{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:XAY775VURTLFNIDB5SD2JPX4E5","short_pith_number":"pith:XAY775VU","schema_version":"1.0","canonical_sha256":"b831fff6b48cd656a061ec87a4befc2751e49f7fec1c6aac37e54faf5c1309df","source":{"kind":"arxiv","id":"1205.7004","version":1},"attestation_state":"computed","paper":{"title":"Resonance widths in a case of multidimensional phase space tunneling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Alain Grigis, Andr\\'e Martinez","submitted_at":"2012-05-31T14:22:58Z","abstract_excerpt":"We consider a semiclassical $2\\times 2$ matrix Schr\\\"odinger operator of the form $P=-h^2\\Delta {\\bf I}_2 + {\\rm diag}(x_n-\\mu, \\tau V_2(x)) +hR(x,hD_x)$, where $\\mu$ and $\\tau$ are two small positive constants, $V_2$ is real-analytic and admits a non degenerate minimum at 0, and $R=(r_{j,k}(x,hD_x))_{1\\leq j,k\\leq 2}$ is a symmetric off-diagonal $2\\times 2$ matrix of first-order differential operators with analytic coefficients. Then, denoting by $e_1$ the first eigenvalue of $-\\Delta + \\la \\tau V_2\"(0)x,x\\ra /2$, and under some ellipticity condition on $r_{1,2}=r_{2,1}^*$, we show that, for "},"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":"1205.7004","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-31T14:22:58Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"415ea44d468d1fb1ef1cf3ee97b6f9db51581071b33853dd1469d08780291882","abstract_canon_sha256":"0032d2dabb4b8e2dbdfe10981e59ede42873abdfbccd8b9c83991f14641b9846"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:36.388014Z","signature_b64":"lhqJbmBvNuYW0FVGD9ZnMMBNiuT0SIJGBTDr9ThW10Zyfu/tB3wv4aUoDmjpEnGj0nyZ1p35cI1D7Rpbg8DgCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b831fff6b48cd656a061ec87a4befc2751e49f7fec1c6aac37e54faf5c1309df","last_reissued_at":"2026-05-18T03:54:36.387251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:36.387251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resonance widths in a case of multidimensional phase space tunneling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Alain Grigis, Andr\\'e Martinez","submitted_at":"2012-05-31T14:22:58Z","abstract_excerpt":"We consider a semiclassical $2\\times 2$ matrix Schr\\\"odinger operator of the form $P=-h^2\\Delta {\\bf I}_2 + {\\rm diag}(x_n-\\mu, \\tau V_2(x)) +hR(x,hD_x)$, where $\\mu$ and $\\tau$ are two small positive constants, $V_2$ is real-analytic and admits a non degenerate minimum at 0, and $R=(r_{j,k}(x,hD_x))_{1\\leq j,k\\leq 2}$ is a symmetric off-diagonal $2\\times 2$ matrix of first-order differential operators with analytic coefficients. Then, denoting by $e_1$ the first eigenvalue of $-\\Delta + \\la \\tau V_2\"(0)x,x\\ra /2$, and under some ellipticity condition on $r_{1,2}=r_{2,1}^*$, we show that, for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.7004","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":"1205.7004","created_at":"2026-05-18T03:54:36.387368+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.7004v1","created_at":"2026-05-18T03:54:36.387368+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.7004","created_at":"2026-05-18T03:54:36.387368+00:00"},{"alias_kind":"pith_short_12","alias_value":"XAY775VURTLF","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"XAY775VURTLFNIDB","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"XAY775VU","created_at":"2026-05-18T12:27:27.928770+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/XAY775VURTLFNIDB5SD2JPX4E5","json":"https://pith.science/pith/XAY775VURTLFNIDB5SD2JPX4E5.json","graph_json":"https://pith.science/api/pith-number/XAY775VURTLFNIDB5SD2JPX4E5/graph.json","events_json":"https://pith.science/api/pith-number/XAY775VURTLFNIDB5SD2JPX4E5/events.json","paper":"https://pith.science/paper/XAY775VU"},"agent_actions":{"view_html":"https://pith.science/pith/XAY775VURTLFNIDB5SD2JPX4E5","download_json":"https://pith.science/pith/XAY775VURTLFNIDB5SD2JPX4E5.json","view_paper":"https://pith.science/paper/XAY775VU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.7004&json=true","fetch_graph":"https://pith.science/api/pith-number/XAY775VURTLFNIDB5SD2JPX4E5/graph.json","fetch_events":"https://pith.science/api/pith-number/XAY775VURTLFNIDB5SD2JPX4E5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XAY775VURTLFNIDB5SD2JPX4E5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XAY775VURTLFNIDB5SD2JPX4E5/action/storage_attestation","attest_author":"https://pith.science/pith/XAY775VURTLFNIDB5SD2JPX4E5/action/author_attestation","sign_citation":"https://pith.science/pith/XAY775VURTLFNIDB5SD2JPX4E5/action/citation_signature","submit_replication":"https://pith.science/pith/XAY775VURTLFNIDB5SD2JPX4E5/action/replication_record"}},"created_at":"2026-05-18T03:54:36.387368+00:00","updated_at":"2026-05-18T03:54:36.387368+00:00"}