{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZZRHQYHXISST3VABS7BKYWFWVO","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":"157e2e5393673cc469ef74b6eb3193f828f6978f0dc8b82a6a46d0578bdb810f","cross_cats_sorted":["cs.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2015-04-30T13:16:48Z","title_canon_sha256":"e918dfae9be50bd4b74428ae5d4dedd319306b7bdc77c75a8f4c76119352e333"},"schema_version":"1.0","source":{"id":"1504.08211","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.08211","created_at":"2026-05-18T00:30:09Z"},{"alias_kind":"arxiv_version","alias_value":"1504.08211v2","created_at":"2026-05-18T00:30:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08211","created_at":"2026-05-18T00:30:09Z"},{"alias_kind":"pith_short_12","alias_value":"ZZRHQYHXISST","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZZRHQYHXISST3VAB","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZZRHQYHX","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:426701931dbd9303b60291e9c8420cb807bb01edec85deb231ac6c3b46332b0a","target":"graph","created_at":"2026-05-18T00:30:09Z","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 beyond worst-case threshold problem (BWC), recently introduced by Bruy\\`ere et al., asks given a quantitative game graph for the synthesis of a strategy that i) enforces some minimal level of performance against any adversary, and ii) achieves a good expectation against a stochastic model of the adversary. They solved the BWC problem for finite-memory strategies and unidimensional mean-payoff objectives and they showed membership of the problem in NP$\\cap$coNP. They also noted that infinite-memory strategies are more powerful than finite-memory ones, but the respective threshold problem wa","authors_text":"Jean-Fran\\c{c}ois Raskin, Lorenzo Clemente","cross_cats":["cs.SY"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2015-04-30T13:16:48Z","title":"Multidimensional beyond worst-case and almost-sure problems for mean-payoff objectives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08211","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:b47cdebbfd6614ac63df62d3991a42f347237a6d93fb198ed94257db6d918b57","target":"record","created_at":"2026-05-18T00:30:09Z","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":"157e2e5393673cc469ef74b6eb3193f828f6978f0dc8b82a6a46d0578bdb810f","cross_cats_sorted":["cs.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2015-04-30T13:16:48Z","title_canon_sha256":"e918dfae9be50bd4b74428ae5d4dedd319306b7bdc77c75a8f4c76119352e333"},"schema_version":"1.0","source":{"id":"1504.08211","kind":"arxiv","version":2}},"canonical_sha256":"ce627860f744a53dd40197c2ac58b6ab9a45cf74a496f4a6651b5ef5624c59f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce627860f744a53dd40197c2ac58b6ab9a45cf74a496f4a6651b5ef5624c59f3","first_computed_at":"2026-05-18T00:30:09.551647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:09.551647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u0QaTxMqzc3ZYxAIb/N+Ka7Nnab+z/wv/p7l2SSCDUQYJIiPVQCvbP/5TpNA2npz+KIAQ3HM93KBFAVCiIGHBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:09.552383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.08211","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b47cdebbfd6614ac63df62d3991a42f347237a6d93fb198ed94257db6d918b57","sha256:426701931dbd9303b60291e9c8420cb807bb01edec85deb231ac6c3b46332b0a"],"state_sha256":"cce6785ac20657a8876d6065786f98f26c8e9477062c39dfef024ccfa4919f77"}