{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ENREMX5SOFIAZ5O27KSBNG7LYP","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":"0fb882b35b8ee8004bee6397e31d7d8ec5901cf22922341cc5d23f52828c0389","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-11-12T20:59:07Z","title_canon_sha256":"c937c1a7d56c50c7d7e64492cdd4e0a4a854a80d44c9ab5837c99b16b65cb25a"},"schema_version":"1.0","source":{"id":"1411.3320","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3320","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3320v1","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3320","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"pith_short_12","alias_value":"ENREMX5SOFIA","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"ENREMX5SOFIAZ5O2","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"ENREMX5S","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:946e0ad590ed8ff507188e198090420dc7f1fe389f9cd74be6ab9d8ffaa6f745","target":"graph","created_at":"2026-05-18T02:37:45Z","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":"This short paper concerns discretization schemes for representing and computing approximate Nash equilibria, with emphasis on graphical games, but briefly touching on normal-form and poly-matrix games. The main technical contribution is a representation theorem that informally states that to account for every exact Nash equilibrium using a nearby approximate Nash equilibrium on a grid over mixed strategies, a uniform discretization size linear on the inverse of the approximation quality and natural game-representation parameters suffices. For graphical games, under natural conditions, the disc","authors_text":"Luis E. Ortiz","cross_cats":["cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-11-12T20:59:07Z","title":"On Sparse Discretization for Graphical Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3320","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:aa57f8ff0995cae0b0639cbdc9d027f5e6f0f41a82d2e559846275f6a01fdb1b","target":"record","created_at":"2026-05-18T02:37:45Z","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":"0fb882b35b8ee8004bee6397e31d7d8ec5901cf22922341cc5d23f52828c0389","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-11-12T20:59:07Z","title_canon_sha256":"c937c1a7d56c50c7d7e64492cdd4e0a4a854a80d44c9ab5837c99b16b65cb25a"},"schema_version":"1.0","source":{"id":"1411.3320","kind":"arxiv","version":1}},"canonical_sha256":"2362465fb271500cf5dafaa4169bebc3fbd0a91375a09a09ed7e05642765020c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2362465fb271500cf5dafaa4169bebc3fbd0a91375a09a09ed7e05642765020c","first_computed_at":"2026-05-18T02:37:45.222627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:45.222627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E3VUKIGywjTYJzmXKDS7ZqhMdR+dxo3dhSeccoSOu8dijTUUw8SeIG/Ur6QkklZS2jrMSMqYtH1O+KrOqqOmCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:45.223125Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3320","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa57f8ff0995cae0b0639cbdc9d027f5e6f0f41a82d2e559846275f6a01fdb1b","sha256:946e0ad590ed8ff507188e198090420dc7f1fe389f9cd74be6ab9d8ffaa6f745"],"state_sha256":"4e130eea65aea85bfd7cbccbe7559117052e4a6bcf755075ddeac323fd19528f"}