{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:6QVJZW5PJYV4AI5EBMKPNGWOC7","short_pith_number":"pith:6QVJZW5P","schema_version":"1.0","canonical_sha256":"f42a9cdbaf4e2bc023a40b14f69ace17ec634c42395a126dbeac83f8da375969","source":{"kind":"arxiv","id":"2311.06281","version":4},"attestation_state":"computed","paper":{"title":"Efficient Parallelization of a Ubiquitous Sequential Computation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Franz A. Heinsen","submitted_at":"2023-10-27T21:58:55Z","abstract_excerpt":"We find a succinct expression for computing the sequence $x_t = a_t x_{t-1} + b_t$ in parallel with two prefix sums, given $t = (1, 2, \\dots, n)$, $a_t \\in \\mathbb{R}^n$, $b_t \\in \\mathbb{R}^n$, and initial value $x_0 \\in \\mathbb{R}$. On $n$ parallel processors, the computation of $n$ elements incurs $\\mathcal{O}(\\log n)$ time and $\\mathcal{O}(n)$ space. Sequences of this form are ubiquitous in science and engineering, making efficient parallelization useful for a vast number of applications. We implement our expression in software, test it on parallel hardware, and verify that it executes fas"},"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":"2311.06281","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2023-10-27T21:58:55Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"987d2ebb30e2fd5d515956371748b282fc69047c47d3a42a06cccbe281c536ba","abstract_canon_sha256":"a66a8c3536da46839d9975182c789556b0f6402cd3c89855131b5df49c18e4fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:28:12.082219Z","signature_b64":"dQb1FX3J1Ns4gTZC6X1B/Q0czhPkuCN664ZvY43yQapYrf3E+bFL3sWBo1fKM0lf5a6oT4IVyy1feSjqZonkAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f42a9cdbaf4e2bc023a40b14f69ace17ec634c42395a126dbeac83f8da375969","last_reissued_at":"2026-07-05T07:28:12.081807Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:28:12.081807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient Parallelization of a Ubiquitous Sequential Computation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Franz A. Heinsen","submitted_at":"2023-10-27T21:58:55Z","abstract_excerpt":"We find a succinct expression for computing the sequence $x_t = a_t x_{t-1} + b_t$ in parallel with two prefix sums, given $t = (1, 2, \\dots, n)$, $a_t \\in \\mathbb{R}^n$, $b_t \\in \\mathbb{R}^n$, and initial value $x_0 \\in \\mathbb{R}$. On $n$ parallel processors, the computation of $n$ elements incurs $\\mathcal{O}(\\log n)$ time and $\\mathcal{O}(n)$ space. Sequences of this form are ubiquitous in science and engineering, making efficient parallelization useful for a vast number of applications. We implement our expression in software, test it on parallel hardware, and verify that it executes fas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.06281","kind":"arxiv","version":4},"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/2311.06281/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2311.06281","created_at":"2026-07-05T07:28:12.081862+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.06281v4","created_at":"2026-07-05T07:28:12.081862+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.06281","created_at":"2026-07-05T07:28:12.081862+00:00"},{"alias_kind":"pith_short_12","alias_value":"6QVJZW5PJYV4","created_at":"2026-07-05T07:28:12.081862+00:00"},{"alias_kind":"pith_short_16","alias_value":"6QVJZW5PJYV4AI5E","created_at":"2026-07-05T07:28:12.081862+00:00"},{"alias_kind":"pith_short_8","alias_value":"6QVJZW5P","created_at":"2026-07-05T07:28:12.081862+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/6QVJZW5PJYV4AI5EBMKPNGWOC7","json":"https://pith.science/pith/6QVJZW5PJYV4AI5EBMKPNGWOC7.json","graph_json":"https://pith.science/api/pith-number/6QVJZW5PJYV4AI5EBMKPNGWOC7/graph.json","events_json":"https://pith.science/api/pith-number/6QVJZW5PJYV4AI5EBMKPNGWOC7/events.json","paper":"https://pith.science/paper/6QVJZW5P"},"agent_actions":{"view_html":"https://pith.science/pith/6QVJZW5PJYV4AI5EBMKPNGWOC7","download_json":"https://pith.science/pith/6QVJZW5PJYV4AI5EBMKPNGWOC7.json","view_paper":"https://pith.science/paper/6QVJZW5P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.06281&json=true","fetch_graph":"https://pith.science/api/pith-number/6QVJZW5PJYV4AI5EBMKPNGWOC7/graph.json","fetch_events":"https://pith.science/api/pith-number/6QVJZW5PJYV4AI5EBMKPNGWOC7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6QVJZW5PJYV4AI5EBMKPNGWOC7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6QVJZW5PJYV4AI5EBMKPNGWOC7/action/storage_attestation","attest_author":"https://pith.science/pith/6QVJZW5PJYV4AI5EBMKPNGWOC7/action/author_attestation","sign_citation":"https://pith.science/pith/6QVJZW5PJYV4AI5EBMKPNGWOC7/action/citation_signature","submit_replication":"https://pith.science/pith/6QVJZW5PJYV4AI5EBMKPNGWOC7/action/replication_record"}},"created_at":"2026-07-05T07:28:12.081862+00:00","updated_at":"2026-07-05T07:28:12.081862+00:00"}