{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KEKQM3WUAWUJWNUBIGAWPVQZ4C","short_pith_number":"pith:KEKQM3WU","canonical_record":{"source":{"id":"1112.4109","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-12-18T02:41:12Z","cross_cats_sorted":[],"title_canon_sha256":"1d85e41a1a4167ec86c2d6eaa302c85b06a715e55e8c89ff4444930841b69513","abstract_canon_sha256":"a4e1e24e983d85ebf28590e40f50a38e9bdbd3ee172289b9a9ba7d7feb4236f9"},"schema_version":"1.0"},"canonical_sha256":"5115066ed405a89b3681418167d619e0bd3517c651abee073ea051ed3f2d2e41","source":{"kind":"arxiv","id":"1112.4109","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4109","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4109v4","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4109","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"pith_short_12","alias_value":"KEKQM3WUAWUJ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KEKQM3WUAWUJWNUB","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KEKQM3WU","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KEKQM3WUAWUJWNUBIGAWPVQZ4C","target":"record","payload":{"canonical_record":{"source":{"id":"1112.4109","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-12-18T02:41:12Z","cross_cats_sorted":[],"title_canon_sha256":"1d85e41a1a4167ec86c2d6eaa302c85b06a715e55e8c89ff4444930841b69513","abstract_canon_sha256":"a4e1e24e983d85ebf28590e40f50a38e9bdbd3ee172289b9a9ba7d7feb4236f9"},"schema_version":"1.0"},"canonical_sha256":"5115066ed405a89b3681418167d619e0bd3517c651abee073ea051ed3f2d2e41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:27.140103Z","signature_b64":"S2xpwz7Ys4pxV4Q771bvfRiB4NLCXiSrUvf1xLD6zDacWSS/PPQODg6i+Q4TS1ySP7vkGCmIdlr4S47ui4JqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5115066ed405a89b3681418167d619e0bd3517c651abee073ea051ed3f2d2e41","last_reissued_at":"2026-05-18T02:21:27.139477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:27.139477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.4109","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:21:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vHAtKcVY6m8CHqvcG4826bYo+PaUV5/SSr24Gl+0cSzrYKO0oFQ0LXB0mSlCcQGt4U8fjZco+/x9D9YdPyvHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:37:03.396191Z"},"content_sha256":"147c9ec9cd21146004502a7bd40e9eeecc34f3070fcd20eac5c84257be38a065","schema_version":"1.0","event_id":"sha256:147c9ec9cd21146004502a7bd40e9eeecc34f3070fcd20eac5c84257be38a065"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KEKQM3WUAWUJWNUBIGAWPVQZ4C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximating Non-Uniform Sparsest Cut via Generalized Spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ali Kemal Sinop, Venkatesan Guruswami","submitted_at":"2011-12-18T02:41:12Z","abstract_excerpt":"We give an approximation algorithm for non-uniform sparsest cut with the following guarantee: For any $\\epsilon,\\delta \\in (0,1)$, given cost and demand graphs with edge weights $C, D$ respectively, we can find a set $T\\subseteq V$ with $\\frac{C(T,V\\setminus T)}{D(T,V\\setminus T)}$ at most $\\frac{1+\\epsilon}{\\delta}$ times the optimal non-uniform sparsest cut value, in time $2^{r/(\\delta\\epsilon)}\\poly(n)$ provided $\\lambda_r \\ge \\Phi^*/(1-\\delta)$. Here $\\lambda_r$ is the $r$'th smallest generalized eigenvalue of the Laplacian matrices of cost and demand graphs; $C(T,V\\setminus T)$ (resp. $D("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4109","kind":"arxiv","version":4},"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":"2026-05-18T02:21:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HdM4GNBcAOP4KQ5GEEzN/Ax9ujupxkY04HCNFsXT6YFT4gzCO0m5MGjNGGHmEQTZ+2ueSBZvnBTJn9KAXEqYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:37:03.396924Z"},"content_sha256":"2f71bd32d6ff472f515eede1808cdc069bd24f27d356ca4b9645d05f9913a722","schema_version":"1.0","event_id":"sha256:2f71bd32d6ff472f515eede1808cdc069bd24f27d356ca4b9645d05f9913a722"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KEKQM3WUAWUJWNUBIGAWPVQZ4C/bundle.json","state_url":"https://pith.science/pith/KEKQM3WUAWUJWNUBIGAWPVQZ4C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KEKQM3WUAWUJWNUBIGAWPVQZ4C/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":"2026-06-01T06:37:03Z","links":{"resolver":"https://pith.science/pith/KEKQM3WUAWUJWNUBIGAWPVQZ4C","bundle":"https://pith.science/pith/KEKQM3WUAWUJWNUBIGAWPVQZ4C/bundle.json","state":"https://pith.science/pith/KEKQM3WUAWUJWNUBIGAWPVQZ4C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KEKQM3WUAWUJWNUBIGAWPVQZ4C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KEKQM3WUAWUJWNUBIGAWPVQZ4C","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":"a4e1e24e983d85ebf28590e40f50a38e9bdbd3ee172289b9a9ba7d7feb4236f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-12-18T02:41:12Z","title_canon_sha256":"1d85e41a1a4167ec86c2d6eaa302c85b06a715e55e8c89ff4444930841b69513"},"schema_version":"1.0","source":{"id":"1112.4109","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4109","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4109v4","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4109","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"pith_short_12","alias_value":"KEKQM3WUAWUJ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KEKQM3WUAWUJWNUB","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KEKQM3WU","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:2f71bd32d6ff472f515eede1808cdc069bd24f27d356ca4b9645d05f9913a722","target":"graph","created_at":"2026-05-18T02:21:27Z","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":"We give an approximation algorithm for non-uniform sparsest cut with the following guarantee: For any $\\epsilon,\\delta \\in (0,1)$, given cost and demand graphs with edge weights $C, D$ respectively, we can find a set $T\\subseteq V$ with $\\frac{C(T,V\\setminus T)}{D(T,V\\setminus T)}$ at most $\\frac{1+\\epsilon}{\\delta}$ times the optimal non-uniform sparsest cut value, in time $2^{r/(\\delta\\epsilon)}\\poly(n)$ provided $\\lambda_r \\ge \\Phi^*/(1-\\delta)$. Here $\\lambda_r$ is the $r$'th smallest generalized eigenvalue of the Laplacian matrices of cost and demand graphs; $C(T,V\\setminus T)$ (resp. $D(","authors_text":"Ali Kemal Sinop, Venkatesan Guruswami","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-12-18T02:41:12Z","title":"Approximating Non-Uniform Sparsest Cut via Generalized Spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4109","kind":"arxiv","version":4},"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":"sha256:147c9ec9cd21146004502a7bd40e9eeecc34f3070fcd20eac5c84257be38a065","target":"record","created_at":"2026-05-18T02:21:27Z","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":"a4e1e24e983d85ebf28590e40f50a38e9bdbd3ee172289b9a9ba7d7feb4236f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-12-18T02:41:12Z","title_canon_sha256":"1d85e41a1a4167ec86c2d6eaa302c85b06a715e55e8c89ff4444930841b69513"},"schema_version":"1.0","source":{"id":"1112.4109","kind":"arxiv","version":4}},"canonical_sha256":"5115066ed405a89b3681418167d619e0bd3517c651abee073ea051ed3f2d2e41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5115066ed405a89b3681418167d619e0bd3517c651abee073ea051ed3f2d2e41","first_computed_at":"2026-05-18T02:21:27.139477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:27.139477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S2xpwz7Ys4pxV4Q771bvfRiB4NLCXiSrUvf1xLD6zDacWSS/PPQODg6i+Q4TS1ySP7vkGCmIdlr4S47ui4JqDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:27.140103Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4109","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:147c9ec9cd21146004502a7bd40e9eeecc34f3070fcd20eac5c84257be38a065","sha256:2f71bd32d6ff472f515eede1808cdc069bd24f27d356ca4b9645d05f9913a722"],"state_sha256":"c275ffdaf83895fac16b295735a49d561fe471862e60299f1e18bf03cc7ff417"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TXyvL5kkF+DXt4SMkDsZCo9KBaCUeTsGhO3oh5I/vdkxA9C4VSCb6pWyFG26Yz2Y6ZVf9tYHAw+MpTTE1kYJBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:37:03.399572Z","bundle_sha256":"3a24a8cf70c170d2e93c9eb63227aef3a471be98454e18ba9f88c4eba9fba18c"}}