{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RBQACFYTXH42YYTP2CWRHXW2RK","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":"d3eb8f96fc3affea71e57df2d1c85b64723c94831968cd12222b800837cef44a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-31T03:58:45Z","title_canon_sha256":"e329d8d7a45b38d6ddd802eb3e72e3783065feeb26239dd586298f9cb16db1e5"},"schema_version":"1.0","source":{"id":"1401.0085","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0085","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0085v1","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0085","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"RBQACFYTXH42","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RBQACFYTXH42YYTP","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RBQACFYT","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:593fb378b652ab8690b0e501c52b490b128dfe2d5f6d9eac2f25099ebd7ef95a","target":"graph","created_at":"2026-05-18T03:03:31Z","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":"In this paper, we introduce a variant of spectral sparsification, called probabilistic $(\\varepsilon,\\delta)$-spectral sparsification. Roughly speaking, it preserves the cut value of any cut $(S,S^{c})$ with an $1\\pm\\varepsilon$ multiplicative error and a $\\delta\\left|S\\right|$ additive error. We show how to produce a probabilistic $(\\varepsilon,\\delta)$-spectral sparsifier with $O(n\\log n/\\varepsilon^{2})$ edges in time $\\tilde{O}(n/\\varepsilon^{2}\\delta)$ time for unweighted undirected graph. This gives fastest known sub-linear time algorithms for different cut problems on unweighted undirec","authors_text":"Yin Tat Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-31T03:58:45Z","title":"Probabilistic Spectral Sparsification In Sublinear Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0085","kind":"arxiv","version":1},"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":"sha256:203d53db2909628b1bf09a3e9c263a35e17328cff76409c675d5956557507edb","target":"record","created_at":"2026-05-18T03:03:31Z","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":"d3eb8f96fc3affea71e57df2d1c85b64723c94831968cd12222b800837cef44a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-31T03:58:45Z","title_canon_sha256":"e329d8d7a45b38d6ddd802eb3e72e3783065feeb26239dd586298f9cb16db1e5"},"schema_version":"1.0","source":{"id":"1401.0085","kind":"arxiv","version":1}},"canonical_sha256":"8860011713b9f9ac626fd0ad13deda8ab4c169ee8ccc70cd26647868219e6725","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8860011713b9f9ac626fd0ad13deda8ab4c169ee8ccc70cd26647868219e6725","first_computed_at":"2026-05-18T03:03:31.092872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:31.092872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PSCgbp+PacgcbWL7HeJzrihomAS1qAmTf6CsZ4AMkDQLPrQ05ul2echuDK7cpfyEa8zwhpwvt1Fq0vZEqo3jCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:31.093360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0085","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:203d53db2909628b1bf09a3e9c263a35e17328cff76409c675d5956557507edb","sha256:593fb378b652ab8690b0e501c52b490b128dfe2d5f6d9eac2f25099ebd7ef95a"],"state_sha256":"3ffaed63ac65f9294aea8679641f45cdb44351b6b4a41041478017f698445934"}