{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:WPL4XELVBV7IUMMY5NT7MX2ZOD","short_pith_number":"pith:WPL4XELV","canonical_record":{"source":{"id":"cond-mat/0410282","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2004-10-12T12:19:02Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"2e0b89bce55ef9368ba23da59b5952399d354b78863b66dc2fd010e4564842f8","abstract_canon_sha256":"67083031ff5972567b32f34531f1003249f6e4fad18ce7a2a98b9b4b9568338f"},"schema_version":"1.0"},"canonical_sha256":"b3d7cb91750d7e8a3198eb67f65f5970c88c8b2098c0626fcffaedbb03fe2c30","source":{"kind":"arxiv","id":"cond-mat/0410282","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0410282","created_at":"2026-05-18T01:06:53Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0410282v1","created_at":"2026-05-18T01:06:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0410282","created_at":"2026-05-18T01:06:53Z"},{"alias_kind":"pith_short_12","alias_value":"WPL4XELVBV7I","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"WPL4XELVBV7IUMMY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"WPL4XELV","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:WPL4XELVBV7IUMMY5NT7MX2ZOD","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0410282","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2004-10-12T12:19:02Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"2e0b89bce55ef9368ba23da59b5952399d354b78863b66dc2fd010e4564842f8","abstract_canon_sha256":"67083031ff5972567b32f34531f1003249f6e4fad18ce7a2a98b9b4b9568338f"},"schema_version":"1.0"},"canonical_sha256":"b3d7cb91750d7e8a3198eb67f65f5970c88c8b2098c0626fcffaedbb03fe2c30","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:53.450724Z","signature_b64":"8oxfGe30wZg6DU/flcc+npd8MkL7V854aTqKLJeLJT9dyxmboyNUdW36J+/ccqlbMT/tEkWHeANwG1d04PBCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3d7cb91750d7e8a3198eb67f65f5970c88c8b2098c0626fcffaedbb03fe2c30","last_reissued_at":"2026-05-18T01:06:53.450194Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:53.450194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0410282","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":"2026-05-18T01:06:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jHbIU8q0eQ5I5pY+TisN+Tb4RV00eucFrHMpKXvfqDJ1CcnfiSsYMVIhM6SFlj4vshF53ISbhnw0CCwya3iNAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:52:03.486501Z"},"content_sha256":"53c3be6797a2b9f8d10ba9231f04aa823d2ab842bd5e1db939f7e2b0cc632f5e","schema_version":"1.0","event_id":"sha256:53c3be6797a2b9f8d10ba9231f04aa823d2ab842bd5e1db939f7e2b0cc632f5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:WPL4XELVBV7IUMMY5NT7MX2ZOD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak and strong chaos in FPU models and beyond","license":"","headline":"","cross_cats":["nlin.CD"],"primary_cat":"cond-mat.stat-mech","authors_text":"E. G. D. Cohen (4) ((1) INAF-Osservatorio di Arcetri, Firenze, Italy (2) Dip. di Fisica, Italy (3) Dip. di Fisica, Italy (4) The Rockefeller University, Lapo Casetti (2), Marco Pettini (1), Monica Cerruti-Sola (1), New York, Roberto Franzosi (3), Universita' di Firenze, Universita' di Pisa, USA)","submitted_at":"2004-10-12T12:19:02Z","abstract_excerpt":"We briefly review some of the most relevant results that our group obtained in the past, while investigating the dynamics of the Fermi-Pasta-Ulam (FPU) models. A first result is the numerical evidence of the existence of two different kinds of transitions in the dynamics of the FPU models: i) a Stochasticity Threshold (ST), characterized by a value of the energy per degree of freedom below which the overwhelming majority of the phase space trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as the number N of degrees of freedom is increased. ii) a Strong Stochasticity T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0410282","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":"2026-05-18T01:06:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SJu6nSR358mH9Qx0YpWWDBqkLNMux4vuUJCzPBO8MkJx2pLBm7YNz6DpWaofypM7TpD1Zh87YM3p6Rj9755cAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:52:03.487264Z"},"content_sha256":"648a31a68504994122b6d1e940056a9aea7ca787ad5c58ff4d74164349fb3d1f","schema_version":"1.0","event_id":"sha256:648a31a68504994122b6d1e940056a9aea7ca787ad5c58ff4d74164349fb3d1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WPL4XELVBV7IUMMY5NT7MX2ZOD/bundle.json","state_url":"https://pith.science/pith/WPL4XELVBV7