{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TSIFM5P7L3PCD7NRRMRMNHWOKC","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":"b54705c0d79c7fd4a359b34eb4e7c411d4a872726e2c8ba510ea7334cdffa0f4","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-05-07T13:46:32Z","title_canon_sha256":"81e3c1400f1e312768c2fd7f624d333c2e698c9d293fe3a1248156063e169af4"},"schema_version":"1.0","source":{"id":"1505.01702","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01702","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01702v2","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01702","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"TSIFM5P7L3PC","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TSIFM5P7L3PCD7NR","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TSIFM5P7","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:76e8a7f2fdee7b4f42be9b1917a8b88efb2a3328876f295095a9b30188d91c4f","target":"graph","created_at":"2026-05-18T01:55:59Z","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":"This paper is a proceedings version of \\cite{CHT-I}, in which we state a Quantum Ergodicity (QE) theorem on a 3D contact manifold, and in which we establish some properties of the Quantum Limits (QL). We consider a sub-Riemannian (sR) metric on a compact 3D manifold with an oriented contact distribution. There exists a privileged choice of the contact form, with an associated Reeb vector field and a canonical volume form that coincides with the Popp measure. We state a QE theorem for the eigenfunctions of any associated sR Laplacian, under the assumption that the Reeb flow is ergodic. The limi","authors_text":"Emmanuel Tr\\'elat (LJLL), Luc Hillairet (MAPMO - FDP), Yves Colin de Verdi\\`ere","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-05-07T13:46:32Z","title":"Quantum ergodicity and quantum limits for sub-Riemannian Laplacians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01702","kind":"arxiv","version":2},"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":"sha256:21ea24dc1c7597bef55ad98fbf88ccc141c42d9ad2c1f81ef36ba9a4ec676283","target":"record","created_at":"2026-05-18T01:55:59Z","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":"b54705c0d79c7fd4a359b34eb4e7c411d4a872726e2c8ba510ea7334cdffa0f4","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-05-07T13:46:32Z","title_canon_sha256":"81e3c1400f1e312768c2fd7f624d333c2e698c9d293fe3a1248156063e169af4"},"schema_version":"1.0","source":{"id":"1505.01702","kind":"arxiv","version":2}},"canonical_sha256":"9c905675ff5ede21fdb18b22c69ece5082a4fbdcf39b723e7fe78bc9d910c8c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c905675ff5ede21fdb18b22c69ece5082a4fbdcf39b723e7fe78bc9d910c8c3","first_computed_at":"2026-05-18T01:55:59.490328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:59.490328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bsw1T0xmtNsq5ikcefsF4T4P9eAqR+31X5BS957rJPTS1ULBb29XyP2vIbAiIszTjVeY/vcCm24fc6db/Jk6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:59.490857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.01702","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21ea24dc1c7597bef55ad98fbf88ccc141c42d9ad2c1f81ef36ba9a4ec676283","sha256:76e8a7f2fdee7b4f42be9b1917a8b88efb2a3328876f295095a9b30188d91c4f"],"state_sha256":"c9a0d0ac230ea973793c4180eb9f0074fa51c892c02daa6df90b6e8cb858c1dd"}