{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MVSKDYPRXMSJNRR25K24D2TVI7","short_pith_number":"pith:MVSKDYPR","canonical_record":{"source":{"id":"1805.06387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-05-16T16:00:19Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"e099b9496d760e1d820899b43c9e1ceb07c4c00db51d53413fe3f239852242ef","abstract_canon_sha256":"83f165186067d88edf4f51021abed312904d7e652f56f567dda9e98773cf2dd6"},"schema_version":"1.0"},"canonical_sha256":"6564a1e1f1bb2496c63aeab5c1ea7547e572cc705e8d89f00a10f21b70388669","source":{"kind":"arxiv","id":"1805.06387","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06387","created_at":"2026-05-18T00:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06387v1","created_at":"2026-05-18T00:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06387","created_at":"2026-05-18T00:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"MVSKDYPRXMSJ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MVSKDYPRXMSJNRR2","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MVSKDYPR","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MVSKDYPRXMSJNRR25K24D2TVI7","target":"record","payload":{"canonical_record":{"source":{"id":"1805.06387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-05-16T16:00:19Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"e099b9496d760e1d820899b43c9e1ceb07c4c00db51d53413fe3f239852242ef","abstract_canon_sha256":"83f165186067d88edf4f51021abed312904d7e652f56f567dda9e98773cf2dd6"},"schema_version":"1.0"},"canonical_sha256":"6564a1e1f1bb2496c63aeab5c1ea7547e572cc705e8d89f00a10f21b70388669","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:47.911342Z","signature_b64":"AxRoD3CtWs31SQ5F0HvnOSV2zZF8zjIyVJBkCWH72CCq+JCpIQg4wIOtX3ycRIAh2PVKocr8BFDidK6GCO3HBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6564a1e1f1bb2496c63aeab5c1ea7547e572cc705e8d89f00a10f21b70388669","last_reissued_at":"2026-05-18T00:15:47.910670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:47.910670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.06387","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HFdBmJeYdVqTcDG1dqEm845XiYtEA8fozWhAlTsJNK/V9VkPL6oGq9fSi65tGTdc1PxEFk4zCE1Sv9foRhs9Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:28:33.972183Z"},"content_sha256":"8581f12b22087c7e38011fea65defbca0b067e864cfc7f7e614f67c62e62e1eb","schema_version":"1.0","event_id":"sha256:8581f12b22087c7e38011fea65defbca0b067e864cfc7f7e614f67c62e62e1eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MVSKDYPRXMSJNRR25K24D2TVI7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Near-Optimal Communication Lower Bounds for Approximate Nash Equilibria","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.CC","authors_text":"Aviad Rubinstein, Mika G\\\"o\\\"os","submitted_at":"2018-05-16T16:00:19Z","abstract_excerpt":"We prove an $N^{2-o(1)}$ lower bound on the randomized communication complexity of finding an $\\epsilon$-approximate Nash equilibrium (for constant $\\epsilon>0$) in a two-player $N\\times N$ game."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06387","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sr5K9MEPKYkHiabGDeDX1Oyc0uvBq8E/nr4YA16l/cBAAbydOj8PoY2x1MK19HlbNLfJz7uaZpOkh21KMv9YCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:28:33.972909Z"},"content_sha256":"a1f57c32b31657138ecfa93843ceb6e864177093c5db5906be66d7d7d6c24f7e","schema_version":"1.0","event_id":"sha256:a1f57c32b31657138ecfa93843ceb6e864177093c5db5906be66d7d7d6c24f7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MVSKDYPRXMSJNRR25K24D2TVI7/bundle.json","state_url":"https://pith.science/pith/MVSKDYPRXMSJNRR25K24D2TVI7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MVSKDYPRXMSJNRR25K24D2TVI7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T20:28:33Z","links":{"resolver":"https://pith.science/pith/MVSKDYPRXMSJNRR25K24D2TVI7","bundle":"https://pith.science/pith/MVSKDYPRXMSJNRR25K24D2TVI7/bundle.json","state":"https://pith.science/pith/MVSKDYPRXMSJNRR25K24D2TVI7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MVSKDYPRXMSJNRR25K24D2TVI7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MVSKDYPRXMSJNRR25K24D2TVI7","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":"83f165186067d88edf4f51021abed312904d7e652f56f567dda9e98773cf2dd6","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-05-16T16:00:19Z","title_canon_sha256":"e099b9496d760e1d820899b43c9e1ceb07c4c00db51d53413fe3f239852242ef"},"schema_version":"1.0","source":{"id":"1805.06387","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06387","created_at":"2026-05-18T00:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06387v1","created_at":"2026-05-18T00:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06387","created_at":"2026-05-18T00:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"MVSKDYPRXMSJ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MVSKDYPRXMSJNRR2","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MVSKDYPR","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:a1f57c32b31657138ecfa93843ceb6e864177093c5db5906be66d7d7d6c24f7e","target":"graph","created_at":"2026-05-18T00:15:47Z","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 prove an $N^{2-o(1)}$ lower bound on the randomized communication complexity of finding an $\\epsilon$-approximate Nash equilibrium (for constant $\\epsilon>0$) in a two-player $N\\times N$ game.","authors_text":"Aviad Rubinstein, Mika G\\\"o\\\"os","cross_cats":["cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-05-16T16:00:19Z","title":"Near-Optimal Communication Lower Bounds for Approximate Nash Equilibria"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06387","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":"sha256:8581f12b22087c7e38011fea65defbca0b067e864cfc7f7e614f67c62e62e1eb","target":"record","created_at":"2026-05-18T00:15:47Z","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":"83f165186067d88edf4f51021abed312904d7e652f56f567dda9e98773cf2dd6","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-05-16T16:00:19Z","title_canon_sha256":"e099b9496d760e1d820899b43c9e1ceb07c4c00db51d53413fe3f239852242ef"},"schema_version":"1.0","source":{"id":"1805.06387","kind":"arxiv","version":1}},"canonical_sha256":"6564a1e1f1bb2496c63aeab5c1ea7547e572cc705e8d89f00a10f21b70388669","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6564a1e1f1bb2496c63aeab5c1ea7547e572cc705e8d89f00a10f21b70388669","first_computed_at":"2026-05-18T00:15:47.910670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:47.910670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AxRoD3CtWs31SQ5F0HvnOSV2zZF8zjIyVJBkCWH72CCq+JCpIQg4wIOtX3ycRIAh2PVKocr8BFDidK6GCO3HBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:47.911342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.06387","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8581f12b22087c7e38011fea65defbca0b067e864cfc7f7e614f67c62e62e1eb","sha256:a1f57c32b31657138ecfa93843ceb6e864177093c5db5906be66d7d7d6c24f7e"],"state_sha256":"99792c4c416b96de08b21e8cb005117ff0db7ea7faccf653ba26e7b107a1d10b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vjJ+3e0DhgTstePVnTuQ5SfEn6HOtM9QcA9e4PUG7OzAlHkHuZLwlENcacI62CqyiOdqRN/YxGlKbKOG27kiCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:28:33.976748Z","bundle_sha256":"2d0b68164cbc99e6a6e2925f1bb7a574824099e22b3d3cea50287f0b4769a614"}}