{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3QYPHZM44AOI6CMZ7KW6AGB266","short_pith_number":"pith:3QYPHZM4","schema_version":"1.0","canonical_sha256":"dc30f3e59ce01c8f0999faade0183af78ea1fac5de6bcba9d8a9cbab29115aee","source":{"kind":"arxiv","id":"1210.4499","version":2},"attestation_state":"computed","paper":{"title":"On the distribution of perturbations of propagated Schr\\\"odinger eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Dmitry Jakobson, John Toth, Yaiza Canzani","submitted_at":"2012-10-16T17:15:17Z","abstract_excerpt":"Let $(M,g_0)$ be a compact Riemmanian manifold of dimension $n$. Let $P_0 (\\h) := -\\h^2\\Delta_{g}+V$ be the semiclassical Schr\\\"{o}dinger operator for $\\h \\in (0,\\h_0]$, and let $E$ be a regular value of its principal symbol $p_0(x,\\xi)=|\\xi|^2_{g_0(x)} +V(x)$. Write $\\varphi_\\h$ for an $L^2$-normalized eigenfunction of $P(\\h)$, $P_0(\\h)\\varphi_\\h =E(\\h)\\varphi_\\h$ and $E(\\h) \\in [E-o(1),E+ o(1)]$. Consider a smooth family of perturbations $g_u$ of $g_0$ with $u$ in the ball $\\mathcal B^k(\\varepsilon) \\subset \\mathbb R^k$ of radius $\\varepsilon>0$. For $P_{u}(\\h) := -\\h^2 \\Delta_{g_u} +V$ and "},"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":"1210.4499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-10-16T17:15:17Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"463b5386046622657500f5b9dbe99b9566d089f8b1f6c49a9128a4113e8e7668","abstract_canon_sha256":"ff56fcb776460a1d4dab8df34586d2395a2fc205a3c593ab59915b7a1f7ed6f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:48.530369Z","signature_b64":"Vjc2iZw4AeGBkVpLj3+i6+eqKMcQF2dq7BqIaBEFvfZnxMae9g8D83yxZyCIhgde/YlqTwsZgQHGN3u/whf+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc30f3e59ce01c8f0999faade0183af78ea1fac5de6bcba9d8a9cbab29115aee","last_reissued_at":"2026-05-18T03:20:48.529624Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:48.529624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the distribution of perturbations of propagated Schr\\\"odinger eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Dmitry Jakobson, John Toth, Yaiza Canzani","submitted_at":"2012-10-16T17:15:17Z","abstract_excerpt":"Let $(M,g_0)$ be a compact Riemmanian manifold of dimension $n$. Let $P_0 (\\h) := -\\h^2\\Delta_{g}+V$ be the semiclassical Schr\\\"{o}dinger operator for $\\h \\in (0,\\h_0]$, and let $E$ be a regular value of its principal symbol $p_0(x,\\xi)=|\\xi|^2_{g_0(x)} +V(x)$. Write $\\varphi_\\h$ for an $L^2$-normalized eigenfunction of $P(\\h)$, $P_0(\\h)\\varphi_\\h =E(\\h)\\varphi_\\h$ and $E(\\h) \\in [E-o(1),E+ o(1)]$. Consider a smooth family of perturbations $g_u$ of $g_0$ with $u$ in the ball $\\mathcal B^k(\\varepsilon) \\subset \\mathbb R^k$ of radius $\\varepsilon>0$. For $P_{u}(\\h) := -\\h^2 \\Delta_{g_u} +V$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4499","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":"1210.4499","created_at":"2026-05-18T03:20:48.529744+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.4499v2","created_at":"2026-05-18T03:20:48.529744+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4499","created_at":"2026-05-18T03:20:48.529744+00:00"},{"alias_kind":"pith_short_12","alias_value":"3QYPHZM44AOI","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"3QYPHZM44AOI6CMZ","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"3QYPHZM4","created_at":"2026-05-18T12:26:53.410803+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/3QYPHZM44AOI6CMZ7KW6AGB266","json":"https://pith.science/pith/3QYPHZM44AOI6CMZ7KW6AGB266.json","graph_json":"https://pith.science/api/pith-number/3QYPHZM44AOI6CMZ7KW6AGB266/graph.json","events_json":"https://pith.science/api/pith-number/3QYPHZM44AOI6CMZ7KW6AGB266/events.json","paper":"https://pith.science/paper/3QYPHZM4"},"agent_actions":{"view_html":"https://pith.science/pith/3QYPHZM44AOI6CMZ7KW6AGB266","download_json":"https://pith.science/pith/3QYPHZM44AOI6CMZ7KW6AGB266.json","view_paper":"https://pith.science/paper/3QYPHZM4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.4499&json=true","fetch_graph":"https://pith.science/api/pith-number/3QYPHZM44AOI6CMZ7KW6AGB266/graph.json","fetch_events":"https://pith.science/api/pith-number/3QYPHZM44AOI6CMZ7KW6AGB266/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3QYPHZM44AOI6CMZ7KW6AGB266/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3QYPHZM44AOI6CMZ7KW6AGB266/action/storage_attestation","attest_author":"https://pith.science/pith/3QYPHZM44AOI6CMZ7KW6AGB266/action/author_attestation","sign_citation":"https://pith.science/pith/3QYPHZM44AOI6CMZ7KW6AGB266/action/citation_signature","submit_replication":"https://pith.science/pith/3QYPHZM44AOI6CMZ7KW6AGB266/action/replication_record"}},"created_at":"2026-05-18T03:20:48.529744+00:00","updated_at":"2026-05-18T03:20:48.529744+00:00"}