{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZWYPBVNXZG3QXHLIQG5O4WTGLM","short_pith_number":"pith:ZWYPBVNX","canonical_record":{"source":{"id":"1101.1040","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-01-05T17:39:16Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"ff62c3da63b14963763c681a712e6f1a2335470b0698cc0af2e9ac3704ba137d","abstract_canon_sha256":"6a1fb59d1e83c117a9ad33230c54dd7d3fef72b295e1f3f06fba9721387f89ba"},"schema_version":"1.0"},"canonical_sha256":"cdb0f0d5b7c9b70b9d6881baee5a665b397b8b6b682fb0759ac248d68dbf57d4","source":{"kind":"arxiv","id":"1101.1040","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1040","created_at":"2026-05-18T02:04:12Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1040v1","created_at":"2026-05-18T02:04:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1040","created_at":"2026-05-18T02:04:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZWYPBVNXZG3Q","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZWYPBVNXZG3QXHLI","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZWYPBVNX","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZWYPBVNXZG3QXHLIQG5O4WTGLM","target":"record","payload":{"canonical_record":{"source":{"id":"1101.1040","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-01-05T17:39:16Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"ff62c3da63b14963763c681a712e6f1a2335470b0698cc0af2e9ac3704ba137d","abstract_canon_sha256":"6a1fb59d1e83c117a9ad33230c54dd7d3fef72b295e1f3f06fba9721387f89ba"},"schema_version":"1.0"},"canonical_sha256":"cdb0f0d5b7c9b70b9d6881baee5a665b397b8b6b682fb0759ac248d68dbf57d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:12.765704Z","signature_b64":"nvXS6NnRSK4tkil/8SSr7XXa9yj3UdSI3YRX8BO6Qrq94sFhQWXw86T+JLRBaRmdERR9AxGHvWaPixrX1C+jAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdb0f0d5b7c9b70b9d6881baee5a665b397b8b6b682fb0759ac248d68dbf57d4","last_reissued_at":"2026-05-18T02:04:12.765203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:12.765203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.1040","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:04:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UgB2MyZl6A5dQMHJMsQ3rit0ImGyTd+5uaiG1xCbhUx0Yt2bglEPjGNTpGORVUTZ2ruGYbYlDvPa79CoW65ODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:41:49.458226Z"},"content_sha256":"33027bd23f9d0e406ea3f4da8edb3784fa4fc3f4d026034f263ed9efce31ec4e","schema_version":"1.0","event_id":"sha256:33027bd23f9d0e406ea3f4da8edb3784fa4fc3f4d026034f263ed9efce31ec4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZWYPBVNXZG3QXHLIQG5O4WTGLM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"quant-ph","authors_text":"Bikashkali Midya, Partha Pratim Dube, Rajkumar Roychoudhury","submitted_at":"2011-01-05T17:39:16Z","abstract_excerpt":"The generalized Swanson Hamiltonian $H_{GS} = w (\\tilde{a}\\tilde{a}^\\dag+ 1/2) + \\alpha \\tilde{a}^2 + \\beta \\tilde{a}^{\\dag^2}$ with $\\tilde{a} = A(x)d/dx + B(x)$, can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as $[\\tilde{a},\\tilde{a}^\\dag]=$ constant. However, the main objective of this paper is to show that though the commutator of $\\tilde{a}$ and $\\tilde{a}^\\dag$ is constant, the generalized Swanson Hami"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1040","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:04:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QzUsjh+1N/8WSYgC51gKZhlDj4zjhs4vGRV9X2H/PQsVo83bkLVaT1M8hN3gedTWsfcnCY0lKQihRmwTtU+jAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:41:49.458595Z"},"content_sha256":"d814c5bea466dc8517ffeb6e4319ab4aaea5e8900cc5d55ee738b769e053b1c4","schema_version":"1.0","event_id":"sha256:d814c5bea466dc8517ffeb6e4319ab4aaea5e8900cc5d55ee738b769e053b1c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZWYPBVNXZG3QXHLIQG5O4WTGLM/bundle.json","state_url":"https://pith.science/pith/ZWYPBVNXZG3QXHLIQG5O4WTGLM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZWYPBVNXZG3QXHLIQG5O4WTGLM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T09:41:49Z","links":{"resolver":"https://pith.science/pith/ZWYPBVNXZG3QXHLIQG5O4WTGLM","bundle":"https://pith.science/pith/ZWYPBVNXZG3QXHLIQG5O4WTGLM/bundle.json","state":"https://pith.science/pith/ZWYPBVNXZG3QXHLIQG5O4WTGLM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZWYPBVNXZG3QXHLIQG5O4WTGLM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZWYPBVNXZG3QXHLIQG5O4WTGLM","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":"6a1fb59d1e83c117a9ad33230c54dd7d3fef72b295e1f3f06fba9721387f89ba","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-01-05T17:39:16Z","title_canon_sha256":"ff62c3da63b14963763c681a712e6f1a2335470b0698cc0af2e9ac3704ba137d"},"schema_version":"1.0","source":{"id":"1101.1040","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1040","created_at":"2026-05-18T02:04:12Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1040v1","created_at":"2026-05-18T02:04:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1040","created_at":"2026-05-18T02:04:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZWYPBVNXZG3Q","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZWYPBVNXZG3QXHLI","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZWYPBVNX","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:d814c5bea466dc8517ffeb6e4319ab4aaea5e8900cc5d55ee738b769e053b1c4","target":"graph","created_at":"2026-05-18T02:04:12Z","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 generalized Swanson Hamiltonian $H_{GS} = w (\\tilde{a}\\tilde{a}^\\dag+ 1/2) + \\alpha \\tilde{a}^2 + \\beta \\tilde{a}^{\\dag^2}$ with $\\tilde{a} = A(x)d/dx + B(x)$, can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as $[\\tilde{a},\\tilde{a}^\\dag]=$ constant. However, the main objective of this paper is to show that though the commutator of $\\tilde{a}$ and $\\tilde{a}^\\dag$ is constant, the generalized Swanson Hami","authors_text":"Bikashkali Midya, Partha Pratim Dube, Rajkumar Roychoudhury","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-01-05T17:39:16Z","title":"Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1040","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":"sha256:33027bd23f9d0e406ea3f4da8edb3784fa4fc3f4d026034f263ed9efce31ec4e","target":"record","created_at":"2026-05-18T02:04:12Z","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":"6a1fb59d1e83c117a9ad33230c54dd7d3fef72b295e1f3f06fba9721387f89ba","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-01-05T17:39:16Z","title_canon_sha256":"ff62c3da63b14963763c681a712e6f1a2335470b0698cc0af2e9ac3704ba137d"},"schema_version":"1.0","source":{"id":"1101.1040","kind":"arxiv","version":1}},"canonical_sha256":"cdb0f0d5b7c9b70b9d6881baee5a665b397b8b6b682fb0759ac248d68dbf57d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdb0f0d5b7c9b70b9d6881baee5a665b397b8b6b682fb0759ac248d68dbf57d4","first_computed_at":"2026-05-18T02:04:12.765203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:12.765203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nvXS6NnRSK4tkil/8SSr7XXa9yj3UdSI3YRX8BO6Qrq94sFhQWXw86T+JLRBaRmdERR9AxGHvWaPixrX1C+jAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:12.765704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1040","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33027bd23f9d0e406ea3f4da8edb3784fa4fc3f4d026034f263ed9efce31ec4e","sha256:d814c5bea466dc8517ffeb6e4319ab4aaea5e8900cc5d55ee738b769e053b1c4"],"state_sha256":"ef4ed06797c81a9cdb813f020272e64a8301045f5906783661c6fd9e0aaa41d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pue93ZXpf/gkn6AGWu0MEDGF2I/KH1PptqXXDEY0S5V22Gv1Bvzs3RbLDSL46PyGCV6QovxLRAU8GBOtLzjQBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:41:49.460556Z","bundle_sha256":"5c0533cdd4481c3999f48e3b44739ce8798ccbba244861ff8d7a9e5acf26a2c5"}}