{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:DLCB7GQ6TKH26RO7W2CB5VHGHT","short_pith_number":"pith:DLCB7GQ6","schema_version":"1.0","canonical_sha256":"1ac41f9a1e9a8faf45dfb6841ed4e63ce313927a2a7e617dcf50159089a210e1","source":{"kind":"arxiv","id":"1103.4536","version":2},"attestation_state":"computed","paper":{"title":"Extensive and Sub-Extensive Chaos in Globally-Coupled Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"nlin.CD","authors_text":"Alessandro Torcini, Antonio Politi, Francesco Ginelli, Hugues Chat\\'e, Kazumasa A. Takeuchi","submitted_at":"2011-03-23T14:40:28Z","abstract_excerpt":"Using a combination of analytical and numerical techniques, we show that chaos in globally-coupled identical dynamical systems, be they dissipative or Hamiltonian, is both extensive and sub-extensive: their spectrum of Lyapunov exponents is asymptotically flat (thus extensive) at the value $\\lambda_0$ given by a single unit forced by the mean-field, but sandwiched between sub-extensive bands containing typically $\\mathcal{O}(\\log N)$ exponents whose values vary as $\\lambda \\simeq \\lambda_\\infty + c/\\log N$ with $\\lambda_\\infty \\neq \\lambda_0$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1103.4536","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-03-23T14:40:28Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"7ddf557d0448c864bed1c778e71ecba4776ed2175604c04eae3305befb3c1604","abstract_canon_sha256":"2e648130e906b29df71b850323e3b63678ba7bc1b4a1adf10b6e7c193f0b5bbe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:45.925304Z","signature_b64":"AY7BOBo9z5rsP6RwJbZd+D0v2CfKWdemko4ZR9+8s2A37RXiAikFp4NVFcarLBVuAI0b8AUxWaAlkK1V43ZRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ac41f9a1e9a8faf45dfb6841ed4e63ce313927a2a7e617dcf50159089a210e1","last_reissued_at":"2026-05-18T03:49:45.924280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:45.924280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extensive and Sub-Extensive Chaos in Globally-Coupled Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"nlin.CD","authors_text":"Alessandro Torcini, Antonio Politi, Francesco Ginelli, Hugues Chat\\'e, Kazumasa A. Takeuchi","submitted_at":"2011-03-23T14:40:28Z","abstract_excerpt":"Using a combination of analytical and numerical techniques, we show that chaos in globally-coupled identical dynamical systems, be they dissipative or Hamiltonian, is both extensive and sub-extensive: their spectrum of Lyapunov exponents is asymptotically flat (thus extensive) at the value $\\lambda_0$ given by a single unit forced by the mean-field, but sandwiched between sub-extensive bands containing typically $\\mathcal{O}(\\log N)$ exponents whose values vary as $\\lambda \\simeq \\lambda_\\infty + c/\\log N$ with $\\lambda_\\infty \\neq \\lambda_0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4536","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1103.4536","created_at":"2026-05-18T03:49:45.924434+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.4536v2","created_at":"2026-05-18T03:49:45.924434+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4536","created_at":"2026-05-18T03:49:45.924434+00:00"},{"alias_kind":"pith_short_12","alias_value":"DLCB7GQ6TKH2","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"DLCB7GQ6TKH26RO7","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"DLCB7GQ6","created_at":"2026-05-18T12:26:26.731475+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DLCB7GQ6TKH26RO7W2CB5VHGHT","json":"https://pith.science/pith/DLCB7GQ6TKH26RO7W2CB5VHGHT.json","graph_json":"https://pith.science/api/pith-number/DLCB7GQ6TKH26RO7W2CB5VHGHT/graph.json","events_json":"https://pith.science/api/pith-number/DLCB7GQ6TKH26RO7W2CB5VHGHT/events.json","paper":"https://pith.science/paper/DLCB7GQ6"},"agent_actions":{"view_html":"https://pith.science/pith/DLCB7GQ6TKH26RO7W2CB5VHGHT","download_json":"https://pith.science/pith/DLCB7GQ6TKH26RO7W2CB5VHGHT.json","view_paper":"https://pith.science/paper/DLCB7GQ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.4536&json=true","fetch_graph":"https://pith.science/api/pith-number/DLCB7GQ6TKH26RO7W2CB5VHGHT/graph.json","fetch_events":"https://pith.science/api/pith-number/DLCB7GQ6TKH26RO7W2CB5VHGHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DLCB7GQ6TKH26RO7W2CB5VHGHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DLCB7GQ6TKH26RO7W2CB5VHGHT/action/storage_attestation","attest_author":"https://pith.science/pith/DLCB7GQ6TKH26RO7W2CB5VHGHT/action/author_attestation","sign_citation":"https://pith.science/pith/DLCB7GQ6TKH26RO7W2CB5VHGHT/action/citation_signature","submit_replication":"https://pith.science/pith/DLCB7GQ6TKH26RO7W2CB5VHGHT/action/replication_record"}},"created_at":"2026-05-18T03:49:45.924434+00:00","updated_at":"2026-05-18T03:49:45.924434+00:00"}