{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MA2U2EEE5L75LNNEU43JOJEAR4","short_pith_number":"pith:MA2U2EEE","canonical_record":{"source":{"id":"1410.7026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-10-26T13:29:18Z","cross_cats_sorted":["cs.GT","cs.MA"],"title_canon_sha256":"5d551979c11a01125a972e12df4e0532503fa8ef30659e9b71c1c9e35b04b0b8","abstract_canon_sha256":"fb2005a031dbb1b1ac53d6b107cd56d5920aa83c8b679fcd224e486039448b2a"},"schema_version":"1.0"},"canonical_sha256":"60354d1084eaffd5b5a4a7369724808f2b4d13d4927a4414ad9c232313722425","source":{"kind":"arxiv","id":"1410.7026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7026","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7026v1","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7026","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"MA2U2EEE5L75","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MA2U2EEE5L75LNNE","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MA2U2EEE","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MA2U2EEE5L75LNNEU43JOJEAR4","target":"record","payload":{"canonical_record":{"source":{"id":"1410.7026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-10-26T13:29:18Z","cross_cats_sorted":["cs.GT","cs.MA"],"title_canon_sha256":"5d551979c11a01125a972e12df4e0532503fa8ef30659e9b71c1c9e35b04b0b8","abstract_canon_sha256":"fb2005a031dbb1b1ac53d6b107cd56d5920aa83c8b679fcd224e486039448b2a"},"schema_version":"1.0"},"canonical_sha256":"60354d1084eaffd5b5a4a7369724808f2b4d13d4927a4414ad9c232313722425","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:18.160117Z","signature_b64":"mNYNLu23slVcQ0I6VX5PVk83j6LCKt65T9anjrGiRlaMDjI208gnsJW3yNHx37w0vzg1+uU3K0PYkNXteA5VBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60354d1084eaffd5b5a4a7369724808f2b4d13d4927a4414ad9c232313722425","last_reissued_at":"2026-05-18T02:39:18.159732Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:18.159732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.7026","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":"2026-05-18T02:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bUn7WwUOFJ3TqK4a3rHOpuj+McUR0KhK7XhiaLoRx4KX/HUM0I9Yml7rT6c9f2hP/79RrnrtA5piCvYmVqzuCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T23:03:10.807720Z"},"content_sha256":"fbc1087499712161f0f2f5318285fbb086f647f92fac37b84ab291baafaec3da","schema_version":"1.0","event_id":"sha256:fbc1087499712161f0f2f5318285fbb086f647f92fac37b84ab291baafaec3da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MA2U2EEE5L75LNNEU43JOJEAR4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal topology of multi-agent systems with two leaders: a zero-sum game perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT","cs.MA"],"primary_cat":"cs.SY","authors_text":"Bin Wu, Jingying Ma, Long Wang, Yuanshi Zheng","submitted_at":"2014-10-26T13:29:18Z","abstract_excerpt":"It is typical to assume that there is no conflict of interest among leaders. Under such assumption, it is known that, for a multi-agent system with two leaders, if the followers' interaction subgraph is undirected and connected, then followers will converge to a convex combination of two leaders' states with linear consensus protocol. In this paper, we introduce the conflict between leaders: by choosing k followers to connect with, every leader attempts all followers converge to himself closer than that of the other. By using graph theory and matrix theory, we formulate this conflict as a stan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7026","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":"2026-05-18T02:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dqBu8ASl8rhHXsMmhImqh0HP6k15/xczdiOHJ9IIDA1gLf5oPhZT7YMhb+AWCS3ztPGkNLo8/I6A/oW8quBaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T23:03:10.808112Z"},"content_sha256":"b80f3b0c11e2b909dcc5546642211aecaec2d0492efc97ea3df141e60dbe0680","schema_version":"1.0","event_id":"sha256:b80f3b0c11e2b909dcc5546642211aecaec2d0492efc97ea3df141e60dbe0680"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MA2U2EEE5L75LNNEU43JOJEAR4/bundle.json","state_url":