{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BUH44TQYBRXJPKEF3CTUHG5YLU","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":"efc1647bc553b92da6a642fe2b219decea676560754254e297233941bfd32036","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-08-18T21:39:20Z","title_canon_sha256":"5864f02b2665308e776a14a373119bb617015dd4357c03e27748de957c376d87"},"schema_version":"1.0","source":{"id":"1108.3860","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3860","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3860v3","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3860","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"pith_short_12","alias_value":"BUH44TQYBRXJ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BUH44TQYBRXJPKEF","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BUH44TQY","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:17321a5b6ca6fcdd13b1ff6f786c6f98791ad53c60fc46e0f746d77e64a9fc84","target":"graph","created_at":"2026-05-18T01:37:29Z","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 complexity of algorithms counting ones in different sets of operations. With addition and logical operations (but no shift) $O(\\log^2(n))$ steps suffice to count ones. Parity can be computed with complexity $O(\\log(n))$, which is the same bound as for methods using shift-operations. If multiplication is available, a solution of time complexity $O(\\log^*(n))$ is possible improving the known bound $O(\\log\\log(n))$.","authors_text":"Holger Petersen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-08-18T21:39:20Z","title":"A SWAR Approach to Counting Ones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3860","kind":"arxiv","version":3},"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":"sha256:37a4308534fad078d3bd534a282eded459a88997203bc870a699c56e249a804d","target":"record","created_at":"2026-05-18T01:37:29Z","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":"efc1647bc553b92da6a642fe2b219decea676560754254e297233941bfd32036","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-08-18T21:39:20Z","title_canon_sha256":"5864f02b2665308e776a14a373119bb617015dd4357c03e27748de957c376d87"},"schema_version":"1.0","source":{"id":"1108.3860","kind":"arxiv","version":3}},"canonical_sha256":"0d0fce4e180c6e97a885d8a7439bb85d246d673837ecafda2ca9afb3b2ab0dc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d0fce4e180c6e97a885d8a7439bb85d246d673837ecafda2ca9afb3b2ab0dc0","first_computed_at":"2026-05-18T01:37:29.091862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:29.091862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cTOZhUjAHCiDcpoaf2QEnrCw9T6OU1cD4gRr0+HOqF09HU7MUUSz+Lxx9x3EwKlxf6R8rjn2Rum5SMnIg4j4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:29.092504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3860","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37a4308534fad078d3bd534a282eded459a88997203bc870a699c56e249a804d","sha256:17321a5b6ca6fcdd13b1ff6f786c6f98791ad53c60fc46e0f746d77e64a9fc84"],"state_sha256":"c2bcc724bd3661976c0a5af9772fc47742ceb65d01b7e857ae53705490916f5e"}