{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VFIWIL7U5KK47TW7Z2WVLBMQZX","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":"a5221c35b2c61981d041dfcf09040dc73fabcabac8b3b2e23165b53287662a8d","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-06-23T16:35:57Z","title_canon_sha256":"8af4eb67c08750b558f9bdf2e12c1e99bf853430f4752185f46e0b135a238d54"},"schema_version":"1.0","source":{"id":"1206.5409","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5409","created_at":"2026-05-18T03:52:40Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5409v1","created_at":"2026-05-18T03:52:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5409","created_at":"2026-05-18T03:52:40Z"},{"alias_kind":"pith_short_12","alias_value":"VFIWIL7U5KK4","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VFIWIL7U5KK47TW7","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VFIWIL7U","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:975d5d2483ffb9b5fac82c8bdde26c58a4bab59c986f1f4c4b297b9ea121d600","target":"graph","created_at":"2026-05-18T03:52:40Z","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 for families of 2-D Hamiltonians $(H_\\lambda(x,\\xi), {\\cal H}_\\lambda(x,\\xi))$, when ${\\cal H}_\\lambda(x,\\xi)$ is the perturbation of a completely integrable Hamiltonian $\\widetilde{\\cal H}$ veriying some isoenergetic non-degeneracy conditions. Assuming $\\hat H_\\lambda$ has only discrete spectrum near $E$, and the energy surface $\\{\\widetilde{\\cal H}_0={\\cal E}\\}$ is separated by some pairwise disjoint Lagrangian tori, we show that most of eigenvalues for $\\hat H_\\lambda$ near $E$ are asymptotically degenerate as $h\\t","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":"2012-06-23T16:35:57Z","title":"The semi-classical Maupertuis-Jacobi correspondence: stable and unstable spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5409","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:ab147bb080a1b1eec555d1acfcf5cff29f2af15e651756cbb474832e72ced45f","target":"record","created_at":"2026-05-18T03:52:40Z","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":"a5221c35b2c61981d041dfcf09040dc73fabcabac8b3b2e23165b53287662a8d","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-06-23T16:35:57Z","title_canon_sha256":"8af4eb67c08750b558f9bdf2e12c1e99bf853430f4752185f46e0b135a238d54"},"schema_version":"1.0","source":{"id":"1206.5409","kind":"arxiv","version":1}},"canonical_sha256":"a951642ff4ea95cfcedfcead558590cdd98e62b399ba16274aa140024a9264cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a951642ff4ea95cfcedfcead558590cdd98e62b399ba16274aa140024a9264cb","first_computed_at":"2026-05-18T03:52:40.187877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:40.187877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eWktZ1EYdE0QXYmUsBaiUG9LbyWZ3AEgQRNyWbK7B8M+Ewkhpdg5nGSRm2KqDtCDxVuJnLVNjEw3ue9a1CiFCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:40.188447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5409","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab147bb080a1b1eec555d1acfcf5cff29f2af15e651756cbb474832e72ced45f","sha256:975d5d2483ffb9b5fac82c8bdde26c58a4bab59c986f1f4c4b297b9ea121d600"],"state_sha256":"a00a25eaba414e403fb96f44d65b3aea8bb753950109882fee26f28359b60455"}