{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:5DXE3GWOFEFVCXXSZ3T4DJCF6P","short_pith_number":"pith:5DXE3GWO","canonical_record":{"source":{"id":"2101.02003","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-01-06T13:18:02Z","cross_cats_sorted":["cs.CC","cs.CG"],"title_canon_sha256":"2ed1f7337964bdb67f4765e65a0704d71f805cc8fc511d8f9654b4e2f6d7b7f7","abstract_canon_sha256":"501d2094552bd6ef6a8ee89483b741ef2ad8c8ade27f76e09daa2c6fd3857dc0"},"schema_version":"1.0"},"canonical_sha256":"e8ee4d9ace290b515ef2cee7c1a445f3dc5907951a334ec19085b8d08f21fa64","source":{"kind":"arxiv","id":"2101.02003","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.02003","created_at":"2026-07-05T02:05:02Z"},{"alias_kind":"arxiv_version","alias_value":"2101.02003v1","created_at":"2026-07-05T02:05:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.02003","created_at":"2026-07-05T02:05:02Z"},{"alias_kind":"pith_short_12","alias_value":"5DXE3GWOFEFV","created_at":"2026-07-05T02:05:02Z"},{"alias_kind":"pith_short_16","alias_value":"5DXE3GWOFEFVCXXS","created_at":"2026-07-05T02:05:02Z"},{"alias_kind":"pith_short_8","alias_value":"5DXE3GWO","created_at":"2026-07-05T02:05:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:5DXE3GWOFEFVCXXSZ3T4DJCF6P","target":"record","payload":{"canonical_record":{"source":{"id":"2101.02003","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-01-06T13:18:02Z","cross_cats_sorted":["cs.CC","cs.CG"],"title_canon_sha256":"2ed1f7337964bdb67f4765e65a0704d71f805cc8fc511d8f9654b4e2f6d7b7f7","abstract_canon_sha256":"501d2094552bd6ef6a8ee89483b741ef2ad8c8ade27f76e09daa2c6fd3857dc0"},"schema_version":"1.0"},"canonical_sha256":"e8ee4d9ace290b515ef2cee7c1a445f3dc5907951a334ec19085b8d08f21fa64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:05:02.369688Z","signature_b64":"mK00ncJ2mvbdw6G4J3m5sK1jegW2bBCp33jsRztO2BxE06/1bnpvteynMP3SZ9erdU5/B6kBbpykbGat5n2lCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8ee4d9ace290b515ef2cee7c1a445f3dc5907951a334ec19085b8d08f21fa64","last_reissued_at":"2026-07-05T02:05:02.369347Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:05:02.369347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2101.02003","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":"2026-07-05T02:05:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+pl3L4W+pB4KhdvAQ1FFEDSX1sNexBgZnCOKiqIFsQpgsHpNyLPT7OT8X2YvyZv4Txzpr//pLOCNY261tgZNDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T01:04:21.897029Z"},"content_sha256":"5bfb98f6a0ac7538604429c1e84f5038e8759d3a353c506447b8920a92fc123a","schema_version":"1.0","event_id":"sha256:5bfb98f6a0ac7538604429c1e84f5038e8759d3a353c506447b8920a92fc123a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:5DXE3GWOFEFVCXXSZ3T4DJCF6P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algorithms and Hardness for Multidimensional Range Updates and Queries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.CG"],"primary_cat":"cs.DS","authors_text":"Angus Ritossa, Joshua Lau","submitted_at":"2021-01-06T13:18:02Z","abstract_excerpt":"Traditional orthogonal range problems allow queries over a static set of points, each with some value. Dynamic variants allow points to be added or removed, one at a time. To support more powerful updates, we introduce the Grid Range class of data structure problems over integer arrays in one or more dimensions. These problems allow range updates (such as filling all cells in a range with a constant) and queries (such as finding the sum or maximum of values in a range). In this work, we consider these operations along with updates that replace each cell in a range with the minimum, maximum, or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.02003","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2101.02003/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:05:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cknpDJitUbgY59Ws5nKt3Ym8Napckte3ubbWfOylHjP1Ke00AvrYZOD9CDR/uU+T+7SAJrO/r7JExIHuXtPlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T01:04:21.897516Z"},"content_sha256":"3230b1b7249bd037d792627f35c98bad05341634c1cffbffb15bb20477a17949","schema_version":"1.0","event_id":"sha256:3230b1b7249bd037d792627f35c98bad05341634c1cffbffb15bb20477a17949"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5DXE3GWOFEFVCXXSZ3T4DJCF6P/bundle.json","state_url":"https://pith.science/pith/5