDGC5+iEd20v7F7GsyQFOHoyh6l4Jm3/S6GvIKrNSQE8X4x/PAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a020229b40e87ba3a5817c5da2630e7f24c7a516f4454c42ee1299a83396882","last_reissued_at":"2026-05-18T01:28:11.779601Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:11.779601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.00628","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":"2026-05-18T01:28:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TO1vnuycgUuJAPKSVEZwaSObWPLRJcExZWpZ5BeCQAh/sxNVc2Eos+kdw/jCoIZ5L1jBxPFpznIdJKW/oL12CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T10:57:59.827483Z"},"content_sha256":"7b1f5b0db364332b81a365b0c5552318d2748307c6b003f8191f482b608fa200","schema_version":"1.0","event_id":"sha256:7b1f5b0db364332b81a365b0c5552318d2748307c6b003f8191f482b608fa200"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FIBAEKNUB2D3UOSYC7C5UJRQ47","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ball*-tree: Efficient spatial indexing for constrained nearest-neighbor search in metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.DS"],"primary_cat":"cs.DB","authors_text":"Ali Hadian, Behrouz Minaei-Bidgoli, Mohamad Dolatshah","submitted_at":"2015-11-02T18:54:49Z","abstract_excerpt":"Emerging location-based systems and data analysis frameworks requires efficient management of spatial data for approximate and exact search. Exact similarity search can be done using space partitioning data structures, such as Kd-tree, R*-tree, and Ball-tree. In this paper, we focus on Ball-tree, an efficient search tree that is specific for spatial queries which use euclidean distance. Each node of a Ball-tree defines a ball, i.e. a hypersphere that contains a subset of the points to be searched.\n  In this paper, we propose Ball*-tree, an improved Ball-tree that is more efficient for spatial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00628","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":"2026-05-18T01:28:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gaKQPuvv37fiEPG5Q9P+7foSWI5ciFhh8t6A13YNz5Hw71GOG0LT3EaAScOy1N6GCwJD40U5SKOKiAK1YNJ2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T10:57:59.827838Z"},"content_sha256":"2944a5f06f016e9266a829a19bb5ef327b09fbdd90bf20c45ec0a83ae43684bd","schema_version":"1.0","event_id":"sha256:2944a5f06f016e9266a829a19bb5ef327b09fbdd90bf20c45ec0a83ae43684bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FIBAEKNUB2D3UOSYC7C5UJRQ47/bundle.json","state_url":"https://pith.science/pith/FIBAEKNUB2D3UOSYC7C5UJRQ47/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FIBAEKNUB2D3UOSYC7C5UJRQ47/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":"2026-07-01T10:57:59Z","links":{"resolver":"https://pith.science/pith/FIBAEKNUB2D3UOSYC7C5UJRQ47","bundle":"https://pith.science/pith/FIBAEKNUB2D3UOSYC7C5UJRQ47/bundle.json","state":"https://pith.science/pith/FIBAEKNUB2D3UOSYC7C5UJRQ47/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FIBAEKNUB2D3UOSYC7C5UJRQ47/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FIBAEKNUB2D3UOSYC7C5UJRQ47","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":"bad9f45d92ca46f42130d64ea43349c2d7d0ea7bd3b99664aaa3647e3b13685c","cross_cats_sorted":["cs.CG","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2015-11-02T18:54:49Z","title_canon_sha256":"ba7db9c058ce23d33048509df775a078f2851611b42b18af03726de7a3d39ac3"},"schema_version":"1.0","source":{"id":"1511.00628","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00628","created_at":"2026-05-18T01:28:11Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00628v1","created_at":"2026-05-18T01:28:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00628","created_at":"2026-05-18T01:28:11Z"},{"alias_kind":"pith_short_12","alias_value":"FIBAEKNUB2D3","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FIBAEKNUB2D3UOSY","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FIBAEKNU","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:2944a5f06f016e9266a829a19bb5ef327b09fbdd90bf20c45ec0a83ae43684bd","target":"graph","created_at":"2026-05-18T01:28:11Z","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":"Emerging location-based systems and data analysis frameworks requires efficient management of spatial data for approximate and exact search. Exact similarity search can be done using space partitioning data structures, such as Kd-tree, R*-tree, and Ball-tree. In this paper, we focus on Ball-tree, an efficient search tree that is specific for spatial queries which use euclidean distance. Each node of a Ball-tree defines a ball, i.e. a hypersphere that contains a subset of the points to be searched.\n  In this paper, we propose Ball*-tree, an improved Ball-tree that is more efficient for spatial ","authors_text":"Ali Hadian, Behrouz Minaei-Bidgoli, Mohamad Dolatshah","cross_cats":["cs.CG","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2015-11-02T18:54:49Z","title":"Ball*-tree: Efficient spatial indexing for constrained nearest-neighbor search in metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00628","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":"sha256:7b1f5b0db364332b81a365b0c5552318d2748307c6b003f8191f482b608fa200","target":"record","created_at":"2026-05-18T01:28:11Z","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":"bad9f45d92ca46f42130d64ea43349c2d7d0ea7bd3b99664aaa3647e3b13685c","cross_cats_sorted":["cs.CG","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2015-11-02T18:54:49Z","title_canon_sha256":"ba7db9c058ce23d33048509df775a078f2851611b42b18af03726de7a3d39ac3"},"schema_version":"1.0","source":{"id":"1511.00628","kind":"arxiv","version":1}},"canonical_sha256":"2a020229b40e87ba3a5817c5da2630e7f24c7a516f4454c42ee1299a83396882","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a020229b40e87ba3a5817c5da2630e7f24c7a516f4454c42ee1299a83396882","first_computed_at":"2026-05-18T01:28:11.779601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:11.779601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tv9sn+hvS5lCrHtIthc6PyFSRd3IDmzLU1ZuDGC5+iEd20v7F7GsyQFOHoyh6l4Jm3/S6GvIKrNSQE8X4x/PAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:11.780263Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.00628","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b1f5b0db364332b81a365b0c5552318d2748307c6b003f8191f482b608fa200","sha256:2944a5f06f016e9266a829a19bb5ef327b09fbdd90bf20c45ec0a83ae43684bd"],"state_sha256":"317bbf52b069f2c1ee9fc29fd7c50d294f9dd9096d6a5b14dd09172678d025a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bttI1N0sqEZyTEWBd2aBll/7BefhvoQ11EjtXJLnrNS06SNgb8vtZKPR/Sf85KRo1KWdvQpFB81Y1z0aKo9tAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T10:57:59.829881Z","bundle_sha256":"b07cb20e37a6eeeadc8a4957a1dda397ac4722e44d1ddd37192d1be281de8494"}}