{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:6EZHJ7U3CQ3SSRCQXOQ5XBW7CR","short_pith_number":"pith:6EZHJ7U3","schema_version":"1.0","canonical_sha256":"f13274fe9b1437294450bba1db86df1461ea0571d4aa07bb8c6d256958b69e56","source":{"kind":"arxiv","id":"1005.0296","version":2},"attestation_state":"computed","paper":{"title":"Semiclassical measures for the Schr\\\"odinger equation on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Fabricio Maci\\`a (UPM), Nalini Anantharaman (LM-Orsay)","submitted_at":"2010-04-29T06:42:16Z","abstract_excerpt":"In this article, the structure of semiclassical measures for solutions to the linear Schr\\\"{o}dinger equation on the torus is analysed. We show that the disintegration of such a measure on every invariant lagrangian torus is absolutely continuous with respect to the Lebesgue measure. We obtain an expression of the Radon-Nikodym derivative in terms of the sequence of initial data and show that it satisfies an explicit propagation law. As a consequence, we also prove an observability inequality, saying that the $L^2$-norm of a solution on any open subset of the torus controls the full $L^2$-norm"},"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":"1005.0296","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-04-29T06:42:16Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"a045683bdf8730b01ca724595f08f1fd5183d3133162303fbfb4018c1a13c18f","abstract_canon_sha256":"ebccc37d1865642422bea0a10de5fdf54e203e10abbf24af92b4a324e36b139e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:16.156111Z","signature_b64":"Ta3TSgY+N41njw5hNg2PA0R/HNyvLtGfh2kOIS1hfeN2hKn6hbvKOPBbxe414KWa9H20BIo5AQFTKdAYoG6jDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f13274fe9b1437294450bba1db86df1461ea0571d4aa07bb8c6d256958b69e56","last_reissued_at":"2026-05-18T04:13:16.155439Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:16.155439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semiclassical measures for the Schr\\\"odinger equation on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Fabricio Maci\\`a (UPM), Nalini Anantharaman (LM-Orsay)","submitted_at":"2010-04-29T06:42:16Z","abstract_excerpt":"In this article, the structure of semiclassical measures for solutions to the linear Schr\\\"{o}dinger equation on the torus is analysed. We show that the disintegration of such a measure on every invariant lagrangian torus is absolutely continuous with respect to the Lebesgue measure. We obtain an expression of the Radon-Nikodym derivative in terms of the sequence of initial data and show that it satisfies an explicit propagation law. As a consequence, we also prove an observability inequality, saying that the $L^2$-norm of a solution on any open subset of the torus controls the full $L^2$-norm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0296","kind":"arxiv","version":2},"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":"1005.0296","created_at":"2026-05-18T04:13:16.155546+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.0296v2","created_at":"2026-05-18T04:13:16.155546+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.0296","created_at":"2026-05-18T04:13:16.155546+00:00"},{"alias_kind":"pith_short_12","alias_value":"6EZHJ7U3CQ3S","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"6EZHJ7U3CQ3SSRCQ","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"6EZHJ7U3","created_at":"2026-05-18T12:26:04.259169+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/6EZHJ7U3CQ3SSRCQXOQ5XBW7CR","json":"https://pith.science/pith/6EZHJ7U3CQ3SSRCQXOQ5XBW7CR.json","graph_json":"https://pith.science/api/pith-number/6EZHJ7U3CQ3SSRCQXOQ5XBW7CR/graph.json","events_json":"https://pith.science/api/pith-number/6EZHJ7U3CQ3SSRCQXOQ5XBW7CR/events.json","paper":"https://pith.science/paper/6EZHJ7U3"},"agent_actions":{"view_html":"https://pith.science/pith/6EZHJ7U3CQ3SSRCQXOQ5XBW7CR","download_json":"https://pith.science/pith/6EZHJ7U3CQ3SSRCQXOQ5XBW7CR.json","view_paper":"https://pith.science/paper/6EZHJ7U3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.0296&json=true","fetch_graph":"https://pith.science/api/pith-number/6EZHJ7U3CQ3SSRCQXOQ5XBW7CR/graph.json","fetch_events":"https://pith.science/api/pith-number/6EZHJ7U3CQ3SSRCQXOQ5XBW7CR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6EZHJ7U3CQ3SSRCQXOQ5XBW7CR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6EZHJ7U3CQ3SSRCQXOQ5XBW7CR/action/storage_attestation","attest_author":"https://pith.science/pith/6EZHJ7U3CQ3SSRCQXOQ5XBW7CR/action/author_attestation","sign_citation":"https://pith.science/pith/6EZHJ7U3CQ3SSRCQXOQ5XBW7CR/action/citation_signature","submit_replication":"https://pith.science/pith/6EZHJ7U3CQ3SSRCQXOQ5XBW7CR/action/replication_record"}},"created_at":"2026-05-18T04:13:16.155546+00:00","updated_at":"2026-05-18T04:13:16.155546+00:00"}