{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V74IKHDCF7EZXOY65LDGLSPWFU","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":"3e2cef729087b0e7b8ea4c6db081c690122a172e3b5cd65f5e1c5fb0e04f13d9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-05-18T14:53:25Z","title_canon_sha256":"27d16df1761c98e6404781e522189861cc3d692e463cf36b6f6ecad75b2a0bce"},"schema_version":"1.0","source":{"id":"1705.06631","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06631","created_at":"2026-05-18T00:44:14Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06631v1","created_at":"2026-05-18T00:44:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06631","created_at":"2026-05-18T00:44:14Z"},{"alias_kind":"pith_short_12","alias_value":"V74IKHDCF7EZ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V74IKHDCF7EZXOY6","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V74IKHDC","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:4e1ca37c402afbdc1d7f0a5d7cedcd9913324ae9e77f6adc76fbde1ca789db74","target":"graph","created_at":"2026-05-18T00:44:14Z","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":"The following game is played on a weighted graph: Alice selects a matching $M$ and Bob selects a number $k$. Alice's payoff is the ratio of the weight of the $k$ heaviest edges of $M$ to the maximum weight of a matching of size at most $k$. If $M$ guarantees a payoff of at least $\\alpha$ then it is called $\\alpha$-robust. In 2002, Hassin and Rubinstein gave an algorithm that returns a $1/\\sqrt{2}$-robust matching, which is best possible.\n  We show that Alice can improve her payoff to $1/\\ln(4)$ by playing a randomized strategy. This result extends to a very general class of independence system","authors_text":"Jannik Matuschke, Jos\\'e A. Soto, Martin Skutella","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-05-18T14:53:25Z","title":"Robust randomized matchings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06631","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":"sha256:31397b2ea09ed17b921cae18e50a1494925d453e51a5957f1c5e1330b318f4c6","target":"record","created_at":"2026-05-18T00:44:14Z","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":"3e2cef729087b0e7b8ea4c6db081c690122a172e3b5cd65f5e1c5fb0e04f13d9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-05-18T14:53:25Z","title_canon_sha256":"27d16df1761c98e6404781e522189861cc3d692e463cf36b6f6ecad75b2a0bce"},"schema_version":"1.0","source":{"id":"1705.06631","kind":"arxiv","version":1}},"canonical_sha256":"aff8851c622fc99bbb1eeac665c9f62d3834fb48dab77d6cf38f0fe8c3d8a9a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aff8851c622fc99bbb1eeac665c9f62d3834fb48dab77d6cf38f0fe8c3d8a9a1","first_computed_at":"2026-05-18T00:44:14.253457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:14.253457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BK/Lgb2zEwyBaqKuT3icxedRH9s7YhaXtAM4oYXJ5Y+19M7dHDQOP3rfS7++7MGswi2JhFan7+R6QW9CKakGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:14.253927Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.06631","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31397b2ea09ed17b921cae18e50a1494925d453e51a5957f1c5e1330b318f4c6","sha256:4e1ca37c402afbdc1d7f0a5d7cedcd9913324ae9e77f6adc76fbde1ca789db74"],"state_sha256":"795ade598e75300c9b344e8d0a3c323488251e450fc647004792fc0207b7a4cf"}