{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CZTPGJ25QSZ5J767O4BLZGV7BY","short_pith_number":"pith:CZTPGJ25","canonical_record":{"source":{"id":"1806.02983","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-08T06:43:49Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"3ed6ec75e8beb163d1300d38db801a9c66290799620e88316c834258b7305698","abstract_canon_sha256":"0a57d9d00e065a6043639ae118c4b9d130e00600435adc392bd2a545c3a32662"},"schema_version":"1.0"},"canonical_sha256":"1666f3275d84b3d4ffdf7702bc9abf0e07352052a2a98586f7c2290d21addaa2","source":{"kind":"arxiv","id":"1806.02983","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02983","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02983v3","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02983","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"CZTPGJ25QSZ5","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"CZTPGJ25QSZ5J767","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"CZTPGJ25","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CZTPGJ25QSZ5J767O4BLZGV7BY","target":"record","payload":{"canonical_record":{"source":{"id":"1806.02983","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-08T06:43:49Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"3ed6ec75e8beb163d1300d38db801a9c66290799620e88316c834258b7305698","abstract_canon_sha256":"0a57d9d00e065a6043639ae118c4b9d130e00600435adc392bd2a545c3a32662"},"schema_version":"1.0"},"canonical_sha256":"1666f3275d84b3d4ffdf7702bc9abf0e07352052a2a98586f7c2290d21addaa2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:09.451785Z","signature_b64":"1G6wsns36I2x/ueADVQ88F8a7fKIYQbsVTlfQzACjwo0aU8gTZyPmlx7/acIe8QVn5cY7MbNLCdsaTsKosF7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1666f3275d84b3d4ffdf7702bc9abf0e07352052a2a98586f7c2290d21addaa2","last_reissued_at":"2026-05-17T23:43:09.451235Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:09.451235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.02983","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SoqeijjbQOXq390IlVtiqMHHY0w2rQFP+OmQUgCZKpVKZvKxDoPxFU282fkVq49oqhKxj+cRQz3kMJ0+sCspCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:00:15.463456Z"},"content_sha256":"1982d3f0e075c8828f7117e1816872e92e4d52f3f2858bbf52a5e87ef3965069","schema_version":"1.0","event_id":"sha256:1982d3f0e075c8828f7117e1816872e92e4d52f3f2858bbf52a5e87ef3965069"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CZTPGJ25QSZ5J767O4BLZGV7BY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Position-dependent mass momentum operator and minimal coupling: point canonical transformation and isospectrality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Omar Mustafa, Zeinab Algadhi","submitted_at":"2018-06-08T06:43:49Z","abstract_excerpt":"The classical and quantum mechanical correspondence for constant mass settings is used, along with some point canonical transformation, to find the position-dependent mass (PDM) classical and quantum Hamiltonians. The comparison between the resulting quantum PDM-Hamiltonian and the von Roos PDM-Hamiltonian implied that the ordering ambiguity parameters of von Roos are strictly determined. Eliminating, in effect, the ordering ambiguity associated with the von Roos PDM-Hamiltonian. This, consequently, played a vital role in the construction and identification of the PDM-momentum operator. The sa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02983","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H4YoopL7fPag3KjWoJPDkOBPZ5cvXGg7p0WokQLnY/cn3e6100yi8TD4XLTqTrM3UH/yQ6T5rudPDZUr3LcmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:00:15.463805Z"},"content_sha256":"1d67bcee5330ce1aee9b82795cbd3022639f40d8b36d5ffc5f01426609b035b2","schema_version":"1.0","event_id":"sha256:1d67bcee5330ce1aee9b82795cbd3022639f40d8b36d5ffc5f01426609b035b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CZTPGJ25QSZ5J767O4BLZGV7BY/bundle.json","state_url":"https://pith.science/pith/CZTPGJ25QSZ5J767O4BLZGV7BY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CZTPGJ25QSZ5J767O4BLZGV7BY/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":"2026-06-08T14:00:15Z","links":{"resolver":"https://pith.science/pith/CZTPGJ25QSZ5J767O4BLZGV7BY","bundle":"https://pith.science/pith/CZTPGJ25QSZ5J767O4BLZGV7BY/bundle.json","state":"https://pith.science/pith/CZTPGJ25QSZ5J767O4BLZGV7BY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CZTPGJ25QSZ5J767O4BLZGV7BY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CZTPGJ25QSZ5J767O4BLZGV7BY","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":"0a57d9d00e065a6043639ae118c4b9d130e00600435adc392bd2a545c3a32662","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-08T06:43:49Z","title_canon_sha256":"3ed6ec75e8beb163d1300d38db801a9c66290799620e88316c834258b7305698"},"schema_version":"1.0","source":{"id":"1806.02983","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02983","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02983v3","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02983","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"CZTPGJ25QSZ5","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"CZTPGJ25QSZ5J767","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"CZTPGJ25","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:1d67bcee5330ce1aee9b82795cbd3022639f40d8b36d5ffc5f01426609b035b2","target":"graph","created_at":"2026-05-17T23:43:09Z","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 classical and quantum mechanical correspondence for constant mass settings is used, along with some point canonical transformation, to find the position-dependent mass (PDM) classical and quantum Hamiltonians. The comparison between the resulting quantum PDM-Hamiltonian and the von Roos PDM-Hamiltonian implied that the ordering ambiguity parameters of von Roos are strictly determined. Eliminating, in effect, the ordering ambiguity associated with the von Roos PDM-Hamiltonian. This, consequently, played a vital role in the construction and identification of the PDM-momentum operator. The sa","authors_text":"Omar Mustafa, Zeinab Algadhi","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-08T06:43:49Z","title":"Position-dependent mass momentum operator and minimal coupling: point canonical transformation and isospectrality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02983","kind":"arxiv","version":3},"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":"sha256:1982d3f0e075c8828f7117e1816872e92e4d52f3f2858bbf52a5e87ef3965069","target":"record","created_at":"2026-05-17T23:43:09Z","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":"0a57d9d00e065a6043639ae118c4b9d130e00600435adc392bd2a545c3a32662","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-08T06:43:49Z","title_canon_sha256":"3ed6ec75e8beb163d1300d38db801a9c66290799620e88316c834258b7305698"},"schema_version":"1.0","source":{"id":"1806.02983","kind":"arxiv","version":3}},"canonical_sha256":"1666f3275d84b3d4ffdf7702bc9abf0e07352052a2a98586f7c2290d21addaa2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1666f3275d84b3d4ffdf7702bc9abf0e07352052a2a98586f7c2290d21addaa2","first_computed_at":"2026-05-17T23:43:09.451235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:09.451235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1G6wsns36I2x/ueADVQ88F8a7fKIYQbsVTlfQzACjwo0aU8gTZyPmlx7/acIe8QVn5cY7MbNLCdsaTsKosF7CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:09.451785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.02983","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1982d3f0e075c8828f7117e1816872e92e4d52f3f2858bbf52a5e87ef3965069","sha256:1d67bcee5330ce1aee9b82795cbd3022639f40d8b36d5ffc5f01426609b035b2"],"state_sha256":"73cb9634da301b765378b34b0d4df18305b7c36105e966571e8cd5384b8b068a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MU7M+wgD9lQkP5+ngtqXrA/3FtUeoQUZdb1oUOi3ixF57HSFuVVWWc55FI0ygQceFrAhia8qGykrNfc3kNimAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:00:15.465781Z","bundle_sha256":"4af12b76e403a8c48d3b0f300a42acbc7cafc3b2cc72c343503d21fa1b73f940"}}