{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LB4Q77KRIB2GSCQ5JGJRUJPHTR","short_pith_number":"pith:LB4Q77KR","canonical_record":{"source":{"id":"1708.02394","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-08T07:43:59Z","cross_cats_sorted":[],"title_canon_sha256":"12e992d12e864a8d77c3ccd7cba4116e4e4212652b9f89f2fa1b3b2cddc3117c","abstract_canon_sha256":"7d025c8433e396f18771a8f66e365e218ed604d5da01931b1421563b8bba8843"},"schema_version":"1.0"},"canonical_sha256":"58790ffd514074690a1d49931a25e79c6059c1b93fd8c7a28e304c0268ce8ff7","source":{"kind":"arxiv","id":"1708.02394","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02394","created_at":"2026-05-17T23:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02394v3","created_at":"2026-05-17T23:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02394","created_at":"2026-05-17T23:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"LB4Q77KRIB2G","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LB4Q77KRIB2GSCQ5","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LB4Q77KR","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LB4Q77KRIB2GSCQ5JGJRUJPHTR","target":"record","payload":{"canonical_record":{"source":{"id":"1708.02394","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-08T07:43:59Z","cross_cats_sorted":[],"title_canon_sha256":"12e992d12e864a8d77c3ccd7cba4116e4e4212652b9f89f2fa1b3b2cddc3117c","abstract_canon_sha256":"7d025c8433e396f18771a8f66e365e218ed604d5da01931b1421563b8bba8843"},"schema_version":"1.0"},"canonical_sha256":"58790ffd514074690a1d49931a25e79c6059c1b93fd8c7a28e304c0268ce8ff7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:22.990292Z","signature_b64":"4EXFy9nSTL/FgPF96EhH2rFJeU6eY5TKKBNF4Y+/TFx7V9T44dz1QbqQmRqYUYoIKLtEg2bYyT2NcXBfeKpwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58790ffd514074690a1d49931a25e79c6059c1b93fd8c7a28e304c0268ce8ff7","last_reissued_at":"2026-05-17T23:44:22.989629Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:22.989629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.02394","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kl31ZGbaHIyhbgonRpf1DTfJXEeevCCKB6dIo2WlIqiQG6sBaK9wn+2gN+7RtDe+X18HjAfjJvwttIBhj+bvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T17:53:39.993433Z"},"content_sha256":"79486ffc2d164e3736a924896719d13c311db915a755d76f990d3e1164ce14b6","schema_version":"1.0","event_id":"sha256:79486ffc2d164e3736a924896719d13c311db915a755d76f990d3e1164ce14b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LB4Q77KRIB2GSCQ5JGJRUJPHTR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Unified Strategy for Solution Seeking in Graphical N-coalition Noncooperative Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Frank L. Lewis, Guoqiang Hu, Lihua Xie, Maojiao Ye","submitted_at":"2017-08-08T07:43:59Z","abstract_excerpt":"This paper aims to reduce the communication and computation costs of the Nash equilibrium seeking strategy for the $N$-coalition noncooperative games proposed in [1]. The objective is achieved in two manners: 1. An interference graph is introduced to describe the interactions among the agents in each coalition. 2. The Nash equilibrium seeking strategy is designed with the interference graphs considered. The convergence property of the proposed Nash equilibrium seeking strategy is analytically investigated. It is shown that the agents' actions generated by the proposed method converge to a neig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02394","kind":"arxiv","version":3},"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":"2026-05-17T23:44:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2CNJOT7mvWKJ5VlvPIFxO99ddVCuEv1vY9kC/Mk2x4knAkqARRTKNkM1oaGpMNGuzqrNwZtxG489Yid7tmroAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T17:53:39.993770Z"},"content_sha256":"999712e1283faebf71a82942b574a501d3ae0800d210d80ecf25e790c06d8e79","schema_version":"1.0","event_id":"sha256:999712e1283faebf71a82942b574a501d3ae0800d210d80ecf25e790c06d8e79"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LB4Q77KRIB2GSCQ5JGJRUJPHTR/bundle.json","state_url":"https://pith.science/pith/LB4Q77KRIB2GSCQ5JGJRUJPHTR