{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:N5SSMOQY6OBASVAJFBIZ6RLMWI","short_pith_number":"pith:N5SSMOQY","schema_version":"1.0","canonical_sha256":"6f65263a18f38209540928519f456cb21c8037dc701fc5117fe96cd92d86443c","source":{"kind":"arxiv","id":"1511.07411","version":1},"attestation_state":"computed","paper":{"title":"Quantum Limits of Eisenstein Series in H^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Niko Laaksonen","submitted_at":"2015-11-23T20:45:48Z","abstract_excerpt":"We study the quantum limits of Eisenstein series off the critical line for $\\mathrm{PSL}_{2}(\\mathcal{O}_{K})\\backslash\\mathbb{H}^{3}$, where $K$ is an imaginary quadratic field of class number one. This generalises the results of Petridis, Raulf and Risager on $\\mathrm{PSL}_{2}(\\mathbb{Z})\\backslash\\mathbb{H}^{2}$. We observe that the measures $\\lvert E(p,\\sigma_{t}+it)\\rvert^{2}d\\mu(p)$ become equidistributed only if $\\sigma_{t}\\rightarrow 1$ as $t\\rightarrow\\infty$. We use these computations to study measures defined in terms of the scattering states, which are shown to converge to the abso"},"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":"1511.07411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-23T20:45:48Z","cross_cats_sorted":[],"title_canon_sha256":"eaca642660a08ff2301ff48537bb3e669bacb82f4d7ad7c14eb88861d5c924aa","abstract_canon_sha256":"7ae5a60e636d79f9676157cdf891a71d11d2454514cfd74e752e7a63d0b7d705"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:11.479899Z","signature_b64":"YJJR7GgC75Od9v9PDHH32Fcnja11DRu09I27w3D1SqslQbdS9zDB6Tbq6xzw/sz/M1QV8oieODZGg94/PGdRAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f65263a18f38209540928519f456cb21c8037dc701fc5117fe96cd92d86443c","last_reissued_at":"2026-05-18T01:26:11.479393Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:11.479393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum Limits of Eisenstein Series in H^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Niko Laaksonen","submitted_at":"2015-11-23T20:45:48Z","abstract_excerpt":"We study the quantum limits of Eisenstein series off the critical line for $\\mathrm{PSL}_{2}(\\mathcal{O}_{K})\\backslash\\mathbb{H}^{3}$, where $K$ is an imaginary quadratic field of class number one. This generalises the results of Petridis, Raulf and Risager on $\\mathrm{PSL}_{2}(\\mathbb{Z})\\backslash\\mathbb{H}^{2}$. We observe that the measures $\\lvert E(p,\\sigma_{t}+it)\\rvert^{2}d\\mu(p)$ become equidistributed only if $\\sigma_{t}\\rightarrow 1$ as $t\\rightarrow\\infty$. We use these computations to study measures defined in terms of the scattering states, which are shown to converge to the abso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07411","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":"1511.07411","created_at":"2026-05-18T01:26:11.479482+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.07411v1","created_at":"2026-05-18T01:26:11.479482+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07411","created_at":"2026-05-18T01:26:11.479482+00:00"},{"alias_kind":"pith_short_12","alias_value":"N5SSMOQY6OBA","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"N5SSMOQY6OBASVAJ","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"N5SSMOQY","created_at":"2026-05-18T12:29:32.376354+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/N5SSMOQY6OBASVAJFBIZ6RLMWI","json":"https://pith.science/pith/N5SSMOQY6OBASVAJFBIZ6RLMWI.json","graph_json":"https://pith.science/api/pith-number/N5SSMOQY6OBASVAJFBIZ6RLMWI/graph.json","events_json":"https://pith.science/api/pith-number/N5SSMOQY6OBASVAJFBIZ6RLMWI/events.json","paper":"https://pith.science/paper/N5SSMOQY"},"agent_actions":{"view_html":"https://pith.science/pith/N5SSMOQY6OBASVAJFBIZ6RLMWI","download_json":"https://pith.science/pith/N5SSMOQY6OBASVAJFBIZ6RLMWI.json","view_paper":"https://pith.science/paper/N5SSMOQY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.07411&json=true","fetch_graph":"https://pith.science/api/pith-number/N5SSMOQY6OBASVAJFBIZ6RLMWI/graph.json","fetch_events":"https://pith.science/api/pith-number/N5SSMOQY6OBASVAJFBIZ6RLMWI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N5SSMOQY6OBASVAJFBIZ6RLMWI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N5SSMOQY6OBASVAJFBIZ6RLMWI/action/storage_attestation","attest_author":"https://pith.science/pith/N5SSMOQY6OBASVAJFBIZ6RLMWI/action/author_attestation","sign_citation":"https://pith.science/pith/N5SSMOQY6OBASVAJFBIZ6RLMWI/action/citation_signature","submit_replication":"https://pith.science/pith/N5SSMOQY6OBASVAJFBIZ6RLMWI/action/replication_record"}},"created_at":"2026-05-18T01:26:11.479482+00:00","updated_at":"2026-05-18T01:26:11.479482+00:00"}