{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:OWWAPJE5RSLUKQWPIYAGIXBXCY","short_pith_number":"pith:OWWAPJE5","schema_version":"1.0","canonical_sha256":"75ac07a49d8c974542cf4600645c37160ea0e9c521dab2d9543f04d493709718","source":{"kind":"arxiv","id":"2109.05151","version":3},"attestation_state":"computed","paper":{"title":"Almost Universally Optimal Distributed Laplacian Solvers via Low-Congestion Shortcuts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DC","authors_text":"Bernhard Haeupler, Christoph Lenzen, Goran Zuzic, Ioannis Anagnostides, Themis Gouleakis","submitted_at":"2021-09-11T01:45:34Z","abstract_excerpt":"In this paper, we refine the (almost) \\emph{existentially optimal} distributed Laplacian solver recently developed by Forster, Goranci, Liu, Peng, Sun, and Ye (FOCS `21) into an (almost) \\emph{universally optimal} distributed Laplacian solver.\n  Specifically, when the topology is known, we show that any Laplacian system on an $n$-node graph with \\emph{shortcut quality} $\\text{SQ}(G)$ can be solved within $n^{o(1)} \\text{SQ}(G) \\log(1/\\varepsilon)$ rounds, where $\\varepsilon$ is the required accuracy. This almost matches our lower bound which guarantees that any correct algorithm on $G$ require"},"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":"2109.05151","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2021-09-11T01:45:34Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"c6086493e5e0a379b7b7999e13f5f4466b087a72796ac8c37622da96a1785842","abstract_canon_sha256":"e555422d6b1ffc200bccfec1adfe9bab2d0ae87c5bba9be322f3b4f4a9f2bbb7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:24:22.669744Z","signature_b64":"1htYrTsrESX/+TToNbeOxG1wKaShWVOJ2UjL7i3vIYOMEWKUcWIm8SlR6Rkb+NIrxMItvG5nhuhNsyQ6BsPdAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75ac07a49d8c974542cf4600645c37160ea0e9c521dab2d9543f04d493709718","last_reissued_at":"2026-07-05T04:24:22.669340Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:24:22.669340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost Universally Optimal Distributed Laplacian Solvers via Low-Congestion Shortcuts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DC","authors_text":"Bernhard Haeupler, Christoph Lenzen, Goran Zuzic, Ioannis Anagnostides, Themis Gouleakis","submitted_at":"2021-09-11T01:45:34Z","abstract_excerpt":"In this paper, we refine the (almost) \\emph{existentially optimal} distributed Laplacian solver recently developed by Forster, Goranci, Liu, Peng, Sun, and Ye (FOCS `21) into an (almost) \\emph{universally optimal} distributed Laplacian solver.\n  Specifically, when the topology is known, we show that any Laplacian system on an $n$-node graph with \\emph{shortcut quality} $\\text{SQ}(G)$ can be solved within $n^{o(1)} \\text{SQ}(G) \\log(1/\\varepsilon)$ rounds, where $\\varepsilon$ is the required accuracy. This almost matches our lower bound which guarantees that any correct algorithm on $G$ require"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.05151","kind":"arxiv","version":3},"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/2109.05151/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":"2109.05151","created_at":"2026-07-05T04:24:22.669399+00:00"},{"alias_kind":"arxiv_version","alias_value":"2109.05151v3","created_at":"2026-07-05T04:24:22.669399+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.05151","created_at":"2026-07-05T04:24:22.669399+00:00"},{"alias_kind":"pith_short_12","alias_value":"OWWAPJE5RSLU","created_at":"2026-07-05T04:24:22.669399+00:00"},{"alias_kind":"pith_short_16","alias_value":"OWWAPJE5RSLUKQWP","created_at":"2026-07-05T04:24:22.669399+00:00"},{"alias_kind":"pith_short_8","alias_value":"OWWAPJE5","created_at":"2026-07-05T04:24:22.669399+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.19898","citing_title":"Distributed Sparsest Cut via Eigenvalue Estimation","ref_index":2022,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OWWAPJE5RSLUKQWPIYAGIXBXCY","json":"https://pith.science/pith/OWWAPJE5RSLUKQWPIYAGIXBXCY.json","graph_json":"https://pith.science/api/pith-number/OWWAPJE5RSLUKQWPIYAGIXBXCY/graph.json","events_json":"https://pith.science/api/pith-number/OWWAPJE5RSLUKQWPIYAGIXBXCY/events.json","paper":"https://pith.science/paper/OWWAPJE5"},"agent_actions":{"view_html":"https://pith.science/pith/OWWAPJE5RSLUKQWPIYAGIXBXCY","download_json":"https://pith.science/pith/OWWAPJE5RSLUKQWPIYAGIXBXCY.json","view_paper":"https://pith.science/paper/OWWAPJE5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2109.05151&json=true","fetch_graph":"https://pith.science/api/pith-number/OWWAPJE5RSLUKQWPIYAGIXBXCY/graph.json","fetch_events":"https://pith.science/api/pith-number/OWWAPJE5RSLUKQWPIYAGIXBXCY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OWWAPJE5RSLUKQWPIYAGIXBXCY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OWWAPJE5RSLUKQWPIYAGIXBXCY/action/storage_attestation","attest_author":"https://pith.science/pith/OWWAPJE5RSLUKQWPIYAGIXBXCY/action/author_attestation","sign_citation":"https://pith.science/pith/OWWAPJE5RSLUKQWPIYAGIXBXCY/action/citation_signature","submit_replication":"https://pith.science/pith/OWWAPJE5RSLUKQWPIYAGIXBXCY/action/replication_record"}},"created_at":"2026-07-05T04:24:22.669399+00:00","updated_at":"2026-07-05T04:24:22.669399+00:00"}