{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:T5OX3QVK7V6EVV4OG3CMDZLV2U","short_pith_number":"pith:T5OX3QVK","schema_version":"1.0","canonical_sha256":"9f5d7dc2aafd7c4ad78e36c4c1e575d53f6dee2129588be0083d097cbb118c91","source":{"kind":"arxiv","id":"1901.08526","version":1},"attestation_state":"computed","paper":{"title":"IR-truncated $\\mathcal{PT}-$symmetric $ix^3$ model and its asymptotic spectral scaling graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP","math.SP","quant-ph"],"primary_cat":"math-ph","authors_text":"Frank Stefani, Uwe Guenther","submitted_at":"2019-01-24T17:42:59Z","abstract_excerpt":"The $\\mathcal{PT}-$symmetric quantum mechanical $V=ix^3$ model over the real line, $x\\in\\mathbb{R}$, is infrared (IR) truncated and considered as Sturm-Liouville problem over a finite interval $x\\in\\left[-L,L\\right]\\subset\\mathbb{R}$. Via WKB and Stokes graph analysis, the location of the complex spectral branches of the $V=ix^3$ model and those of more general $V=-(ix)^{2n+1}$ models over $x\\in\\left[-L,L\\right]\\subset\\mathbb{R}$ are obtained. The corresponding eigenvalues are mapped onto $L-$invariant asymptotic spectral scaling graphs $\\mathcal{R}\\subset \\mathbb{C}$. These scaling graphs are"},"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":"1901.08526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-01-24T17:42:59Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP","math.SP","quant-ph"],"title_canon_sha256":"dceae019fc4958c022116e388abc93fd92c1ae54ccc08082ed5c3964c4517c49","abstract_canon_sha256":"2451bf039a57160996cffe0fcb11d183f0796bf6221cdae50042e3392253b2ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:35.267580Z","signature_b64":"lEtHjidAj2SGppv8lmjPj0EMGUpmHKjC4r+Er7r5dw/63sfHt+8W4dNnrXDzKPcc2nsU0iPJlUfNXYZGd8QlDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f5d7dc2aafd7c4ad78e36c4c1e575d53f6dee2129588be0083d097cbb118c91","last_reissued_at":"2026-05-17T23:55:35.266753Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:35.266753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"IR-truncated $\\mathcal{PT}-$symmetric $ix^3$ model and its asymptotic spectral scaling graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP","math.SP","quant-ph"],"primary_cat":"math-ph","authors_text":"Frank Stefani, Uwe Guenther","submitted_at":"2019-01-24T17:42:59Z","abstract_excerpt":"The $\\mathcal{PT}-$symmetric quantum mechanical $V=ix^3$ model over the real line, $x\\in\\mathbb{R}$, is infrared (IR) truncated and considered as Sturm-Liouville problem over a finite interval $x\\in\\left[-L,L\\right]\\subset\\mathbb{R}$. Via WKB and Stokes graph analysis, the location of the complex spectral branches of the $V=ix^3$ model and those of more general $V=-(ix)^{2n+1}$ models over $x\\in\\left[-L,L\\right]\\subset\\mathbb{R}$ are obtained. The corresponding eigenvalues are mapped onto $L-$invariant asymptotic spectral scaling graphs $\\mathcal{R}\\subset \\mathbb{C}$. These scaling graphs are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08526","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":"1901.08526","created_at":"2026-05-17T23:55:35.266893+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.08526v1","created_at":"2026-05-17T23:55:35.266893+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.08526","created_at":"2026-05-17T23:55:35.266893+00:00"},{"alias_kind":"pith_short_12","alias_value":"T5OX3QVK7V6E","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"T5OX3QVK7V6EVV4O","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"T5OX3QVK","created_at":"2026-05-18T12:33:27.125529+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/T5OX3QVK7V6EVV4OG3CMDZLV2U","json":"https://pith.science/pith/T5OX3QVK7V6EVV4OG3CMDZLV2U.json","graph_json":"https://pith.science/api/pith-number/T5OX3QVK7V6EVV4OG3CMDZLV2U/graph.json","events_json":"https://pith.science/api/pith-number/T5OX3QVK7V6EVV4OG3CMDZLV2U/events.json","paper":"https://pith.science/paper/T5OX3QVK"},"agent_actions":{"view_html":"https://pith.science/pith/T5OX3QVK7V6EVV4OG3CMDZLV2U","download_json":"https://pith.science/pith/T5OX3QVK7V6EVV4OG3CMDZLV2U.json","view_paper":"https://pith.science/paper/T5OX3QVK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.08526&json=true","fetch_graph":"https://pith.science/api/pith-number/T5OX3QVK7V6EVV4OG3CMDZLV2U/graph.json","fetch_events":"https://pith.science/api/pith-number/T5OX3QVK7V6EVV4OG3CMDZLV2U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T5OX3QVK7V6EVV4OG3CMDZLV2U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T5OX3QVK7V6EVV4OG3CMDZLV2U/action/storage_attestation","attest_author":"https://pith.science/pith/T5OX3QVK7V6EVV4OG3CMDZLV2U/action/author_attestation","sign_citation":"https://pith.science/pith/T5OX3QVK7V6EVV4OG3CMDZLV2U/action/citation_signature","submit_replication":"https://pith.science/pith/T5OX3QVK7V6EVV4OG3CMDZLV2U/action/replication_record"}},"created_at":"2026-05-17T23:55:35.266893+00:00","updated_at":"2026-05-17T23:55:35.266893+00:00"}