{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:5J6XZ2OXV3OMHOS2O2JM7PF2RR","short_pith_number":"pith:5J6XZ2OX","schema_version":"1.0","canonical_sha256":"ea7d7ce9d7aedcc3ba5a7692cfbcba8c65a7ffc812c6f8d482f86cfc2c20266f","source":{"kind":"arxiv","id":"2607.25059","version":1},"attestation_state":"computed","paper":{"title":"Parallel Spectral Graph Sparsification via Low Diameter Decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.DS","authors_text":"Gernot Z\\\"ocklein, Yves Baumann","submitted_at":"2026-07-27T20:42:27Z","abstract_excerpt":"We present a new solver-free parallel spectral sparsification algorithm for weighted graphs that relies only on parallel low-diameter decompositions and independent sampling. This yields the first algorithmic improvement over prior, solver-free parallel sparsification approaches since Koutis (2014) and, for the first time for a practical algorithm, eliminates any dependence on the target approximation accuracy $\\epsilon$ in the algorithm's work and depth.\n  Our algorithm works by sub-sampling edges according to their robust connectivity, as introduced by Kapralov and Panigrahy (2012). We show "},"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":"2607.25059","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-27T20:42:27Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"b123893e139f6aabfd8435ee1d4760ecb4f906e03559048b282078991d44e230","abstract_canon_sha256":"1da742bfd5e8ea4facde68306318fc72df25d6fa4f03d7176b0e443091865ec7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-29T00:25:00.419772Z","signature_b64":"vBlafZ4ewPojzCx4FMaXlKPSvoogj/5ZxZmQuFnIQedCEvUS9eMVg+Rdp8nmwIQWp4/estFtua2rPCW4Bw9JDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea7d7ce9d7aedcc3ba5a7692cfbcba8c65a7ffc812c6f8d482f86cfc2c20266f","last_reissued_at":"2026-07-29T00:25:00.418923Z","signature_status":"signed_v1","first_computed_at":"2026-07-29T00:25:00.418923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parallel Spectral Graph Sparsification via Low Diameter Decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.DS","authors_text":"Gernot Z\\\"ocklein, Yves Baumann","submitted_at":"2026-07-27T20:42:27Z","abstract_excerpt":"We present a new solver-free parallel spectral sparsification algorithm for weighted graphs that relies only on parallel low-diameter decompositions and independent sampling. This yields the first algorithmic improvement over prior, solver-free parallel sparsification approaches since Koutis (2014) and, for the first time for a practical algorithm, eliminates any dependence on the target approximation accuracy $\\epsilon$ in the algorithm's work and depth.\n  Our algorithm works by sub-sampling edges according to their robust connectivity, as introduced by Kapralov and Panigrahy (2012). We show "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25059","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.25059/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":"2607.25059","created_at":"2026-07-29T00:25:00.419364+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.25059v1","created_at":"2026-07-29T00:25:00.419364+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.25059","created_at":"2026-07-29T00:25:00.419364+00:00"},{"alias_kind":"pith_short_12","alias_value":"5J6XZ2OXV3OM","created_at":"2026-07-29T00:25:00.419364+00:00"},{"alias_kind":"pith_short_16","alias_value":"5J6XZ2OXV3OMHOS2","created_at":"2026-07-29T00:25:00.419364+00:00"},{"alias_kind":"pith_short_8","alias_value":"5J6XZ2OX","created_at":"2026-07-29T00:25:00.419364+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/5J6XZ2OXV3OMHOS2O2JM7PF2RR","json":"https://pith.science/pith/5J6XZ2OXV3OMHOS2O2JM7PF2RR.json","graph_json":"https://pith.science/api/pith-number/5J6XZ2OXV3OMHOS2O2JM7PF2RR/graph.json","events_json":"https://pith.science/api/pith-number/5J6XZ2OXV3OMHOS2O2JM7PF2RR/events.json","paper":"https://pith.science/paper/5J6XZ2OX"},"agent_actions":{"view_html":"https://pith.science/pith/5J6XZ2OXV3OMHOS2O2JM7PF2RR","download_json":"https://pith.science/pith/5J6XZ2OXV3OMHOS2O2JM7PF2RR.json","view_paper":"https://pith.science/paper/5J6XZ2OX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.25059&json=true","fetch_graph":"https://pith.science/api/pith-number/5J6XZ2OXV3OMHOS2O2JM7PF2RR/graph.json","fetch_events":"https://pith.science/api/pith-number/5J6XZ2OXV3OMHOS2O2JM7PF2RR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5J6XZ2OXV3OMHOS2O2JM7PF2RR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5J6XZ2OXV3OMHOS2O2JM7PF2RR/action/storage_attestation","attest_author":"https://pith.science/pith/5J6XZ2OXV3OMHOS2O2JM7PF2RR/action/author_attestation","sign_citation":"https://pith.science/pith/5J6XZ2OXV3OMHOS2O2JM7PF2RR/action/citation_signature","submit_replication":"https://pith.science/pith/5J6XZ2OXV3OMHOS2O2JM7PF2RR/action/replication_record"}},"created_at":"2026-07-29T00:25:00.419364+00:00","updated_at":"2026-07-29T00:25:00.419364+00:00"}