{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:R227Q7GLUWHSTERDHIFVJFU5SI","short_pith_number":"pith:R227Q7GL","canonical_record":{"source":{"id":"1109.0312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-09-01T21:57:42Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"e2aeff502a70a42596a0b5ad971888c15750f51c65f91a928168dbc3375675f0","abstract_canon_sha256":"70ffd29b104da9f86b7ac4ca31769c986036456b157c51b7ec1e298b91a1d98e"},"schema_version":"1.0"},"canonical_sha256":"8eb5f87ccba58f2992233a0b54969d9218d0537413163a1ee4bb687b72b3af93","source":{"kind":"arxiv","id":"1109.0312","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0312","created_at":"2026-05-18T04:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0312v1","created_at":"2026-05-18T04:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0312","created_at":"2026-05-18T04:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"R227Q7GLUWHS","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"R227Q7GLUWHSTERD","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"R227Q7GL","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:R227Q7GLUWHSTERDHIFVJFU5SI","target":"record","payload":{"canonical_record":{"source":{"id":"1109.0312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-09-01T21:57:42Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"e2aeff502a70a42596a0b5ad971888c15750f51c65f91a928168dbc3375675f0","abstract_canon_sha256":"70ffd29b104da9f86b7ac4ca31769c986036456b157c51b7ec1e298b91a1d98e"},"schema_version":"1.0"},"canonical_sha256":"8eb5f87ccba58f2992233a0b54969d9218d0537413163a1ee4bb687b72b3af93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:16.058117Z","signature_b64":"Vx8z+4gIpYPuloXJoPovXQokEWDKoiOi6lBUQOMHqZaYjBtCc/ZaK+agEabTw3KTDU+NynDIyalcSzzapvAEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8eb5f87ccba58f2992233a0b54969d9218d0537413163a1ee4bb687b72b3af93","last_reissued_at":"2026-05-18T04:14:16.057513Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:16.057513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.0312","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":"2026-05-18T04:14:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wrro8wL4gkXfwIF9YIgFKnXdmEhoepHHMOhfrEc5X5Y37DdKONh46Reb4c+UUH3NUUwOngkocbCGhmaTmQ4BCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:25:02.732900Z"},"content_sha256":"8f3c9d40480ffd87e3477a781bfed498ccb80ba5317587ec4c1d3912497dfbbd","schema_version":"1.0","event_id":"sha256:8f3c9d40480ffd87e3477a781bfed498ccb80ba5317587ec4c1d3912497dfbbd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:R227Q7GLUWHSTERDHIFVJFU5SI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fully Retroactive Approximate Range and Nearest Neighbor Searching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Joseph A. Simons, Michael T. Goodrich","submitted_at":"2011-09-01T21:57:42Z","abstract_excerpt":"We describe fully retroactive dynamic data structures for approximate range reporting and approximate nearest neighbor reporting. We show how to maintain, for any positive constant $d$, a set of $n$ points in $\\R^d$ indexed by time such that we can perform insertions or deletions at any point in the timeline in $O(\\log n)$ amortized time. We support, for any small constant $\\epsilon>0$, $(1+\\epsilon)$-approximate range reporting queries at any point in the timeline in $O(\\log n + k)$ time, where $k$ is the output size. We also show how to answer $(1+\\epsilon)$-approximate nearest neighbor quer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0312","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":"2026-05-18T04:14:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S/XuQkAEpszVVWi6wpjeIdCuzs3dd5h3JW+80WtyOcANsISkMFTP6W/CO2WG1u/+zt2zvwxLrv73UkCu18WYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:25:02.733284Z"},"content_sha256":"ab4713ad61c8db1befe4fcdcfa7d78d344d50335fe28e9e7d171649e6f4984a6","schema_version":"1.0","event_id":"sha256:ab4713ad61c8db1befe4fcdcfa7d78d344d50335fe28e9e7d171649e6f4984a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R227Q7GLUWHSTERDHIFVJFU5SI/bundle.json","state_url":"https://pith.science