{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:JGCE6ESTQGL3GRRJYAD57UIM5N","short_pith_number":"pith:JGCE6EST","schema_version":"1.0","canonical_sha256":"49844f12538197b34629c007dfd10ceb442297f98107573076f69645b3f123f6","source":{"kind":"arxiv","id":"2608.11111","version":1},"attestation_state":"computed","paper":{"title":"Generic Spectral Determination of Semiclassical Schr\\\"odinger Operators with $\\mathbb Z_2$-Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Qiaoling Wei","submitted_at":"2026-08-11T16:20:24Z","abstract_excerpt":"Consider the two-dimensional semiclassical Schr\\\"odinger operator $P_\\hbar=-\\frac{\\hbar^2}{2}\\Delta+V$ on $\\mathbb R^2$, where $V$ has a nondegenerate well at the origin, its harmonic frequencies are rationally independent, and $V$ is $\\mathbb Z_2$-symmetric. We prove that, generically, the first three layers of the quantum Birkhoff normal form (QBNF) determine the full Taylor series of $V$ at the origin, up to the unavoidable spatial inversion $V(x)\\mapsto V(-x)$. The generic condition depends only on the jet of $V$ through order ten. Consequently, for real analytic potentials with a unique i"},"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":"2608.11111","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-08-11T16:20:24Z","cross_cats_sorted":[],"title_canon_sha256":"83ce97c713194c94e6bd5825c80f50b348b3c920b8b9062b57e2fc6894ff3d06","abstract_canon_sha256":"6571baac36f0ea6456d9bd2db66a3fdd823cb37c3f793a827a129891e4816f1e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-12T01:24:37.663091Z","signature_b64":"kg8WRGbYFma0Vtit3ZhL/xaqG31HFvpGayrp/hUJ39/qkQbwEsR0pQIiQYL/8El67EM68b3bG+Qy/WjvZxNxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49844f12538197b34629c007dfd10ceb442297f98107573076f69645b3f123f6","last_reissued_at":"2026-08-12T01:24:37.661482Z","signature_status":"signed_v1","first_computed_at":"2026-08-12T01:24:37.661482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generic Spectral Determination of Semiclassical Schr\\\"odinger Operators with $\\mathbb Z_2$-Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Qiaoling Wei","submitted_at":"2026-08-11T16:20:24Z","abstract_excerpt":"Consider the two-dimensional semiclassical Schr\\\"odinger operator $P_\\hbar=-\\frac{\\hbar^2}{2}\\Delta+V$ on $\\mathbb R^2$, where $V$ has a nondegenerate well at the origin, its harmonic frequencies are rationally independent, and $V$ is $\\mathbb Z_2$-symmetric. We prove that, generically, the first three layers of the quantum Birkhoff normal form (QBNF) determine the full Taylor series of $V$ at the origin, up to the unavoidable spatial inversion $V(x)\\mapsto V(-x)$. The generic condition depends only on the jet of $V$ through order ten. Consequently, for real analytic potentials with a unique i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11111","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.11111/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2608.11111","created_at":"2026-08-12T01:24:37.665350+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.11111v1","created_at":"2026-08-12T01:24:37.665350+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11111","created_at":"2026-08-12T01:24:37.665350+00:00"},{"alias_kind":"pith_short_12","alias_value":"JGCE6ESTQGL3","created_at":"2026-08-12T01:24:37.665350+00:00"},{"alias_kind":"pith_short_16","alias_value":"JGCE6ESTQGL3GRRJ","created_at":"2026-08-12T01:24:37.665350+00:00"},{"alias_kind":"pith_short_8","alias_value":"JGCE6EST","created_at":"2026-08-12T01:24:37.665350+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/JGCE6ESTQGL3GRRJYAD57UIM5N","json":"https://pith.science/pith/JGCE6ESTQGL3GRRJYAD57UIM5N.json","graph_json":"https://pith.science/api/pith-number/JGCE6ESTQGL3GRRJYAD57UIM5N/graph.json","events_json":"https://pith.science/api/pith-number/JGCE6ESTQGL3GRRJYAD57UIM5N/events.json","paper":"https://pith.science/paper/JGCE6EST"},"agent_actions":{"view_html":"https://pith.science/pith/JGCE6ESTQGL3GRRJYAD57UIM5N","download_json":"https://pith.science/pith/JGCE6ESTQGL3GRRJYAD57UIM5N.json","view_paper":"https://pith.science/paper/JGCE6EST","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.11111&json=true","fetch_graph":"https://pith.science/api/pith-number/JGCE6ESTQGL3GRRJYAD57UIM5N/graph.json","fetch_events":"https://pith.science/api/pith-number/JGCE6ESTQGL3GRRJYAD57UIM5N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JGCE6ESTQGL3GRRJYAD57UIM5N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JGCE6ESTQGL3GRRJYAD57UIM5N/action/storage_attestation","attest_author":"https://pith.science/pith/JGCE6ESTQGL3GRRJYAD57UIM5N/action/author_attestation","sign_citation":"https://pith.science/pith/JGCE6ESTQGL3GRRJYAD57UIM5N/action/citation_signature","submit_replication":"https://pith.science/pith/JGCE6ESTQGL3GRRJYAD57UIM5N/action/replication_record"}},"created_at":"2026-08-12T01:24:37.665350+00:00","updated_at":"2026-08-12T01:24:37.665350+00:00"}