{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QNRFVWEFYA35B2UE3PR5WNZEYP","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":"2c4101e1945d119600a5c8a4c1162d4ab09dc7ea505f7c0606d39732df89b552","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-20T09:18:16Z","title_canon_sha256":"d2f3ff83c8112f04a58a86364c048af5e3741d259ead4e73416d49070d221176"},"schema_version":"1.0","source":{"id":"1110.4475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4475","created_at":"2026-05-18T04:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4475v1","created_at":"2026-05-18T04:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4475","created_at":"2026-05-18T04:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"QNRFVWEFYA35","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QNRFVWEFYA35B2UE","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QNRFVWEF","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:90d7fdc73334a674e406871fda2047fbf523d46a80d9167d9061633bda671cc2","target":"graph","created_at":"2026-05-18T04:10:36Z","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 prove that the non-linear part of the Hamiltonian of the KdV equation on the circle, written as a function of the actions, defines a continuous convex function on the $\\ell^2$ space and derive for it lower and upper bounds in terms of some functions of the $\\ell^2$-norm. The proof is based on a new representation of the Hamiltonian in terms of the quasimomentum and its analysis using the conformal mapping theory.","authors_text":"Evgeny Korotyaev, Sergei Kuksin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-20T09:18:16Z","title":"KdV Hamiltonian as function of actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4475","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":"sha256:33873bdf396fbfe78cde08383da406b8f46e2e7324d4a01c1df23029df76ec99","target":"record","created_at":"2026-05-18T04:10:36Z","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":"2c4101e1945d119600a5c8a4c1162d4ab09dc7ea505f7c0606d39732df89b552","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-20T09:18:16Z","title_canon_sha256":"d2f3ff83c8112f04a58a86364c048af5e3741d259ead4e73416d49070d221176"},"schema_version":"1.0","source":{"id":"1110.4475","kind":"arxiv","version":1}},"canonical_sha256":"83625ad885c037d0ea84dbe3db3724c3febcf32948628ca37eee7276f78be319","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83625ad885c037d0ea84dbe3db3724c3febcf32948628ca37eee7276f78be319","first_computed_at":"2026-05-18T04:10:36.672447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:36.672447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aMCwdAml5Yg8xuyCZiNCispRthWt9tzPajh2CJG+WGixrpTXtDGIpkZTCH/VczDrvqbQYv7l7Lc9rQHkIYyTAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:36.673158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33873bdf396fbfe78cde08383da406b8f46e2e7324d4a01c1df23029df76ec99","sha256:90d7fdc73334a674e406871fda2047fbf523d46a80d9167d9061633bda671cc2"],"state_sha256":"d1e7e6fa1e9998ef17e9745c52652fdc350218da0f8565a520cfe25e8f0f58d3"}