{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RBQACFYTXH42YYTP2CWRHXW2RK","short_pith_number":"pith:RBQACFYT","canonical_record":{"source":{"id":"1401.0085","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-31T03:58:45Z","cross_cats_sorted":[],"title_canon_sha256":"e329d8d7a45b38d6ddd802eb3e72e3783065feeb26239dd586298f9cb16db1e5","abstract_canon_sha256":"d3eb8f96fc3affea71e57df2d1c85b64723c94831968cd12222b800837cef44a"},"schema_version":"1.0"},"canonical_sha256":"8860011713b9f9ac626fd0ad13deda8ab4c169ee8ccc70cd26647868219e6725","source":{"kind":"arxiv","id":"1401.0085","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RBQACFYTXH42YYTP2CWRHXW2RK","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0085","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-31T03:58:45Z","cross_cats_sorted":[],"title_canon_sha256":"e329d8d7a45b38d6ddd802eb3e72e3783065feeb26239dd586298f9cb16db1e5","abstract_canon_sha256":"d3eb8f96fc3affea71e57df2d1c85b64723c94831968cd12222b800837cef44a"},"schema_version":"1.0"},"canonical_sha256":"8860011713b9f9ac626fd0ad13deda8ab4c169ee8ccc70cd26647868219e6725","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:31.093360Z","signature_b64":"PSCgbp+PacgcbWL7HeJzrihomAS1qAmTf6CsZ4AMkDQLPrQ05ul2echuDK7cpfyEa8zwhpwvt1Fq0vZEqo3jCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8860011713b9f9ac626fd0ad13deda8ab4c169ee8ccc70cd26647868219e6725","last_reissued_at":"2026-05-18T03:03:31.092872Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:31.092872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0085","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZQGkXgSy1gbq7rZYVqsulkTk/3+YjO+b/9yL6JLZ8fqqES2Qspdj/lnvR7qRA+Oh2oQlQ+hflkQEUpOcN0DpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:29:09.734773Z"},"content_sha256":"203d53db2909628b1bf09a3e9c263a35e17328cff76409c675d5956557507edb","schema_version":"1.0","event_id":"sha256:203d53db2909628b1bf09a3e9c263a35e17328cff76409c675d5956557507edb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RBQACFYTXH42YYTP2CWRHXW2RK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Probabilistic Spectral Sparsification In Sublinear Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Yin Tat Lee","submitted_at":"2013-12-31T03:58:45Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0085","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LXT4GuZdoreitxZ1BKvcg2tcAtfK6z09fDjKbiB8RsIaHqnf4FPMJld617ifXq1nZcf79b8oqb6o2hRd1671Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:29:09.735122Z"},"content_sha256":"593fb378b652ab8690b0e501c52b490b128dfe2d5f6d9eac2f25099ebd7ef95a","schema_version":"1.0","event_id":"sha256:593fb378b652ab8690b0e501c52b490b128dfe2d5f6d9eac2f25099ebd7ef95a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBQACFYTXH42YYTP2CWRHXW2RK/bundle.json","state_url":"https://pith.science/pith/RBQACFYTXH42YYTP2CWRHXW2RK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBQACFYTXH42YYTP2CWRHXW2RK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-29T19:29:09Z","links":{"resolver":"https://pith.science/pith/RBQACFYTXH42YYTP2CWRHXW2RK","bundle":"https://pith.science/pith/RBQACFYTXH42YYTP2CWRHXW2RK/bundle.json","state":"https://pith.science/pith/RBQACFYTXH42YYTP2CWRHXW2RK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBQACFYTXH42YYTP2CWRHXW2RK/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AXjADaAoeHiGHGVO78+mk9DA+8xOoIM6ddZIri7gvTlCF7HSHeMN0a58b3yse6NyY0C8bevlow+tqAh+lOHwDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T19:29:09.737812Z","bundle_sha256":"9c2eceec46e157e888e18c17bdb7086c42b08e996a61f7dcc8f7570383aa7d8a"}}