{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:YZ75B7OPI2CHWJJY3A6EMTLYX7","short_pith_number":"pith:YZ75B7OP","schema_version":"1.0","canonical_sha256":"c67fd0fdcf46847b2538d83c464d78bfde1454426c39113a08711156acaf4fc5","source":{"kind":"arxiv","id":"1011.3480","version":1},"attestation_state":"computed","paper":{"title":"Counting Colours in Compressed Strings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Juha K\\\"arkk\\\"ainen, Travis Gagie","submitted_at":"2010-11-15T19:30:19Z","abstract_excerpt":"Suppose we are asked to preprocess a string \\(s [1..n]\\) such that later, given a substring's endpoints, we can quickly count how many distinct characters it contains. In this paper we give a data structure for this problem that takes \\(n H_0 (s) + \\Oh{n} + \\oh{n H_0 (s)}\\) bits, where \\(H_0 (s)\\) is the 0th-order empirical entropy of $s$, and answers queries in $\\Oh{\\log^{1 + \\epsilon} n}$ time for any constant \\(\\epsilon > 0\\). We also show how our data structure can be made partially dynamic."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1011.3480","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-15T19:30:19Z","cross_cats_sorted":[],"title_canon_sha256":"0c2130daf962295b5cb74e5456ab75d78850448148dc1fa248d562574f731701","abstract_canon_sha256":"e818a0c832ee3258040b9081c13fc0618fb4ab084d9e249ec6d2ec8318636cd1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:55.755750Z","signature_b64":"xmevqmbMcBeeLyBpeS0TcBomawdqIey1OZs2FRPo+I30tbjJO3D3LS1+xdH/8Vm/wCuaB75SUaFoH4rv9Xw9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c67fd0fdcf46847b2538d83c464d78bfde1454426c39113a08711156acaf4fc5","last_reissued_at":"2026-05-18T04:35:55.755121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:55.755121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting Colours in Compressed Strings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Juha K\\\"arkk\\\"ainen, Travis Gagie","submitted_at":"2010-11-15T19:30:19Z","abstract_excerpt":"Suppose we are asked to preprocess a string \\(s [1..n]\\) such that later, given a substring's endpoints, we can quickly count how many distinct characters it contains. In this paper we give a data structure for this problem that takes \\(n H_0 (s) + \\Oh{n} + \\oh{n H_0 (s)}\\) bits, where \\(H_0 (s)\\) is the 0th-order empirical entropy of $s$, and answers queries in $\\Oh{\\log^{1 + \\epsilon} n}$ time for any constant \\(\\epsilon > 0\\). We also show how our data structure can be made partially dynamic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3480","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1011.3480","created_at":"2026-05-18T04:35:55.755222+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.3480v1","created_at":"2026-05-18T04:35:55.755222+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3480","created_at":"2026-05-18T04:35:55.755222+00:00"},{"alias_kind":"pith_short_12","alias_value":"YZ75B7OPI2CH","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"YZ75B7OPI2CHWJJY","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"YZ75B7OP","created_at":"2026-05-18T12:26:17.028572+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YZ75B7OPI2CHWJJY3A6EMTLYX7","json":"https://pith.science/pith/YZ75B7OPI2CHWJJY3A6EMTLYX7.json","graph_json":"https://pith.science/api/pith-number/YZ75B7OPI2CHWJJY3A6EMTLYX7/graph.json","events_json":"https://pith.science/api/pith-number/YZ75B7OPI2CHWJJY3A6EMTLYX7/events.json","paper":"https://pith.science/paper/YZ75B7OP"},"agent_actions":{"view_html":"https://pith.science/pith/YZ75B7OPI2CHWJJY3A6EMTLYX7","download_json":"https://pith.science/pith/YZ75B7OPI2CHWJJY3A6EMTLYX7.json","view_paper":"https://pith.science/paper/YZ75B7OP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.3480&json=true","fetch_graph":"https://pith.science/api/pith-number/YZ75B7OPI2CHWJJY3A6EMTLYX7/graph.json","fetch_events":"https://pith.science/api/pith-number/YZ75B7OPI2CHWJJY3A6EMTLYX7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YZ75B7OPI2CHWJJY3A6EMTLYX7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YZ75B7OPI2CHWJJY3A6EMTLYX7/action/storage_attestation","attest_author":"https://pith.science/pith/YZ75B7OPI2CHWJJY3A6EMTLYX7/action/author_attestation","sign_citation":"https://pith.science/pith/YZ75B7OPI2CHWJJY3A6EMTLYX7/action/citation_signature","submit_replication":"https://pith.science/pith/YZ75B7OPI2CHWJJY3A6EMTLYX7/action/replication_record"}},"created_at":"2026-05-18T04:35:55.755222+00:00","updated_at":"2026-05-18T04:35:55.755222+00:00"}