{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2FZJSSMXLXJIJ5ZVBI3463Y5CS","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":"0cb56073a17f41497df28c440f19e2c79617a90829bf3fd07114132323fab858","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-16T12:48:48Z","title_canon_sha256":"3d2aab8fbf7046cdcf66a399f9c1328e99576025c7b06d8a4d27b9e22286706b"},"schema_version":"1.0","source":{"id":"1305.3785","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3785","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3785v1","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3785","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"pith_short_12","alias_value":"2FZJSSMXLXJI","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2FZJSSMXLXJIJ5ZV","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2FZJSSMX","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:f09deae88520776bb4fa82a0b152078d05678093d8e7056455dca82862e619b8","target":"graph","created_at":"2026-05-18T03:25:33Z","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 investigate semi-classical properties of Maupertuis-Jacobi correspondence in 2-D for families of Hamiltonians $(H_\\lambda(x,\\xi), {\\cal H}_\\lambda(x,\\xi))$, when ${\\cal H}_\\lambda(x,\\xi)$ is the perturbation of completely integrable Hamiltonian $\\widetilde{\\cal H}$ veriying some isoenergetic non-degeneracy conditions. Assuming the Weyl $h$-PDO $H^w_\\lambda$ has only discrete spectrum near $E$, and the energy surface $\\{\\widetilde{\\cal H}={\\cal E}\\}$ is separated by some pairwise disjoint lagrangian tori, we show that most of eigenvalues for $\\hat H_\\lambda$ near $E$ are asymptotically degen","authors_text":"Michel Rouleux, Sergey Dobrokhotov","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-16T12:48:48Z","title":"The semiclassical Maupertuis-Jacobi correspondence for quasi-periodic Hamiltonian flows: stable and unstable spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3785","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":"sha256:4e53d5609e284d76dbaf951cc7dd5533d4abed71565c65f36640b29d9bc19e7b","target":"record","created_at":"2026-05-18T03:25:33Z","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":"0cb56073a17f41497df28c440f19e2c79617a90829bf3fd07114132323fab858","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-16T12:48:48Z","title_canon_sha256":"3d2aab8fbf7046cdcf66a399f9c1328e99576025c7b06d8a4d27b9e22286706b"},"schema_version":"1.0","source":{"id":"1305.3785","kind":"arxiv","version":1}},"canonical_sha256":"d1729949975dd284f7350a37cf6f1d14a277e84f5c7ef46cef60fb0a6f865ca8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1729949975dd284f7350a37cf6f1d14a277e84f5c7ef46cef60fb0a6f865ca8","first_computed_at":"2026-05-18T03:25:33.901779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:33.901779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GkqYFwXzKwf3zuyAh/HfiXsu9/Mhe0nIeLpqtBdzQROfAbA2w5vExLOOz4nfz8CqWEB/YM4Q9X+RbeRiw3kcDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:33.902558Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.3785","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e53d5609e284d76dbaf951cc7dd5533d4abed71565c65f36640b29d9bc19e7b","sha256:f09deae88520776bb4fa82a0b152078d05678093d8e7056455dca82862e619b8"],"state_sha256":"eb956f12f04154a282531c113cfc493140258e7bc0610892e6a4e9695699cbdc"}