{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LLTCQG3FJJRABRUTBKEE35UYR3","short_pith_number":"pith:LLTCQG3F","schema_version":"1.0","canonical_sha256":"5ae6281b654a6200c6930a884df6988ed11f85aa01b3c0d9f3a431124d5d6631","source":{"kind":"arxiv","id":"1203.2901","version":3},"attestation_state":"computed","paper":{"title":"Spectral Rigidity for Periodic Schr\\\"odinger Operators in Dimension 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Alden Waters","submitted_at":"2012-03-13T19:23:23Z","abstract_excerpt":"We consider two dimensional real-valued analytic potentials for the Schr\\\"odinger equation which are periodic over a lattice $L$. Under certain assumptions on the form of the potential and the lattice $L$, we can show there is a large class of analytic potentials which are Floquet rigid and dense in the set of $C^\\infty(R^2/L)$ potentials. The result extends the work of Eskin et. al, in \"On isospectral periodic potentials in $R^n$, II.\""},"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":"1203.2901","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-13T19:23:23Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"99fb302917cf9fb2723c6d5987d7651089fdd2e81a9ecc07863d012b5b2e6327","abstract_canon_sha256":"78d32bfe4811a150014a33087dee94cd5921007488d7cea33c595be4e3e001fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:13.331846Z","signature_b64":"Fa4zqkNTQgY4wfoM+hUoGW47pXWaMIQansh/PaA3HoCphR/zeUVYnmsBYRpP3VMVRsIrFbJnValoVzPAKB0SDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ae6281b654a6200c6930a884df6988ed11f85aa01b3c0d9f3a431124d5d6631","last_reissued_at":"2026-05-18T02:46:13.331233Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:13.331233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral Rigidity for Periodic Schr\\\"odinger Operators in Dimension 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Alden Waters","submitted_at":"2012-03-13T19:23:23Z","abstract_excerpt":"We consider two dimensional real-valued analytic potentials for the Schr\\\"odinger equation which are periodic over a lattice $L$. Under certain assumptions on the form of the potential and the lattice $L$, we can show there is a large class of analytic potentials which are Floquet rigid and dense in the set of $C^\\infty(R^2/L)$ potentials. The result extends the work of Eskin et. al, in \"On isospectral periodic potentials in $R^n$, II.\""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2901","kind":"arxiv","version":3},"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":"1203.2901","created_at":"2026-05-18T02:46:13.331333+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.2901v3","created_at":"2026-05-18T02:46:13.331333+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2901","created_at":"2026-05-18T02:46:13.331333+00:00"},{"alias_kind":"pith_short_12","alias_value":"LLTCQG3FJJRA","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LLTCQG3FJJRABRUT","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LLTCQG3F","created_at":"2026-05-18T12:27:14.488303+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/LLTCQG3FJJRABRUTBKEE35UYR3","json":"https://pith.science/pith/LLTCQG3FJJRABRUTBKEE35UYR3.json","graph_json":"https://pith.science/api/pith-number/LLTCQG3FJJRABRUTBKEE35UYR3/graph.json","events_json":"https://pith.science/api/pith-number/LLTCQG3FJJRABRUTBKEE35UYR3/events.json","paper":"https://pith.science/paper/LLTCQG3F"},"agent_actions":{"view_html":"https://pith.science/pith/LLTCQG3FJJRABRUTBKEE35UYR3","download_json":"https://pith.science/pith/LLTCQG3FJJRABRUTBKEE35UYR3.json","view_paper":"https://pith.science/paper/LLTCQG3F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.2901&json=true","fetch_graph":"https://pith.science/api/pith-number/LLTCQG3FJJRABRUTBKEE35UYR3/graph.json","fetch_events":"https://pith.science/api/pith-number/LLTCQG3FJJRABRUTBKEE35UYR3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LLTCQG3FJJRABRUTBKEE35UYR3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LLTCQG3FJJRABRUTBKEE35UYR3/action/storage_attestation","attest_author":"https://pith.science/pith/LLTCQG3FJJRABRUTBKEE35UYR3/action/author_attestation","sign_citation":"https://pith.science/pith/LLTCQG3FJJRABRUTBKEE35UYR3/action/citation_signature","submit_replication":"https://pith.science/pith/LLTCQG3FJJRABRUTBKEE35UYR3/action/replication_record"}},"created_at":"2026-05-18T02:46:13.331333+00:00","updated_at":"2026-05-18T02:46:13.331333+00:00"}