{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NQV5Z6OSGKYVOMMI63I5NJOCQK","short_pith_number":"pith:NQV5Z6OS","canonical_record":{"source":{"id":"1107.2626","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-07-13T18:42:39Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"95620ffeeb69664d9e60ffe12754808efb55758ce5c8f21ef9db007c077d1e4d","abstract_canon_sha256":"1f2609e9d933774a0c23a13102cc663b9c88174dbfdd6c355d0bcf8201971ce0"},"schema_version":"1.0"},"canonical_sha256":"6c2bdcf9d232b1573188f6d1d6a5c2828f1ecdd02c9e7f4ddce3b67336f54e95","source":{"kind":"arxiv","id":"1107.2626","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2626","created_at":"2026-05-18T02:01:18Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2626v2","created_at":"2026-05-18T02:01:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2626","created_at":"2026-05-18T02:01:18Z"},{"alias_kind":"pith_short_12","alias_value":"NQV5Z6OSGKYV","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NQV5Z6OSGKYVOMMI","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NQV5Z6OS","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NQV5Z6OSGKYVOMMI63I5NJOCQK","target":"record","payload":{"canonical_record":{"source":{"id":"1107.2626","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-07-13T18:42:39Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"95620ffeeb69664d9e60ffe12754808efb55758ce5c8f21ef9db007c077d1e4d","abstract_canon_sha256":"1f2609e9d933774a0c23a13102cc663b9c88174dbfdd6c355d0bcf8201971ce0"},"schema_version":"1.0"},"canonical_sha256":"6c2bdcf9d232b1573188f6d1d6a5c2828f1ecdd02c9e7f4ddce3b67336f54e95","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:18.903544Z","signature_b64":"Hk3mOY05BkubeD//jGRgFqPqmxh77skXBnfAKYawLGPGFLXzLxx5g0/e7o+1KK2aiCpvbYO/InmZpDvWsxXKAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c2bdcf9d232b1573188f6d1d6a5c2828f1ecdd02c9e7f4ddce3b67336f54e95","last_reissued_at":"2026-05-18T02:01:18.903040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:18.903040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.2626","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:01:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qUAggLBfss5ajDJ7o5Orb/Ma8BYylrImrKN3GAD7UudX5aRqtRBFU3DcrOFI1+ksoBz20+FCmefFu6qdkdgEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:25:03.240654Z"},"content_sha256":"ba48edda55ca79307acdb6b5e03ee5a58ed68ae38297ea09a6fb459879cde070","schema_version":"1.0","event_id":"sha256:ba48edda55ca79307acdb6b5e03ee5a58ed68ae38297ea09a6fb459879cde070"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NQV5Z6OSGKYVOMMI63I5NJOCQK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The two-stage dynamics in the Fermi-Pasta-Ulam problem: from regular to diffusive behavior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"nlin.CD","authors_text":"Antonio Ponno, Charalampos Skokos, Helen Christodoulidi, Sergej Flach","submitted_at":"2011-07-13T18:42:39Z","abstract_excerpt":"A numerical and analytical study of the relaxation to equilibrium of both the Fermi-Pasta-Ulam (FPU) alpha-model and the integrable Toda model, when the fundamental mode is initially excited, is reported. We show that the dynamics of both systems is almost identical on the short term, when the energies of the initially unexcited modes grow in geometric progression with time, through a secular avalanche process. At the end of this first stage of the dynamics the time-averaged modal energy spectrum of the Toda system stabilizes to its final profile, well described, at low energy, by the spectrum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2626","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:01:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lTN8xxWZlRSPtvCdqWS14Y3JV3lGArWNKsYiiSA5xecaBz4ILlDXqx+kV6yC41MRl1kU29J2DEcHaKuCYcgCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:25:03.241280Z"},"content_sha256":"db000bb92942dd0a0db381212111371584e141da95783ccd8dd4ba2540878dd0","schema_version":"1.0","event_id":"sha256:db000bb92942dd0a0db381212111371584e141da95783ccd8dd4ba2540878dd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NQV5Z6OSGKYVOMMI63I5NJOCQK/bundle.json","state_url":"https://pith.science/pith/NQV5Z6OSGKYVOMMI63I5NJOCQK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NQV5Z6OSGKYVOMMI63I5NJOCQK/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":"2026-05-27T19:25:03Z","links":{"resolver":"https://pith.science/pith/NQV5Z6OSGKYVOMMI63I5NJOCQK","bundle":"https://pith.science/pith/NQV5Z6OSGKYVOMMI63I5NJOCQK/bundle.json","state":"https://pith.science/pith/NQV5Z6OSGKYVOMMI63I5NJOCQK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NQV5Z6OSGKYVOMMI63I5NJOCQK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NQV5Z6OSGKYVOMMI63I5NJOCQK","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":"1f2609e9d933774a0c23a13102cc663b9c88174dbfdd6c355d0bcf8201971ce0","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-07-13T18:42:39Z","title_canon_sha256":"95620ffeeb69664d9e60ffe12754808efb55758ce5c8f21ef9db007c077d1e4d"},"schema_version":"1.0","source":{"id":"1107.2626","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2626","created_at":"2026-05-18T02:01:18Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2626v2","created_at":"2026-05-18T02:01:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2626","created_at":"2026-05-18T02:01:18Z"},{"alias_kind":"pith_short_12","alias_value":"NQV5Z6OSGKYV","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NQV5Z6OSGKYVOMMI","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NQV5Z6OS","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:db000bb92942dd0a0db381212111371584e141da95783ccd8dd4ba2540878dd0","target":"graph","created_at":"2026-05-18T02:01:18Z","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":"A numerical and analytical study of the relaxation to equilibrium of both the Fermi-Pasta-Ulam (FPU) alpha-model and the integrable Toda model, when the fundamental mode is initially excited, is reported. We show that the dynamics of both systems is almost identical on the short term, when the energies of the initially unexcited modes grow in geometric progression with time, through a secular avalanche process. At the end of this first stage of the dynamics the time-averaged modal energy spectrum of the Toda system stabilizes to its final profile, well described, at low energy, by the spectrum","authors_text":"Antonio Ponno, Charalampos Skokos, Helen Christodoulidi, Sergej Flach","cross_cats":["nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-07-13T18:42:39Z","title":"The two-stage dynamics in the Fermi-Pasta-Ulam problem: from regular to diffusive behavior"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2626","kind":"arxiv","version":2},"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:ba48edda55ca79307acdb6b5e03ee5a58ed68ae38297ea09a6fb459879cde070","target":"record","created_at":"2026-05-18T02:01:18Z","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":"1f2609e9d933774a0c23a13102cc663b9c88174dbfdd6c355d0bcf8201971ce0","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-07-13T18:42:39Z","title_canon_sha256":"95620ffeeb69664d9e60ffe12754808efb55758ce5c8f21ef9db007c077d1e4d"},"schema_version":"1.0","source":{"id":"1107.2626","kind":"arxiv","version":2}},"canonical_sha256":"6c2bdcf9d232b1573188f6d1d6a5c2828f1ecdd02c9e7f4ddce3b67336f54e95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c2bdcf9d232b1573188f6d1d6a5c2828f1ecdd02c9e7f4ddce3b67336f54e95","first_computed_at":"2026-05-18T02:01:18.903040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:18.903040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hk3mOY05BkubeD//jGRgFqPqmxh77skXBnfAKYawLGPGFLXzLxx5g0/e7o+1KK2aiCpvbYO/InmZpDvWsxXKAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:18.903544Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2626","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba48edda55ca79307acdb6b5e03ee5a58ed68ae38297ea09a6fb459879cde070","sha256:db000bb92942dd0a0db381212111371584e141da95783ccd8dd4ba2540878dd0"],"state_sha256":"4414a2f4646f708e0587f7aa091eae2ee8092d913f4eb057abd2f62cc50ff9b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vD60GHXqexAYnWEcEoHpej+gV/V5NwdhtEJzS8E+D/zlmmBahPDqn7YMlGSs3a4zYJAl620bcnlhyIAjNsQHDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:25:03.244342Z","bundle_sha256":"5bb1e571c3f82a27431e1cf9ea9c223568314659d67bee7e7742b4c3ad3d97d5"}}