{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HRFYWMRSYT6AMUZRLPVTPCI7XM","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":"631835795ff3f78c7dd23409034ccb628bed94dfa4ffd75fe0903e839658c736","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-07-04T11:52:25Z","title_canon_sha256":"ab3c4ced8c9d7fed7c74a8bbef78aa492a861cd98b586f2750c3290e9912a607"},"schema_version":"1.0","source":{"id":"1207.0948","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0948","created_at":"2026-05-18T03:51:47Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0948v1","created_at":"2026-05-18T03:51:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0948","created_at":"2026-05-18T03:51:47Z"},{"alias_kind":"pith_short_12","alias_value":"HRFYWMRSYT6A","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HRFYWMRSYT6AMUZR","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HRFYWMRS","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:6ebb0b72d26025ab0c8e52349c07724466e201242329aafa312be3ce4e231198","target":"graph","created_at":"2026-05-18T03:51:47Z","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":"The Hill operators $Ly=-y\"+v(x)y$, considered with complex valued $\\pi$-periodic potentials $v$ and subject to periodic, antiperiodic or Neumann boundary conditions have discrete spectra. For sufficiently large $n,$ close to $n^2$ there are two periodic (if $n$ is even) or antiperiodic (if $n$ is odd) eigenvalues $\\lambda_n^-$, $\\lambda_n^+$ and one Neumann eigenvalue $\\nu_n$. We study the geometry of \"the spectral triangle\" with vertices ($\\lambda_n^+$,$\\lambda_n^-$,$\\nu_n$), and show that the rate of decay of triangle size characterizes the potential smoothness. Moreover, it is proved, for $","authors_text":"Ahmet Batal","cross_cats":["math-ph","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-07-04T11:52:25Z","title":"Characterization of potential smoothness and Riesz basis property of the Hill-Scr\\\"odinger operator in terms of periodic, antiperiodic and Neumann spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0948","kind":"arxiv","version":1},"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":"sha256:1b02ecc9a1e5d7676bf26f4cdb2b51b3cfd215e700789e04d98c15de3de0c07b","target":"record","created_at":"2026-05-18T03:51:47Z","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":"631835795ff3f78c7dd23409034ccb628bed94dfa4ffd75fe0903e839658c736","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-07-04T11:52:25Z","title_canon_sha256":"ab3c4ced8c9d7fed7c74a8bbef78aa492a861cd98b586f2750c3290e9912a607"},"schema_version":"1.0","source":{"id":"1207.0948","kind":"arxiv","version":1}},"canonical_sha256":"3c4b8b3232c4fc0653315beb37891fbb0e2dfe67cbb744d75adf2f937262bf2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c4b8b3232c4fc0653315beb37891fbb0e2dfe67cbb744d75adf2f937262bf2a","first_computed_at":"2026-05-18T03:51:47.885360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:47.885360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UsiOSDmS3u0ekQjm9xiFRJoHLiFCkHPjI0O1nX4S48EX6zfCot5IShMo3l6H3Q1rIfloWgiGaX32MyeN+ZhLCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:47.885929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.0948","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b02ecc9a1e5d7676bf26f4cdb2b51b3cfd215e700789e04d98c15de3de0c07b","sha256:6ebb0b72d26025ab0c8e52349c07724466e201242329aafa312be3ce4e231198"],"state_sha256":"46c166ed7419a0cbbba6d5e69aafb70c7893d0b2b37461ada5cc1867ccea07a8"}