IUMMY5NT7MX2ZOD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WPL4XELVBV7IUMMY5NT7MX2ZOD/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":"2026-05-28T22:52:03Z","links":{"resolver":"https://pith.science/pith/WPL4XELVBV7IUMMY5NT7MX2ZOD","bundle":"https://pith.science/pith/WPL4XELVBV7IUMMY5NT7MX2ZOD/bundle.json","state":"https://pith.science/pith/WPL4XELVBV7IUMMY5NT7MX2ZOD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WPL4XELVBV7IUMMY5NT7MX2ZOD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:WPL4XELVBV7IUMMY5NT7MX2ZOD","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":"67083031ff5972567b32f34531f1003249f6e4fad18ce7a2a98b9b4b9568338f","cross_cats_sorted":["nlin.CD"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2004-10-12T12:19:02Z","title_canon_sha256":"2e0b89bce55ef9368ba23da59b5952399d354b78863b66dc2fd010e4564842f8"},"schema_version":"1.0","source":{"id":"cond-mat/0410282","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0410282","created_at":"2026-05-18T01:06:53Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0410282v1","created_at":"2026-05-18T01:06:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0410282","created_at":"2026-05-18T01:06:53Z"},{"alias_kind":"pith_short_12","alias_value":"WPL4XELVBV7I","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"WPL4XELVBV7IUMMY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"WPL4XELV","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:648a31a68504994122b6d1e940056a9aea7ca787ad5c58ff4d74164349fb3d1f","target":"graph","created_at":"2026-05-18T01:06:53Z","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 briefly review some of the most relevant results that our group obtained in the past, while investigating the dynamics of the Fermi-Pasta-Ulam (FPU) models. A first result is the numerical evidence of the existence of two different kinds of transitions in the dynamics of the FPU models: i) a Stochasticity Threshold (ST), characterized by a value of the energy per degree of freedom below which the overwhelming majority of the phase space trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as the number N of degrees of freedom is increased. ii) a Strong Stochasticity T","authors_text":"E. G. D. Cohen (4) ((1) INAF-Osservatorio di Arcetri, Firenze, Italy (2) Dip. di Fisica, Italy (3) Dip. di Fisica, Italy (4) The Rockefeller University, Lapo Casetti (2), Marco Pettini (1), Monica Cerruti-Sola (1), New York, Roberto Franzosi (3), Universita' di Firenze, Universita' di Pisa, USA)","cross_cats":["nlin.CD"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2004-10-12T12:19:02Z","title":"Weak and strong chaos in FPU models and beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0410282","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":"sha256:53c3be6797a2b9f8d10ba9231f04aa823d2ab842bd5e1db939f7e2b0cc632f5e","target":"record","created_at":"2026-05-18T01:06:53Z","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":"67083031ff5972567b32f34531f1003249f6e4fad18ce7a2a98b9b4b9568338f","cross_cats_sorted":["nlin.CD"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2004-10-12T12:19:02Z","title_canon_sha256":"2e0b89bce55ef9368ba23da59b5952399d354b78863b66dc2fd010e4564842f8"},"schema_version":"1.0","source":{"id":"cond-mat/0410282","kind":"arxiv","version":1}},"canonical_sha256":"b3d7cb91750d7e8a3198eb67f65f5970c88c8b2098c0626fcffaedbb03fe2c30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3d7cb91750d7e8a3198eb67f65f5970c88c8b2098c0626fcffaedbb03fe2c30","first_computed_at":"2026-05-18T01:06:53.450194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:53.450194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8oxfGe30wZg6DU/flcc+npd8MkL7V854aTqKLJeLJT9dyxmboyNUdW36J+/ccqlbMT/tEkWHeANwG1d04PBCCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:53.450724Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0410282","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53c3be6797a2b9f8d10ba9231f04aa823d2ab842bd5e1db939f7e2b0cc632f5e","sha256:648a31a68504994122b6d1e940056a9aea7ca787ad5c58ff4d74164349fb3d1f"],"state_sha256":"14a83828795acca03f154f78d877c928c5a81df2f6e3e5b5e4ba5a6f4782e9e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+3A0aKvXqrh6ZdFYt1cmdw0R0VlfVfwfwNymGitCdVUE+Z3lb7D8h8DPpe5Fy7nVWQ5IgJMpHTBv2I9/GQhTDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:52:03.491306Z","bundle_sha256":"ced7f20c2f9fdba053115d3af0392d8dab8cc273458878e68f2ba7d822445da3"}}