{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:NSZMOQFT3I7UHPAHH4AD6BZ4BO","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":"9939399dd1e02d047fbca66792a39cf84a75a2da7e6f34e807c95e6d092019f5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2023-10-11T19:59:44Z","title_canon_sha256":"1e042deb46adba9bc11f1e04641022782f55efb87caa1f0bf4706037dbac6dad"},"schema_version":"1.0","source":{"id":"2310.07857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.07857","created_at":"2026-07-05T06:59:57Z"},{"alias_kind":"arxiv_version","alias_value":"2310.07857v1","created_at":"2026-07-05T06:59:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.07857","created_at":"2026-07-05T06:59:57Z"},{"alias_kind":"pith_short_12","alias_value":"NSZMOQFT3I7U","created_at":"2026-07-05T06:59:57Z"},{"alias_kind":"pith_short_16","alias_value":"NSZMOQFT3I7UHPAH","created_at":"2026-07-05T06:59:57Z"},{"alias_kind":"pith_short_8","alias_value":"NSZMOQFT","created_at":"2026-07-05T06:59:57Z"}],"graph_snapshots":[{"event_id":"sha256:b8bcb4be0c383b4f7f4d935d42e7401eb41822f4082fa8b5f51089584de79bf8","target":"graph","created_at":"2026-07-05T06:59:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.07857/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a large graph $G$ with a subset $|T|=k$ of its vertices called terminals, a quality-$q$ flow sparsifier is a small graph $G'$ that contains $T$ and preserves all multicommodity flows that can be routed between terminals in $T$, to within factor $q$. The problem of constructing flow sparsifiers with good (small) quality and (small) size has been a central problem in graph compression for decades.\n  A natural approach of constructing $O(1)$-quality flow sparsifiers, which was adopted in most previous constructions, is contraction. Andoni, Krauthgamer, and Gupta constructed a sketch of size","authors_text":"Yu Chen, Zihan Tan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2023-10-11T19:59:44Z","title":"On $(1+\\varepsilon)$-Approximate Flow Sparsifiers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.07857","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":"sha256:2741fa4bcea338ea80b6eddcdfe75a92958cecda8e32ca63ac6410a0e1e0c144","target":"record","created_at":"2026-07-05T06:59:57Z","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":"9939399dd1e02d047fbca66792a39cf84a75a2da7e6f34e807c95e6d092019f5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2023-10-11T19:59:44Z","title_canon_sha256":"1e042deb46adba9bc11f1e04641022782f55efb87caa1f0bf4706037dbac6dad"},"schema_version":"1.0","source":{"id":"2310.07857","kind":"arxiv","version":1}},"canonical_sha256":"6cb2c740b3da3f43bc073f003f073c0b95b61e656abccaf5be772a2ebcf5e52e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cb2c740b3da3f43bc073f003f073c0b95b61e656abccaf5be772a2ebcf5e52e","first_computed_at":"2026-07-05T06:59:57.458294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:59:57.458294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xh6O1E1GlpON5cQ5BfE9qwAIBQqkX8HYiM+LrJo9VI2+oz6URmXZWB65CuhT0PTKZCLhQT5hrWj7OtTf1KHsDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:59:57.458789Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.07857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2741fa4bcea338ea80b6eddcdfe75a92958cecda8e32ca63ac6410a0e1e0c144","sha256:b8bcb4be0c383b4f7f4d935d42e7401eb41822f4082fa8b5f51089584de79bf8"],"state_sha256":"b15b362c4b8952e09ff7fc6ed28702d5d9b46c03fb7281d727a8052d099b1ac3"}