{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BVP2QUI54D3CCDQW4TDY2BBLF7","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":"1c52edc3b78cfb32d6b1f264b19cba79a5e161d5757c4e267aa0ee63afcf1cd6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-17T13:33:23Z","title_canon_sha256":"6acedf26f72c68ba371bcfa38780c6c6be262dbd210558c4192ab5083abcf2a4"},"schema_version":"1.0","source":{"id":"1412.5381","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5381","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5381v1","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5381","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"BVP2QUI54D3C","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BVP2QUI54D3CCDQW","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BVP2QUI5","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:82a65607850d419280d07da7aa9a112922da58ddf3d70703459761a2079f0546","target":"graph","created_at":"2026-05-18T02:31:03Z","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 show that the shadow vertex simplex algorithm can be used to solve linear programs in strongly polynomial time with respect to the number $n$ of variables, the number $m$ of constraints, and $1/\\delta$, where $\\delta$ is a parameter that measures the flatness of the vertices of the polyhedron. This extends our recent result that the shadow vertex algorithm finds paths of polynomial length (w.r.t. $n$, $m$, and $1/\\delta$) between two given vertices of a polyhedron.\n  Our result also complements a recent result due to Eisenbrand and Vempala who have shown that a certain version of the random","authors_text":"Anna Gro{\\ss}wendt, Heiko R\\\"oglin, Tobias Brunsch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-17T13:33:23Z","title":"Solving Totally Unimodular LPs with the Shadow Vertex Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5381","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:d41f1aefb29c3c40a7d67b01ab9dfd89d3c485c0f00f3a83d2292c33da7f3068","target":"record","created_at":"2026-05-18T02:31:03Z","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":"1c52edc3b78cfb32d6b1f264b19cba79a5e161d5757c4e267aa0ee63afcf1cd6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-17T13:33:23Z","title_canon_sha256":"6acedf26f72c68ba371bcfa38780c6c6be262dbd210558c4192ab5083abcf2a4"},"schema_version":"1.0","source":{"id":"1412.5381","kind":"arxiv","version":1}},"canonical_sha256":"0d5fa8511de0f6210e16e4c78d042b2ff4cd28c1f0eda30f4b0488f634f95d8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d5fa8511de0f6210e16e4c78d042b2ff4cd28c1f0eda30f4b0488f634f95d8e","first_computed_at":"2026-05-18T02:31:03.084385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:03.084385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kO3iyL9jnTjAZDRZwctyy4faOEqHKjoJXWheIHi7jxVS62xCwsHRhfrRnWw/HDCgqv7XpxHqDSgoPnzu7nFbAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:03.084780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5381","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d41f1aefb29c3c40a7d67b01ab9dfd89d3c485c0f00f3a83d2292c33da7f3068","sha256:82a65607850d419280d07da7aa9a112922da58ddf3d70703459761a2079f0546"],"state_sha256":"363ba1610416ce62f6a65fa709d21ef36a23af1afc8df45235fd7b8595973496"}