{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:AQAE3DBZQGRCUIJPURQCU32Q3F","short_pith_number":"pith:AQAE3DBZ","schema_version":"1.0","canonical_sha256":"04004d8c3981a22a212fa4602a6f50d940fc93b4efbaa0bd1c00ef2905b009bf","source":{"kind":"arxiv","id":"1111.3187","version":1},"attestation_state":"computed","paper":{"title":"Wigner measures and the semi-classical limit to the Aubry-Mather measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR","quant-ph"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Diogo A. Gomes, Joana Mohr","submitted_at":"2011-11-14T12:03:17Z","abstract_excerpt":"In this paper we investigate the asymptotic behavior of the semi-classical limit of Wigner measures defined on the tangent bundle of the one-dimensional torus. In particular we show the convergence of Wigner measures to the Mather measure on the tangent bundle, for energy levels above the minimum of the effective Hamiltonian.\n  The Wigner measures $\\mu_h$ we consider are associated to $\\psi_h,$ a distinguished critical solution of the Evans' quantum action given by $\\psi_h=a_h\\,e^{i\\frac{u_h}h}$, with $a_h(x)=e^{\\frac{v^*_h(x)-v_h(x)}{2h}}$, $u_h(x)=P\\cdot x+\\frac{v^*_h(x)+v_h(x)}{2},$ and $v_"},"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":"1111.3187","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-14T12:03:17Z","cross_cats_sorted":["math-ph","math.MP","math.PR","quant-ph"],"title_canon_sha256":"c20fe71a624a001fedc2ee27efb7c3b4f81b88bdb35b890fe22fdc65c81dfa0d","abstract_canon_sha256":"ddc6095bba844ccaeb48403a8a9c166ff86e54e01098410a037d2e7b57ac79be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:22.846852Z","signature_b64":"ZMdqqT6uRQOSc+q2AnRV+/tPGkv9ut5/Ut/7s9gs1zoOUsF86q86WbWS39COxhRptHUjAztiQmdumNxsW8BCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04004d8c3981a22a212fa4602a6f50d940fc93b4efbaa0bd1c00ef2905b009bf","last_reissued_at":"2026-05-18T04:08:22.846387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:22.846387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wigner measures and the semi-classical limit to the Aubry-Mather measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR","quant-ph"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Diogo A. Gomes, Joana Mohr","submitted_at":"2011-11-14T12:03:17Z","abstract_excerpt":"In this paper we investigate the asymptotic behavior of the semi-classical limit of Wigner measures defined on the tangent bundle of the one-dimensional torus. In particular we show the convergence of Wigner measures to the Mather measure on the tangent bundle, for energy levels above the minimum of the effective Hamiltonian.\n  The Wigner measures $\\mu_h$ we consider are associated to $\\psi_h,$ a distinguished critical solution of the Evans' quantum action given by $\\psi_h=a_h\\,e^{i\\frac{u_h}h}$, with $a_h(x)=e^{\\frac{v^*_h(x)-v_h(x)}{2h}}$, $u_h(x)=P\\cdot x+\\frac{v^*_h(x)+v_h(x)}{2},$ and $v_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3187","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":"1111.3187","created_at":"2026-05-18T04:08:22.846457+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.3187v1","created_at":"2026-05-18T04:08:22.846457+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3187","created_at":"2026-05-18T04:08:22.846457+00:00"},{"alias_kind":"pith_short_12","alias_value":"AQAE3DBZQGRC","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"AQAE3DBZQGRCUIJP","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"AQAE3DBZ","created_at":"2026-05-18T12:26:24.575870+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/AQAE3DBZQGRCUIJPURQCU32Q3F","json":"https://pith.science/pith/AQAE3DBZQGRCUIJPURQCU32Q3F.json","graph_json":"https://pith.science/api/pith-number/AQAE3DBZQGRCUIJPURQCU32Q3F/graph.json","events_json":"https://pith.science/api/pith-number/AQAE3DBZQGRCUIJPURQCU32Q3F/events.json","paper":"https://pith.science/paper/AQAE3DBZ"},"agent_actions":{"view_html":"https://pith.science/pith/AQAE3DBZQGRCUIJPURQCU32Q3F","download_json":"https://pith.science/pith/AQAE3DBZQGRCUIJPURQCU32Q3F.json","view_paper":"https://pith.science/paper/AQAE3DBZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.3187&json=true","fetch_graph":"https://pith.science/api/pith-number/AQAE3DBZQGRCUIJPURQCU32Q3F/graph.json","fetch_events":"https://pith.science/api/pith-number/AQAE3DBZQGRCUIJPURQCU32Q3F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AQAE3DBZQGRCUIJPURQCU32Q3F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AQAE3DBZQGRCUIJPURQCU32Q3F/action/storage_attestation","attest_author":"https://pith.science/pith/AQAE3DBZQGRCUIJPURQCU32Q3F/action/author_attestation","sign_citation":"https://pith.science/pith/AQAE3DBZQGRCUIJPURQCU32Q3F/action/citation_signature","submit_replication":"https://pith.science/pith/AQAE3DBZQGRCUIJPURQCU32Q3F/action/replication_record"}},"created_at":"2026-05-18T04:08:22.846457+00:00","updated_at":"2026-05-18T04:08:22.846457+00:00"}