{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FA324N22RPIH7NTYSQZHS27ZRR","short_pith_number":"pith:FA324N22","canonical_record":{"source":{"id":"1712.03224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-07T19:22:48Z","cross_cats_sorted":["nlin.AO","physics.soc-ph"],"title_canon_sha256":"d80b595cff996c3d98f91bea1e9ae8a5b719c1801d165c84ba4dd74d1b0e5800","abstract_canon_sha256":"96703bdd07deb6f6e234dacf38c31a8e05f7547e714cffec8a459d788c8fa7f7"},"schema_version":"1.0"},"canonical_sha256":"2837ae375a8bd07fb6789432796bf98c6ad803d35acc4aebbe28955021ff1369","source":{"kind":"arxiv","id":"1712.03224","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.03224","created_at":"2026-05-18T00:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"1712.03224v1","created_at":"2026-05-18T00:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03224","created_at":"2026-05-18T00:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"FA324N22RPIH","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FA324N22RPIH7NTY","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FA324N22","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FA324N22RPIH7NTYSQZHS27ZRR","target":"record","payload":{"canonical_record":{"source":{"id":"1712.03224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-07T19:22:48Z","cross_cats_sorted":["nlin.AO","physics.soc-ph"],"title_canon_sha256":"d80b595cff996c3d98f91bea1e9ae8a5b719c1801d165c84ba4dd74d1b0e5800","abstract_canon_sha256":"96703bdd07deb6f6e234dacf38c31a8e05f7547e714cffec8a459d788c8fa7f7"},"schema_version":"1.0"},"canonical_sha256":"2837ae375a8bd07fb6789432796bf98c6ad803d35acc4aebbe28955021ff1369","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:21.940102Z","signature_b64":"hb0iDWTdVwOr3H4C/bjPTPsdraMaroSzWdjASmA+5oyXgRZuKMw/4ILuwVZDdMG+CFyZRyHq2VqKwJVMR8FtAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2837ae375a8bd07fb6789432796bf98c6ad803d35acc4aebbe28955021ff1369","last_reissued_at":"2026-05-18T00:28:21.939374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:21.939374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.03224","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":"2026-05-18T00:28:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vBD/s7VlGwb5YYTqgEY5Utn3SKHLDbNJlS/IUyqQbYbcClGq+/Cu4ZJmLQ4LKYJ68QcIle0eAK8TyyEcsbhWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:06:19.418400Z"},"content_sha256":"392ef71705362747e153a489a09d9b26d672ff59b70e7507a91c6dc92f28b4c4","schema_version":"1.0","event_id":"sha256:392ef71705362747e153a489a09d9b26d672ff59b70e7507a91c6dc92f28b4c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FA324N22RPIH7NTYSQZHS27ZRR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boltzmann games in heterogeneous consensus dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO","physics.soc-ph"],"primary_cat":"math.OC","authors_text":"Giacomo Albi, Lorenzo Pareschi, Mattia Zanella","submitted_at":"2017-12-07T19:22:48Z","abstract_excerpt":"We consider a constrained hierarchical opinion dynamics in the case of leaders' competition and with complete information among leaders. Each leaders' group tries to drive the followers' opinion towards a desired state accordingly to a specific strategy. By using the Boltzmann-type control approach we analyze the best-reply strategy for each leaders' population. Derivation of the corresponding Fokker-Planck model permits to investigate the asymptotic behaviour of the solution. Heterogeneous followers populations are then considered where the effect of knowledge impacts the leaders' credibility"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03224","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":"2026-05-18T00:28:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GHaA8NQPsSouyY3wRwz7+C3hUdojOWk+YfPvxKR6/vKK9tr13O5/OXt9Xp81Ksavz+05Ytfk8rXwsFqSoaRoCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:06:19.419049Z"},"content_sha256":"c817c1e33074af3fc886added6b7bfe1723a9aede954de6692ccbbb965ec99b0","schema_version":"1.0","event_id":"sha256:c817c1e33074af3fc886added6b7bfe1723a9aede954de6692ccbbb965ec99b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FA324N22RPIH7NTYSQZHS27ZRR/bundle.json","state_url":"https://pith.science/pith/FA324N22RPIH7NTYSQZHS27ZRR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FA324N22RPIH7NTYSQZHS27ZRR/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":"2026-05-28T23:06:19Z","links":{"resolver":"https://pith.science/pith/FA324N22RPIH7NTYSQZHS27ZRR","bundle":"https://pith.science/pith/FA324N22RPIH7NTYSQZHS27ZRR/bundle.json","state":"https://pith.science/pith/FA324N22RPIH7NTYSQZHS27ZRR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FA324N22RPIH7NTYSQZHS27ZRR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FA324N22RPIH7NTYSQZHS27ZRR","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":"96703bdd07deb6f6e234dacf38c31a8e05f7547e714cffec8a459d788c8fa7f7","cross_cats_sorted":["nlin.AO","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-07T19:22:48Z","title_canon_sha256":"d80b595cff996c3d98f91bea1e9ae8a5b719c1801d165c84ba4dd74d1b0e5800"},"schema_version":"1.0","source":{"id":"1712.03224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.03224","created_at":"2026-05-18T00:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"1712.03224v1","created_at":"2026-05-18T00:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03224","created_at":"2026-05-18T00:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"FA324N22RPIH","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FA324N22RPIH7NTY","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FA324N22","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:c817c1e33074af3fc886added6b7bfe1723a9aede954de6692ccbbb965ec99b0","target":"graph","created_at":"2026-05-18T00:28:21Z","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 consider a constrained hierarchical opinion dynamics in the case of leaders' competition and with complete information among leaders. Each leaders' group tries to drive the followers' opinion towards a desired state accordingly to a specific strategy. By using the Boltzmann-type control approach we analyze the best-reply strategy for each leaders' population. Derivation of the corresponding Fokker-Planck model permits to investigate the asymptotic behaviour of the solution. Heterogeneous followers populations are then considered where the effect of knowledge impacts the leaders' credibility","authors_text":"Giacomo Albi, Lorenzo Pareschi, Mattia Zanella","cross_cats":["nlin.AO","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-07T19:22:48Z","title":"Boltzmann games in heterogeneous consensus dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03224","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":"sha256:392ef71705362747e153a489a09d9b26d672ff59b70e7507a91c6dc92f28b4c4","target":"record","created_at":"2026-05-18T00:28:21Z","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":"96703bdd07deb6f6e234dacf38c31a8e05f7547e714cffec8a459d788c8fa7f7","cross_cats_sorted":["nlin.AO","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-07T19:22:48Z","title_canon_sha256":"d80b595cff996c3d98f91bea1e9ae8a5b719c1801d165c84ba4dd74d1b0e5800"},"schema_version":"1.0","source":{"id":"1712.03224","kind":"arxiv","version":1}},"canonical_sha256":"2837ae375a8bd07fb6789432796bf98c6ad803d35acc4aebbe28955021ff1369","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2837ae375a8bd07fb6789432796bf98c6ad803d35acc4aebbe28955021ff1369","first_computed_at":"2026-05-18T00:28:21.939374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:21.939374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hb0iDWTdVwOr3H4C/bjPTPsdraMaroSzWdjASmA+5oyXgRZuKMw/4ILuwVZDdMG+CFyZRyHq2VqKwJVMR8FtAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:21.940102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.03224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:392ef71705362747e153a489a09d9b26d672ff59b70e7507a91c6dc92f28b4c4","sha256:c817c1e33074af3fc886added6b7bfe1723a9aede954de6692ccbbb965ec99b0"],"state_sha256":"ce40c356a68c3f0e73e67ad003dba2804d249d11674414b582764b968f7ebcac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8JhGW5pRGz1OxShyzJK2G/GNtNWd1FWCMllRM6jF7DKQ3tzztWEMvpSst3w35O8mb0mEYqvu/pq6HOxM8NnBCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:06:19.422218Z","bundle_sha256":"a594eea3245fb681746a8f8a6c94e1f3f555eeb2c2b34ba4d15d3bfcab3dea07"}}