{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JTS4ZBCYJN6ZQG6IFPOFO4YDAI","short_pith_number":"pith:JTS4ZBCY","schema_version":"1.0","canonical_sha256":"4ce5cc84584b7d981bc82bdc577303020145480d5c2dbc92e495e9a2a177fa66","source":{"kind":"arxiv","id":"1706.10005","version":1},"attestation_state":"computed","paper":{"title":"Distance Descending Ordering Method: an $O(n)$ Algorithm for Inverting the Mass Matrix in Simulation of Macromolecules with Long Branches","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"Peiwen Li, Xiankun Xu","submitted_at":"2017-06-30T02:46:29Z","abstract_excerpt":"Fixman's work in 1974 and the follow-up studies have developed a method that can factorize the inverse of mass matrix into an arithmetic combination of three sparse matrices---one of them is positive definite and need to be further factorized by using the Cholesky decomposition or similar methods. When the molecule subjected to study is of serial chain structure, this method can achieve $O(n)$ computational complexity. However, for molecules with long branches, Cholesky decomposition about the corresponding positive definite matrix will introduce massive fill-in due to its nonzero structure, w"},"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":"1706.10005","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2017-06-30T02:46:29Z","cross_cats_sorted":[],"title_canon_sha256":"ea63c17a78d83aa9b78203a8718a9da6719e628dcf7e409a1905d893aa592003","abstract_canon_sha256":"5a5cb9a6a301da661c1850cc73873c017387bf26faa1a57a6f6817c9345eab0e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:31.075808Z","signature_b64":"Acf9BdNhDQTrFPTHxEQDs8n4vtXKZFCFNt5VrLvHtrFCri0ExCoqDXukKv+0LXUlpfOq/exM6ZbRfPWY6kCAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ce5cc84584b7d981bc82bdc577303020145480d5c2dbc92e495e9a2a177fa66","last_reissued_at":"2026-05-18T00:35:31.075414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:31.075414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distance Descending Ordering Method: an $O(n)$ Algorithm for Inverting the Mass Matrix in Simulation of Macromolecules with Long Branches","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"Peiwen Li, Xiankun Xu","submitted_at":"2017-06-30T02:46:29Z","abstract_excerpt":"Fixman's work in 1974 and the follow-up studies have developed a method that can factorize the inverse of mass matrix into an arithmetic combination of three sparse matrices---one of them is positive definite and need to be further factorized by using the Cholesky decomposition or similar methods. When the molecule subjected to study is of serial chain structure, this method can achieve $O(n)$ computational complexity. However, for molecules with long branches, Cholesky decomposition about the corresponding positive definite matrix will introduce massive fill-in due to its nonzero structure, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10005","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":"1706.10005","created_at":"2026-05-18T00:35:31.075466+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.10005v1","created_at":"2026-05-18T00:35:31.075466+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.10005","created_at":"2026-05-18T00:35:31.075466+00:00"},{"alias_kind":"pith_short_12","alias_value":"JTS4ZBCYJN6Z","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JTS4ZBCYJN6ZQG6I","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JTS4ZBCY","created_at":"2026-05-18T12:31:24.725408+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/JTS4ZBCYJN6ZQG6IFPOFO4YDAI","json":"https://pith.science/pith/JTS4ZBCYJN6ZQG6IFPOFO4YDAI.json","graph_json":"https://pith.science/api/pith-number/JTS4ZBCYJN6ZQG6IFPOFO4YDAI/graph.json","events_json":"https://pith.science/api/pith-number/JTS4ZBCYJN6ZQG6IFPOFO4YDAI/events.json","paper":"https://pith.science/paper/JTS4ZBCY"},"agent_actions":{"view_html":"https://pith.science/pith/JTS4ZBCYJN6ZQG6IFPOFO4YDAI","download_json":"https://pith.science/pith/JTS4ZBCYJN6ZQG6IFPOFO4YDAI.json","view_paper":"https://pith.science/paper/JTS4ZBCY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.10005&json=true","fetch_graph":"https://pith.science/api/pith-number/JTS4ZBCYJN6ZQG6IFPOFO4YDAI/graph.json","fetch_events":"https://pith.science/api/pith-number/JTS4ZBCYJN6ZQG6IFPOFO4YDAI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JTS4ZBCYJN6ZQG6IFPOFO4YDAI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JTS4ZBCYJN6ZQG6IFPOFO4YDAI/action/storage_attestation","attest_author":"https://pith.science/pith/JTS4ZBCYJN6ZQG6IFPOFO4YDAI/action/author_attestation","sign_citation":"https://pith.science/pith/JTS4ZBCYJN6ZQG6IFPOFO4YDAI/action/citation_signature","submit_replication":"https://pith.science/pith/JTS4ZBCYJN6ZQG6IFPOFO4YDAI/action/replication_record"}},"created_at":"2026-05-18T00:35:31.075466+00:00","updated_at":"2026-05-18T00:35:31.075466+00:00"}