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LB4Q77KRIB2GSCQ5JGJRUJPHTR/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":"2026-06-26T17:53:39Z","links":{"resolver":"https://pith.science/pith/LB4Q77KRIB2GSCQ5JGJRUJPHTR","bundle":"https://pith.science/pith/LB4Q77KRIB2GSCQ5JGJRUJPHTR/bundle.json","state":"https://pith.science/pith/LB4Q77KRIB2GSCQ5JGJRUJPHTR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LB4Q77KRIB2GSCQ5JGJRUJPHTR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LB4Q77KRIB2GSCQ5JGJRUJPHTR","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":"7d025c8433e396f18771a8f66e365e218ed604d5da01931b1421563b8bba8843","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-08T07:43:59Z","title_canon_sha256":"12e992d12e864a8d77c3ccd7cba4116e4e4212652b9f89f2fa1b3b2cddc3117c"},"schema_version":"1.0","source":{"id":"1708.02394","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02394","created_at":"2026-05-17T23:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02394v3","created_at":"2026-05-17T23:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02394","created_at":"2026-05-17T23:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"LB4Q77KRIB2G","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LB4Q77KRIB2GSCQ5","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LB4Q77KR","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:999712e1283faebf71a82942b574a501d3ae0800d210d80ecf25e790c06d8e79","target":"graph","created_at":"2026-05-17T23:44:22Z","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 paper aims to reduce the communication and computation costs of the Nash equilibrium seeking strategy for the $N$-coalition noncooperative games proposed in [1]. The objective is achieved in two manners: 1. An interference graph is introduced to describe the interactions among the agents in each coalition. 2. The Nash equilibrium seeking strategy is designed with the interference graphs considered. The convergence property of the proposed Nash equilibrium seeking strategy is analytically investigated. It is shown that the agents' actions generated by the proposed method converge to a neig","authors_text":"Frank L. Lewis, Guoqiang Hu, Lihua Xie, Maojiao Ye","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-08T07:43:59Z","title":"A Unified Strategy for Solution Seeking in Graphical N-coalition Noncooperative Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02394","kind":"arxiv","version":3},"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":"sha256:79486ffc2d164e3736a924896719d13c311db915a755d76f990d3e1164ce14b6","target":"record","created_at":"2026-05-17T23:44:22Z","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":"7d025c8433e396f18771a8f66e365e218ed604d5da01931b1421563b8bba8843","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-08T07:43:59Z","title_canon_sha256":"12e992d12e864a8d77c3ccd7cba4116e4e4212652b9f89f2fa1b3b2cddc3117c"},"schema_version":"1.0","source":{"id":"1708.02394","kind":"arxiv","version":3}},"canonical_sha256":"58790ffd514074690a1d49931a25e79c6059c1b93fd8c7a28e304c0268ce8ff7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58790ffd514074690a1d49931a25e79c6059c1b93fd8c7a28e304c0268ce8ff7","first_computed_at":"2026-05-17T23:44:22.989629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:22.989629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4EXFy9nSTL/FgPF96EhH2rFJeU6eY5TKKBNF4Y+/TFx7V9T44dz1QbqQmRqYUYoIKLtEg2bYyT2NcXBfeKpwDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:22.990292Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.02394","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79486ffc2d164e3736a924896719d13c311db915a755d76f990d3e1164ce14b6","sha256:999712e1283faebf71a82942b574a501d3ae0800d210d80ecf25e790c06d8e79"],"state_sha256":"e55acae1072a72e6742bd82b73cb0a71cb08217b046f476586a08a4ebda73e63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AeTakDF+XNYcLt8GxVwv+7pLx52dnvzhymMUmR1gBs6ylpvvvVxOwzqvOoI6z69KmzxenTDeuYMD/SFVBKA/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T17:53:39.995615Z","bundle_sha256":"7703e99bed185d45b9ee5b4fc6f8bd28d818c308b1c4a1b04cd6f6758f21c93f"}}