{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:X6XEFW2XE4D7ZWTPSYRHEOL5IL","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":"9be51529acece381ef8cac70cdbcb21c9a74572a8ff6d40bec6963aad407626f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-03-27T14:42:11Z","title_canon_sha256":"595712734bef7b18b3e01351784d7ddba05c6b380267e90765b650d748182567"},"schema_version":"1.0","source":{"id":"1403.7058","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7058","created_at":"2026-05-18T02:38:10Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7058v2","created_at":"2026-05-18T02:38:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7058","created_at":"2026-05-18T02:38:10Z"},{"alias_kind":"pith_short_12","alias_value":"X6XEFW2XE4D7","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"X6XEFW2XE4D7ZWTP","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"X6XEFW2X","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:4712a0e116ca5aad2fe86aac339dc8154fb6f2a068f7bb8ff653781bfcdc5106","target":"graph","created_at":"2026-05-18T02:38:10Z","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 study the problem of sketching an input graph, so that given the sketch, one can estimate the weight of any cut in the graph within factor $1+\\epsilon$. We present lower and upper bounds on the size of a randomized sketch, focusing on the dependence on the accuracy parameter $\\epsilon>0$.\n  First, we prove that for every $\\epsilon > 1/\\sqrt n$, every sketch that succeeds (with constant probability) in estimating the weight of all cuts $(S,\\bar S)$ in an $n$-vertex graph (simultaneously), must be of size $\\Omega(n/\\epsilon^2)$ bits. In the special case where the sketch is itself a weighted g","authors_text":"Alexandr Andoni, David P. Woodruff, Robert Krauthgamer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-03-27T14:42:11Z","title":"The Sketching Complexity of Graph Cuts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7058","kind":"arxiv","version":2},"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":"sha256:560bc875d340a0cda8127a48a4e15f47a6f0b9fe35f16b2beed3b3e70e589fdb","target":"record","created_at":"2026-05-18T02:38:10Z","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":"9be51529acece381ef8cac70cdbcb21c9a74572a8ff6d40bec6963aad407626f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-03-27T14:42:11Z","title_canon_sha256":"595712734bef7b18b3e01351784d7ddba05c6b380267e90765b650d748182567"},"schema_version":"1.0","source":{"id":"1403.7058","kind":"arxiv","version":2}},"canonical_sha256":"bfae42db572707fcda6f962272397d42f0554c30db06fda1a6dad7f8fee142c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfae42db572707fcda6f962272397d42f0554c30db06fda1a6dad7f8fee142c0","first_computed_at":"2026-05-18T02:38:10.105714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:10.105714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8Apw+9hKSoPVcl6oDrvg3r2420hicMtPImIcOvCO5mkw6ZVVWPna8l2EO6e2u+xeNv96wHQ6Uwzdg6W6G21qDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:10.106361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.7058","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:560bc875d340a0cda8127a48a4e15f47a6f0b9fe35f16b2beed3b3e70e589fdb","sha256:4712a0e116ca5aad2fe86aac339dc8154fb6f2a068f7bb8ff653781bfcdc5106"],"state_sha256":"1b3acb61c634cb3504062c6e4dcd0a8e5e2f0ae3ec10aa9794e844daaa68de5f"}