{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7FTE5IJ6TPUJVS7WVB746IYI26","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":"aed6d6c9d48f434b134016ef4fdcd0631e0ebebb054da3b5bb70b8ec8b1d542d","cross_cats_sorted":["cs.GT","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2026-06-21T22:08:00Z","title_canon_sha256":"a6de6cdda596da784e2b4810d947b6182364ba5feece7ef1b38d818338c05a3f"},"schema_version":"1.0","source":{"id":"2606.22688","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22688","created_at":"2026-06-23T02:13:44Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22688v1","created_at":"2026-06-23T02:13:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22688","created_at":"2026-06-23T02:13:44Z"},{"alias_kind":"pith_short_12","alias_value":"7FTE5IJ6TPUJ","created_at":"2026-06-23T02:13:44Z"},{"alias_kind":"pith_short_16","alias_value":"7FTE5IJ6TPUJVS7W","created_at":"2026-06-23T02:13:44Z"},{"alias_kind":"pith_short_8","alias_value":"7FTE5IJ6","created_at":"2026-06-23T02:13:44Z"}],"graph_snapshots":[{"event_id":"sha256:1762d600e0d7ae1273d51a1cdee7120263352302efbef201e63bf8486c37c906","target":"graph","created_at":"2026-06-23T02:13:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.22688/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Self-play with naive gradient ascent cycles in two-player zero-sum games: the last iterate orbits the equilibrium. Modern methods restore last-iterate convergence by regularizing toward a reference policy -- MMD a fixed one (reaching only the regularized equilibrium), R-NaD a periodic snapshot (the engine of DeepNash). We study GARIP, which anchors to the running average, and isolate what the choice of reference controls. Our central result is a mechanism: collapse tracks the peak lag of the reference, and among causal convex averages of a fixed mean lag the running average (flat profile, peak","authors_text":"Can Savc{\\i}","cross_cats":["cs.GT","cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2026-06-21T22:08:00Z","title":"GARIP: A Running-Average Moving Reference for Last-Iterate Self-Play in Two-Player Zero-Sum Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22688","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":"sha256:684ed2a7904ec66a2108556c1e1b1a8dc20d0c49dc0b5de9ac49b284b21fe2e3","target":"record","created_at":"2026-06-23T02:13:44Z","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":"aed6d6c9d48f434b134016ef4fdcd0631e0ebebb054da3b5bb70b8ec8b1d542d","cross_cats_sorted":["cs.GT","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2026-06-21T22:08:00Z","title_canon_sha256":"a6de6cdda596da784e2b4810d947b6182364ba5feece7ef1b38d818338c05a3f"},"schema_version":"1.0","source":{"id":"2606.22688","kind":"arxiv","version":1}},"canonical_sha256":"f9664ea13e9be89acbf6a87fcf2308d7a965331af8f726f7df89f99674cbd71d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9664ea13e9be89acbf6a87fcf2308d7a965331af8f726f7df89f99674cbd71d","first_computed_at":"2026-06-23T02:13:44.872020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:44.872020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r0DS54vVvsBKTANUqS8uT7loLsxUha7HqYcliRAB1QAKyE86GxpdgnV8iefnxxLOyz5vPLgPQmKx3egvUx3rDA==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:44.872425Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22688","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:684ed2a7904ec66a2108556c1e1b1a8dc20d0c49dc0b5de9ac49b284b21fe2e3","sha256:1762d600e0d7ae1273d51a1cdee7120263352302efbef201e63bf8486c37c906"],"state_sha256":"16b435f6bed9876451deda7882ed5e59d8f7b3ed5e6ad4f173a25fb94efdaf44"}