DXE3GWOFEFVCXXSZ3T4DJCF6P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5DXE3GWOFEFVCXXSZ3T4DJCF6P/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":"2026-08-22T01:04:21Z","links":{"resolver":"https://pith.science/pith/5DXE3GWOFEFVCXXSZ3T4DJCF6P","bundle":"https://pith.science/pith/5DXE3GWOFEFVCXXSZ3T4DJCF6P/bundle.json","state":"https://pith.science/pith/5DXE3GWOFEFVCXXSZ3T4DJCF6P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5DXE3GWOFEFVCXXSZ3T4DJCF6P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:5DXE3GWOFEFVCXXSZ3T4DJCF6P","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":"501d2094552bd6ef6a8ee89483b741ef2ad8c8ade27f76e09daa2c6fd3857dc0","cross_cats_sorted":["cs.CC","cs.CG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-01-06T13:18:02Z","title_canon_sha256":"2ed1f7337964bdb67f4765e65a0704d71f805cc8fc511d8f9654b4e2f6d7b7f7"},"schema_version":"1.0","source":{"id":"2101.02003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.02003","created_at":"2026-07-05T02:05:02Z"},{"alias_kind":"arxiv_version","alias_value":"2101.02003v1","created_at":"2026-07-05T02:05:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.02003","created_at":"2026-07-05T02:05:02Z"},{"alias_kind":"pith_short_12","alias_value":"5DXE3GWOFEFV","created_at":"2026-07-05T02:05:02Z"},{"alias_kind":"pith_short_16","alias_value":"5DXE3GWOFEFVCXXS","created_at":"2026-07-05T02:05:02Z"},{"alias_kind":"pith_short_8","alias_value":"5DXE3GWO","created_at":"2026-07-05T02:05:02Z"}],"graph_snapshots":[{"event_id":"sha256:3230b1b7249bd037d792627f35c98bad05341634c1cffbffb15bb20477a17949","target":"graph","created_at":"2026-07-05T02:05:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2101.02003/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Traditional orthogonal range problems allow queries over a static set of points, each with some value. Dynamic variants allow points to be added or removed, one at a time. To support more powerful updates, we introduce the Grid Range class of data structure problems over integer arrays in one or more dimensions. These problems allow range updates (such as filling all cells in a range with a constant) and queries (such as finding the sum or maximum of values in a range). In this work, we consider these operations along with updates that replace each cell in a range with the minimum, maximum, or","authors_text":"Angus Ritossa, Joshua Lau","cross_cats":["cs.CC","cs.CG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-01-06T13:18:02Z","title":"Algorithms and Hardness for Multidimensional Range Updates and Queries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.02003","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":"sha256:5bfb98f6a0ac7538604429c1e84f5038e8759d3a353c506447b8920a92fc123a","target":"record","created_at":"2026-07-05T02:05:02Z","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":"501d2094552bd6ef6a8ee89483b741ef2ad8c8ade27f76e09daa2c6fd3857dc0","cross_cats_sorted":["cs.CC","cs.CG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-01-06T13:18:02Z","title_canon_sha256":"2ed1f7337964bdb67f4765e65a0704d71f805cc8fc511d8f9654b4e2f6d7b7f7"},"schema_version":"1.0","source":{"id":"2101.02003","kind":"arxiv","version":1}},"canonical_sha256":"e8ee4d9ace290b515ef2cee7c1a445f3dc5907951a334ec19085b8d08f21fa64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8ee4d9ace290b515ef2cee7c1a445f3dc5907951a334ec19085b8d08f21fa64","first_computed_at":"2026-07-05T02:05:02.369347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:05:02.369347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mK00ncJ2mvbdw6G4J3m5sK1jegW2bBCp33jsRztO2BxE06/1bnpvteynMP3SZ9erdU5/B6kBbpykbGat5n2lCw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:05:02.369688Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.02003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bfb98f6a0ac7538604429c1e84f5038e8759d3a353c506447b8920a92fc123a","sha256:3230b1b7249bd037d792627f35c98bad05341634c1cffbffb15bb20477a17949"],"state_sha256":"4e2e7c00f578ccfe8439e70cdfb617d634dd0efce00d0b46c56d2b60961a71a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WzlcmCm5SQahPBdyZtuFq48uOfNQv3QQA+bGGKpei/mAqUNGSOOia2pBPNcGxw3nUsGT7ro0ejmIRxh+Rlv0BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T01:04:21.900943Z","bundle_sha256":"e6e9d1e21d01f794245022b0910a78979291bae936a2b65d8d5486f24aa1f819"}}