/pith/R227Q7GLUWHSTERDHIFVJFU5SI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R227Q7GLUWHSTERDHIFVJFU5SI/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":"2026-06-24T22:25:02Z","links":{"resolver":"https://pith.science/pith/R227Q7GLUWHSTERDHIFVJFU5SI","bundle":"https://pith.science/pith/R227Q7GLUWHSTERDHIFVJFU5SI/bundle.json","state":"https://pith.science/pith/R227Q7GLUWHSTERDHIFVJFU5SI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R227Q7GLUWHSTERDHIFVJFU5SI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:R227Q7GLUWHSTERDHIFVJFU5SI","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":"70ffd29b104da9f86b7ac4ca31769c986036456b157c51b7ec1e298b91a1d98e","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-09-01T21:57:42Z","title_canon_sha256":"e2aeff502a70a42596a0b5ad971888c15750f51c65f91a928168dbc3375675f0"},"schema_version":"1.0","source":{"id":"1109.0312","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0312","created_at":"2026-05-18T04:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0312v1","created_at":"2026-05-18T04:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0312","created_at":"2026-05-18T04:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"R227Q7GLUWHS","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"R227Q7GLUWHSTERD","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"R227Q7GL","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:ab4713ad61c8db1befe4fcdcfa7d78d344d50335fe28e9e7d171649e6f4984a6","target":"graph","created_at":"2026-05-18T04:14:16Z","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 describe fully retroactive dynamic data structures for approximate range reporting and approximate nearest neighbor reporting. We show how to maintain, for any positive constant $d$, a set of $n$ points in $\\R^d$ indexed by time such that we can perform insertions or deletions at any point in the timeline in $O(\\log n)$ amortized time. We support, for any small constant $\\epsilon>0$, $(1+\\epsilon)$-approximate range reporting queries at any point in the timeline in $O(\\log n + k)$ time, where $k$ is the output size. We also show how to answer $(1+\\epsilon)$-approximate nearest neighbor quer","authors_text":"Joseph A. Simons, Michael T. Goodrich","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-09-01T21:57:42Z","title":"Fully Retroactive Approximate Range and Nearest Neighbor Searching"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0312","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":"sha256:8f3c9d40480ffd87e3477a781bfed498ccb80ba5317587ec4c1d3912497dfbbd","target":"record","created_at":"2026-05-18T04:14:16Z","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":"70ffd29b104da9f86b7ac4ca31769c986036456b157c51b7ec1e298b91a1d98e","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-09-01T21:57:42Z","title_canon_sha256":"e2aeff502a70a42596a0b5ad971888c15750f51c65f91a928168dbc3375675f0"},"schema_version":"1.0","source":{"id":"1109.0312","kind":"arxiv","version":1}},"canonical_sha256":"8eb5f87ccba58f2992233a0b54969d9218d0537413163a1ee4bb687b72b3af93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8eb5f87ccba58f2992233a0b54969d9218d0537413163a1ee4bb687b72b3af93","first_computed_at":"2026-05-18T04:14:16.057513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:16.057513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vx8z+4gIpYPuloXJoPovXQokEWDKoiOi6lBUQOMHqZaYjBtCc/ZaK+agEabTw3KTDU+NynDIyalcSzzapvAEBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:16.058117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0312","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f3c9d40480ffd87e3477a781bfed498ccb80ba5317587ec4c1d3912497dfbbd","sha256:ab4713ad61c8db1befe4fcdcfa7d78d344d50335fe28e9e7d171649e6f4984a6"],"state_sha256":"f9615a0e55e403e6a5f44333bfca06068147a193343a1451caabed8816bf0e2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IbO6b8pojkpEtSA0GESwQForuZF8qMtN2kLtbiehaUI1MZO/frcfr3zdf0rOc9EB0dZQvMxp4WTccPWSDKVLBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:25:02.735308Z","bundle_sha256":"0da659d07a318387e16fd71d5fe12a77ea2232c387c11f2db6062898d6c19cde"}}