"https://pith.science/pith/MA2U2EEE5L75LNNEU43JOJEAR4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MA2U2EEE5L75LNNEU43JOJEAR4/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":"2026-05-21T23:03:10Z","links":{"resolver":"https://pith.science/pith/MA2U2EEE5L75LNNEU43JOJEAR4","bundle":"https://pith.science/pith/MA2U2EEE5L75LNNEU43JOJEAR4/bundle.json","state":"https://pith.science/pith/MA2U2EEE5L75LNNEU43JOJEAR4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MA2U2EEE5L75LNNEU43JOJEAR4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MA2U2EEE5L75LNNEU43JOJEAR4","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":"fb2005a031dbb1b1ac53d6b107cd56d5920aa83c8b679fcd224e486039448b2a","cross_cats_sorted":["cs.GT","cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-10-26T13:29:18Z","title_canon_sha256":"5d551979c11a01125a972e12df4e0532503fa8ef30659e9b71c1c9e35b04b0b8"},"schema_version":"1.0","source":{"id":"1410.7026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7026","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7026v1","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7026","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"MA2U2EEE5L75","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MA2U2EEE5L75LNNE","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MA2U2EEE","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:b80f3b0c11e2b909dcc5546642211aecaec2d0492efc97ea3df141e60dbe0680","target":"graph","created_at":"2026-05-18T02:39:18Z","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":"It is typical to assume that there is no conflict of interest among leaders. Under such assumption, it is known that, for a multi-agent system with two leaders, if the followers' interaction subgraph is undirected and connected, then followers will converge to a convex combination of two leaders' states with linear consensus protocol. In this paper, we introduce the conflict between leaders: by choosing k followers to connect with, every leader attempts all followers converge to himself closer than that of the other. By using graph theory and matrix theory, we formulate this conflict as a stan","authors_text":"Bin Wu, Jingying Ma, Long Wang, Yuanshi Zheng","cross_cats":["cs.GT","cs.MA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-10-26T13:29:18Z","title":"Optimal topology of multi-agent systems with two leaders: a zero-sum game perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7026","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:fbc1087499712161f0f2f5318285fbb086f647f92fac37b84ab291baafaec3da","target":"record","created_at":"2026-05-18T02:39:18Z","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":"fb2005a031dbb1b1ac53d6b107cd56d5920aa83c8b679fcd224e486039448b2a","cross_cats_sorted":["cs.GT","cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-10-26T13:29:18Z","title_canon_sha256":"5d551979c11a01125a972e12df4e0532503fa8ef30659e9b71c1c9e35b04b0b8"},"schema_version":"1.0","source":{"id":"1410.7026","kind":"arxiv","version":1}},"canonical_sha256":"60354d1084eaffd5b5a4a7369724808f2b4d13d4927a4414ad9c232313722425","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60354d1084eaffd5b5a4a7369724808f2b4d13d4927a4414ad9c232313722425","first_computed_at":"2026-05-18T02:39:18.159732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:18.159732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mNYNLu23slVcQ0I6VX5PVk83j6LCKt65T9anjrGiRlaMDjI208gnsJW3yNHx37w0vzg1+uU3K0PYkNXteA5VBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:18.160117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbc1087499712161f0f2f5318285fbb086f647f92fac37b84ab291baafaec3da","sha256:b80f3b0c11e2b909dcc5546642211aecaec2d0492efc97ea3df141e60dbe0680"],"state_sha256":"b9a5205fe254ec02f4f10b9f6e17bf6cf09da61a94e35fcbf477c54661d8f9ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hc3pRv0MPuzCb324rgg5baCzos9gZa+Qrm+mQ18lLYXWb5S8sIrN0VuWZFiy0fZFJ1cmzHj4JeP8i7GlSr+pBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T23:03:10.810349Z","bundle_sha256":"0e3f0e88ed1fced0252eae3aee43cee186ffa510b571f7e432b75d2401e50195"}}