{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:EDOZMBYQFCBLD3CYSCLS3MPBPV","short_pith_number":"pith:EDOZMBYQ","schema_version":"1.0","canonical_sha256":"20dd9607102882b1ec5890972db1e17d48507dd23f755835647f36dbf5d8f684","source":{"kind":"arxiv","id":"1309.5441","version":1},"attestation_state":"computed","paper":{"title":"Dynamics of periodic Toda chains with a large number of particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Dario Bambusi, Thierry Paul (CMLS-EcolePolytechnique), Thomas Kappeler","submitted_at":"2013-09-21T05:59:50Z","abstract_excerpt":"For periodic Toda chains with a large number $N$ of particles we consider states which are $N^{-2}-$close to the equilibrium and constructed by discretizing any given $C^2-$functions with mesh size $N^{-1}$. For such states we derive asymptotic expansions of the Toda frequencies $(\\omega^N_n)_{0 < n < N}$ and the actions $(I^N_n)_{0 < n < N},$ both listed in the standard way, in powers of $N^{-1}$ as $N \\to \\infty$. %listed in accordance with the ordering of the frequencies at the equilibrium, %$(2 \\sin \\frac{n\\pi} {N})_{0 < n < N}$. At the two edges $n \\sim 1$ and $N -n \\sim 1$, the expansion"},"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":"1309.5441","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-21T05:59:50Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d664d77b95a3df801dad8aff2653b07cca32e53587346e0280327fe5a6c0b114","abstract_canon_sha256":"54ff0602135c6b38ec98f82a1c21afae4b352d3983858c1bd33532dd50f454c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:45.645436Z","signature_b64":"6KSyfmn0OdAVsgNZDARPKlB9+Tf54+1tj+p1fUGZ1jn2Wq9Q9lIi1S9uQG23bExA5nifL9NpPkH51j40e0UZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20dd9607102882b1ec5890972db1e17d48507dd23f755835647f36dbf5d8f684","last_reissued_at":"2026-05-18T03:12:45.644768Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:45.644768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamics of periodic Toda chains with a large number of particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Dario Bambusi, Thierry Paul (CMLS-EcolePolytechnique), Thomas Kappeler","submitted_at":"2013-09-21T05:59:50Z","abstract_excerpt":"For periodic Toda chains with a large number $N$ of particles we consider states which are $N^{-2}-$close to the equilibrium and constructed by discretizing any given $C^2-$functions with mesh size $N^{-1}$. For such states we derive asymptotic expansions of the Toda frequencies $(\\omega^N_n)_{0 < n < N}$ and the actions $(I^N_n)_{0 < n < N},$ both listed in the standard way, in powers of $N^{-1}$ as $N \\to \\infty$. %listed in accordance with the ordering of the frequencies at the equilibrium, %$(2 \\sin \\frac{n\\pi} {N})_{0 < n < N}$. At the two edges $n \\sim 1$ and $N -n \\sim 1$, the expansion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5441","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1309.5441","created_at":"2026-05-18T03:12:45.644879+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.5441v1","created_at":"2026-05-18T03:12:45.644879+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5441","created_at":"2026-05-18T03:12:45.644879+00:00"},{"alias_kind":"pith_short_12","alias_value":"EDOZMBYQFCBL","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EDOZMBYQFCBLD3CY","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EDOZMBYQ","created_at":"2026-05-18T12:27:43.054852+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/EDOZMBYQFCBLD3CYSCLS3MPBPV","json":"https://pith.science/pith/EDOZMBYQFCBLD3CYSCLS3MPBPV.json","graph_json":"https://pith.science/api/pith-number/EDOZMBYQFCBLD3CYSCLS3MPBPV/graph.json","events_json":"https://pith.science/api/pith-number/EDOZMBYQFCBLD3CYSCLS3MPBPV/events.json","paper":"https://pith.science/paper/EDOZMBYQ"},"agent_actions":{"view_html":"https://pith.science/pith/EDOZMBYQFCBLD3CYSCLS3MPBPV","download_json":"https://pith.science/pith/EDOZMBYQFCBLD3CYSCLS3MPBPV.json","view_paper":"https://pith.science/paper/EDOZMBYQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.5441&json=true","fetch_graph":"https://pith.science/api/pith-number/EDOZMBYQFCBLD3CYSCLS3MPBPV/graph.json","fetch_events":"https://pith.science/api/pith-number/EDOZMBYQFCBLD3CYSCLS3MPBPV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EDOZMBYQFCBLD3CYSCLS3MPBPV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EDOZMBYQFCBLD3CYSCLS3MPBPV/action/storage_attestation","attest_author":"https://pith.science/pith/EDOZMBYQFCBLD3CYSCLS3MPBPV/action/author_attestation","sign_citation":"https://pith.science/pith/EDOZMBYQFCBLD3CYSCLS3MPBPV/action/citation_signature","submit_replication":"https://pith.science/pith/EDOZMBYQFCBLD3CYSCLS3MPBPV/action/replication_record"}},"created_at":"2026-05-18T03:12:45.644879+00:00","updated_at":"2026-05-18T03:12:45.644879+00:00"}