{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EBCKH3M2CCLXXIA7HFVHKOB5G5","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":"dbcc0986eeac57b8bc8533e828f76df5289f26a5379234cca34ba9b7648b1115","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2018-09-10T02:29:06Z","title_canon_sha256":"62994bb1a6699a6218c0cde1472a13b9270b2ff2837956c59f5b9aaa65b80754"},"schema_version":"1.0","source":{"id":"1809.03887","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03887","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03887v1","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03887","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"EBCKH3M2CCLX","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EBCKH3M2CCLXXIA7","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EBCKH3M2","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:f70a631c2e8bbed69ad7441a4fe578b3b09a6a9780786dec54d2f803ca4294ea","target":"graph","created_at":"2026-05-18T00:05:57Z","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"},"paper":{"abstract_excerpt":"We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable properties as their qualitative counterparts and additionally retain the optimality of solutions. Moreover, we introduce vertex-ranked games as a general-purpose target for quantitative reductions and show how to solve them. In such games, the value of a play is determined only by a qualitative winning condition and a ranking of the vertices.\n  We provide quantitat","authors_text":"Alexander Weinert (Saarland University, Germany)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2018-09-10T02:29:06Z","title":"Quantitative Reductions and Vertex-Ranked Infinite Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03887","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:b1ce3098a663cf06567ccb65bb64cc95af3a4771c524d438cda4829a75ddd8ff","target":"record","created_at":"2026-05-18T00:05:57Z","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":"dbcc0986eeac57b8bc8533e828f76df5289f26a5379234cca34ba9b7648b1115","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2018-09-10T02:29:06Z","title_canon_sha256":"62994bb1a6699a6218c0cde1472a13b9270b2ff2837956c59f5b9aaa65b80754"},"schema_version":"1.0","source":{"id":"1809.03887","kind":"arxiv","version":1}},"canonical_sha256":"2044a3ed9a10977ba01f396a75383d3744114439c70c93375f994b5218107699","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2044a3ed9a10977ba01f396a75383d3744114439c70c93375f994b5218107699","first_computed_at":"2026-05-18T00:05:57.817020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:57.817020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cpfqMH/s6nW0QgoGd2TJrNTeQbhgfmWvogI/eYSo18Knc9boQmCX3C4N3hviHlv7Hn4q8oaKrjIhLCVnRMnEBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:57.817450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.03887","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1ce3098a663cf06567ccb65bb64cc95af3a4771c524d438cda4829a75ddd8ff","sha256:f70a631c2e8bbed69ad7441a4fe578b3b09a6a9780786dec54d2f803ca4294ea"],"state_sha256":"73ff509dbf000e1a663bfadc254e0a01adca5c85934f66a59303e5241244f0c8"}