{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:EPAYOX6KPH7D2KA4QDXNIVGSUG","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":"5a80285cce0176866f602e5267c7e19d6bf54a9a7f7c29b8316b041d3f548afc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-12-17T10:47:21Z","title_canon_sha256":"e8a8f0bcd6fb3a0a38fdac1f6aa2dd5825534b04350f27f97e96d486e790f445"},"schema_version":"1.0","source":{"id":"0812.3243","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3243","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3243v1","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3243","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"EPAYOX6KPH7D","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"EPAYOX6KPH7D2KA4","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"EPAYOX6K","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:95b4f073712691a7a98d59476d22cd1f4e7204ddc122b149b8c62a358d9a0358","target":"graph","created_at":"2026-05-18T02:15:04Z","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 apply the Nyquist method to the Hamiltonian Mean Field (HMF) model in order to settle the linear dynamical stability of a spatially homogeneous distribution function with respect to the Vlasov equation. We consider the case of Maxwell (isothermal) and Tsallis (polytropic) distributions and show that the system is stable above a critical kinetic temperature T_c and unstable below it. Then, we consider a symmetric double-humped distribution, made of the superposition of two decentered Maxwellians, and show the existence of a re-entrant phase in the stability diagram. When we consider an asymm","authors_text":"L. Delfini, P.H. Chavanis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-12-17T10:47:21Z","title":"Dynamical stability of systems with long-range interactions: application of the Nyquist method to the HMF model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3243","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":"sha256:04dd6058fe9c617d9e3d5220853318425cb032beeea6cc3c2a505aee0a1205bd","target":"record","created_at":"2026-05-18T02:15:04Z","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":"5a80285cce0176866f602e5267c7e19d6bf54a9a7f7c29b8316b041d3f548afc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-12-17T10:47:21Z","title_canon_sha256":"e8a8f0bcd6fb3a0a38fdac1f6aa2dd5825534b04350f27f97e96d486e790f445"},"schema_version":"1.0","source":{"id":"0812.3243","kind":"arxiv","version":1}},"canonical_sha256":"23c1875fca79fe3d281c80eed454d2a1be45edc5767a1d65501e02eb5892d50f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23c1875fca79fe3d281c80eed454d2a1be45edc5767a1d65501e02eb5892d50f","first_computed_at":"2026-05-18T02:15:04.586173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:04.586173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fhiHLrMP3R1zbKZTT6bBarFwkZc9/aBKViZ++QxiVqfFFr+QmZ8t22SaSApIeuKvVXuzzZB6KXSjlvJ3fRl0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:04.586588Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.3243","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04dd6058fe9c617d9e3d5220853318425cb032beeea6cc3c2a505aee0a1205bd","sha256:95b4f073712691a7a98d59476d22cd1f4e7204ddc122b149b8c62a358d9a0358"],"state_sha256":"9bc88fc2ac12786d2b2a0194f61de18faf61ab9e46dd2bb63488cc914e473147"}