{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:S7DCR3KW5WMXVORLIG33WMB27Q","short_pith_number":"pith:S7DCR3KW","canonical_record":{"source":{"id":"1804.03636","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-10T17:28:47Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT","math.ST","stat.TH"],"title_canon_sha256":"8240acd657f0b70bf19b01cf4a2c36985f7670d6710242cfc3705bebad1ac778","abstract_canon_sha256":"07ef21563977e0f3f65e7675ff0102ed48aa983d8ac39eba39516eb3028df8d7"},"schema_version":"1.0"},"canonical_sha256":"97c628ed56ed997aba2b41b7bb303afc0e83caa754be2a80e06f8f471cea72e5","source":{"kind":"arxiv","id":"1804.03636","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03636","created_at":"2026-05-17T23:53:44Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03636v2","created_at":"2026-05-17T23:53:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03636","created_at":"2026-05-17T23:53:44Z"},{"alias_kind":"pith_short_12","alias_value":"S7DCR3KW5WMX","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S7DCR3KW5WMXVORL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S7DCR3KW","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:S7DCR3KW5WMXVORLIG33WMB27Q","target":"record","payload":{"canonical_record":{"source":{"id":"1804.03636","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-10T17:28:47Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT","math.ST","stat.TH"],"title_canon_sha256":"8240acd657f0b70bf19b01cf4a2c36985f7670d6710242cfc3705bebad1ac778","abstract_canon_sha256":"07ef21563977e0f3f65e7675ff0102ed48aa983d8ac39eba39516eb3028df8d7"},"schema_version":"1.0"},"canonical_sha256":"97c628ed56ed997aba2b41b7bb303afc0e83caa754be2a80e06f8f471cea72e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:44.208139Z","signature_b64":"NytY88293eeB3o/96FKh34sKXufW8QZYzaKw9W+3i/PlUSGowbYfC8BmEmKWNxBn4VwwmpkxdPvgj66ExRTiDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97c628ed56ed997aba2b41b7bb303afc0e83caa754be2a80e06f8f471cea72e5","last_reissued_at":"2026-05-17T23:53:44.207664Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:44.207664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.03636","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":"2026-05-17T23:53:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3GkXES7szyJjmXjCUy8bneXDuzhJNSwX4ZbX7PEp1DxHLyzN22Jvza7/3AsWJRkuhUbsTtB0kQHOBdtfhywVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:26:23.566525Z"},"content_sha256":"716e583f6853fc45270870b82790ad678d0717f9783aad3c5e3277c14a47a1fb","schema_version":"1.0","event_id":"sha256:716e583f6853fc45270870b82790ad678d0717f9783aad3c5e3277c14a47a1fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:S7DCR3KW5WMXVORLIG33WMB27Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Testing Identity of Multidimensional Histograms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Daniel M. Kane, Ilias Diakonikolas, John Peebles","submitted_at":"2018-04-10T17:28:47Z","abstract_excerpt":"We investigate the problem of identity testing for multidimensional histogram distributions. A distribution $p: D \\rightarrow \\mathbb{R}_+$, where $D \\subseteq \\mathbb{R}^d$, is called a $k$-histogram if there exists a partition of the domain into $k$ axis-aligned rectangles such that $p$ is constant within each such rectangle. Histograms are one of the most fundamental nonparametric families of distributions and have been extensively studied in computer science and statistics. We give the first identity tester for this problem with {\\em sub-learning} sample complexity in any fixed dimension a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03636","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":"2026-05-17T23:53:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WmSCA+jMEm9SDGVJ+8RMc0FuhRpn6S1D1Cv3VLzMK05vhYHX26/4R9K/ZzOUyHjfknguXEIf7AWwM7ZQtPLmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:26:23.566882Z"},"content_sha256":"2d910649956c02af9797b73eb45c7356fc67d04d365c67de218beece06ba0197","schema_version":"1.0","event_id":"sha256:2d910649956c02af9797b73eb45c7356fc67d04d365c67de218beece06ba0197"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S7DCR3KW5WMXVORLIG33WMB27Q/bundle.json","state_url":"https://pith.science/pith/S7DCR