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This new class includes the equivalent non-Hermitian - Hermitian Hamiltonian pair, $p^{2}-gx^{4}$ and $p^{2}+4gx^{4}-2\\hbar \\sqrt{g}x,$ found by Jones and Mateo six years ago as a special case. When $a=\\left(b^{2}-4g\\hbar ^{2}\\right) /16g$ and $a<-\\hbar^2/4,$ although $h$ and $H$ are still isospectral, $b$ is complex and $h$ is no longer the Hermitian counterpart o"},"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":"1407.4633","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-07-17T11:14:47Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"915e1dd252e668c73f49793bbe3ae9324e61103ed864322413514af99639fa59","abstract_canon_sha256":"b8d5631955ad8a90fad200ba327db281a3762a8467381eb64192f57ce2b3c237"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:23.641013Z","signature_b64":"PLX1d4NUUWlEdObUxP59Uup72X/XMmNNEeAp61rVqYt15u2TxszieJgWRtLqB9bu/nPuhLZV4qPohnBIijV7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2d36066536764d7990faa52d4c78a8807dcff691d4460e48424ee29e7e51c22","last_reissued_at":"2026-05-18T02:47:23.640620Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:23.640620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isospectral Hermitian counterpart of complex non Hermitian Hamiltonian $p^{2}-gx^{4}+a/x^{2}$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Asiri Nanayakkara, Thilagarajah Mathanaranjan","submitted_at":"2014-07-17T11:14:47Z","abstract_excerpt":"In this paper we show that the non-Hermitian Hamiltonians $H=p^{2}-gx^{4}+a/x^2$ and the conventional Hermitian Hamiltonians $h=p^2+4gx^{4}+bx$ ($a,b\\in \\mathbb{R}$) are isospectral if $a=(b^2-4g\\hbar^2)/16g$ and $a\\geq -\\hbar^2/4$. This new class includes the equivalent non-Hermitian - Hermitian Hamiltonian pair, $p^{2}-gx^{4}$ and $p^{2}+4gx^{4}-2\\hbar \\sqrt{g}x,$ found by Jones and Mateo six years ago as a special case. When $a=\\left(b^{2}-4g\\hbar ^{2}\\right) /16g$ and $a<-\\hbar^2/4,$ although $h$ and $H$ are still isospectral, $b$ is complex and $h$ is no longer the Hermitian counterpart o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4633","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":"1407.4633","created_at":"2026-05-18T02:47:23.640686+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.4633v1","created_at":"2026-05-18T02:47:23.640686+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4633","created_at":"2026-05-18T02:47:23.640686+00:00"},{"alias_kind":"pith_short_12","alias_value":"WLJWAZSTM5SN","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"WLJWAZSTM5SNPGIP","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"WLJWAZST","created_at":"2026-05-18T12:28:54.890064+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/WLJWAZSTM5SNPGIPVJJNJR4KRA","json":"https://pith.science/pith/WLJWAZSTM5SNPGIPVJJNJR4KRA.json","graph_json":"https://pith.science/api/pith-number/WLJWAZSTM5SNPGIPVJJNJR4KRA/graph.json","events_json":"https://pith.science/api/pith-number/WLJWAZSTM5SNPGIPVJJNJR4KRA/events.json","paper":"https://pith.science/paper/WLJWAZST"},"agent_actions":{"view_html":"https://pith.science/pith/WLJWAZSTM5SNPGIPVJJNJR4KRA","download_json":"https://pith.science/pith/WLJWAZSTM5SNPGIPVJJNJR4KRA.json","view_paper":"https://pith.science/paper/WLJWAZST","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.4633&json=true","fetch_graph":"https://pith.science/api/pith-number/WLJWAZSTM5SNPGIPVJJNJR4KRA/graph.json","fetch_events":"https://pith.science/api/pith-number/WLJWAZSTM5SNPGIPVJJNJR4KRA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WLJWAZSTM5SNPGIPVJJNJR4KRA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WLJWAZSTM5SNPGIPVJJNJR4KRA/action/storage_attestation","attest_author":"https://pith.science/pith/WLJWAZSTM5SNPGIPVJJNJR4KRA/action/author_attestation","sign_citation":"https://pith.science/pith/WLJWAZSTM5SNPGIPVJJNJR4KRA/action/citation_signature","submit_replication":"https://pith.science/pith/WLJWAZSTM5SNPGIPVJJNJR4KRA/action/replication_record"}},"created_at":"2026-05-18T02:47:23.640686+00:00","updated_at":"2026-05-18T02:47:23.640686+00:00"}