3KW5WMXVORLIG33WMB27Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S7DCR3KW5WMXVORLIG33WMB27Q/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":"2026-06-05T14:26:23Z","links":{"resolver":"https://pith.science/pith/S7DCR3KW5WMXVORLIG33WMB27Q","bundle":"https://pith.science/pith/S7DCR3KW5WMXVORLIG33WMB27Q/bundle.json","state":"https://pith.science/pith/S7DCR3KW5WMXVORLIG33WMB27Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S7DCR3KW5WMXVORLIG33WMB27Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:S7DCR3KW5WMXVORLIG33WMB27Q","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":"07ef21563977e0f3f65e7675ff0102ed48aa983d8ac39eba39516eb3028df8d7","cross_cats_sorted":["cs.IT","cs.LG","math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-10T17:28:47Z","title_canon_sha256":"8240acd657f0b70bf19b01cf4a2c36985f7670d6710242cfc3705bebad1ac778"},"schema_version":"1.0","source":{"id":"1804.03636","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03636","created_at":"2026-05-17T23:53:44Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03636v2","created_at":"2026-05-17T23:53:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03636","created_at":"2026-05-17T23:53:44Z"},{"alias_kind":"pith_short_12","alias_value":"S7DCR3KW5WMX","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S7DCR3KW5WMXVORL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S7DCR3KW","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:2d910649956c02af9797b73eb45c7356fc67d04d365c67de218beece06ba0197","target":"graph","created_at":"2026-05-17T23:53:44Z","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 investigate the problem of identity testing for multidimensional histogram distributions. A distribution $p: D \\rightarrow \\mathbb{R}_+$, where $D \\subseteq \\mathbb{R}^d$, is called a $k$-histogram if there exists a partition of the domain into $k$ axis-aligned rectangles such that $p$ is constant within each such rectangle. Histograms are one of the most fundamental nonparametric families of distributions and have been extensively studied in computer science and statistics. We give the first identity tester for this problem with {\\em sub-learning} sample complexity in any fixed dimension a","authors_text":"Daniel M. Kane, Ilias Diakonikolas, John Peebles","cross_cats":["cs.IT","cs.LG","math.IT","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-10T17:28:47Z","title":"Testing Identity of Multidimensional Histograms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03636","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":"sha256:716e583f6853fc45270870b82790ad678d0717f9783aad3c5e3277c14a47a1fb","target":"record","created_at":"2026-05-17T23:53:44Z","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":"07ef21563977e0f3f65e7675ff0102ed48aa983d8ac39eba39516eb3028df8d7","cross_cats_sorted":["cs.IT","cs.LG","math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-10T17:28:47Z","title_canon_sha256":"8240acd657f0b70bf19b01cf4a2c36985f7670d6710242cfc3705bebad1ac778"},"schema_version":"1.0","source":{"id":"1804.03636","kind":"arxiv","version":2}},"canonical_sha256":"97c628ed56ed997aba2b41b7bb303afc0e83caa754be2a80e06f8f471cea72e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97c628ed56ed997aba2b41b7bb303afc0e83caa754be2a80e06f8f471cea72e5","first_computed_at":"2026-05-17T23:53:44.207664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:44.207664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NytY88293eeB3o/96FKh34sKXufW8QZYzaKw9W+3i/PlUSGowbYfC8BmEmKWNxBn4VwwmpkxdPvgj66ExRTiDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:44.208139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03636","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:716e583f6853fc45270870b82790ad678d0717f9783aad3c5e3277c14a47a1fb","sha256:2d910649956c02af9797b73eb45c7356fc67d04d365c67de218beece06ba0197"],"state_sha256":"e9ec50687f875a71e10be376999a9a084c11cd519d1c9e2c6235301996bedfa4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ro+J3u054ZPOxufX42NKiiBNnovgC90ziqtObY4V/F/R4g+fC5RBkf5QTtL3r3gre8JcvSgnufHfNhUtTXywBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T14:26:23.569000Z","bundle_sha256":"2c473d63155ede709c69749c7243fb0edcd3a0fce06545cccb43518f0c22933b"}}