{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PK25R4TUTBPCM4BHY5M6JD33TY","short_pith_number":"pith:PK25R4TU","canonical_record":{"source":{"id":"1712.02253","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-12-06T16:11:45Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"45abc1a6be3cebbb07d4333d191b8dc38db2049aff6cedd1b5b0f5d7b67399c7","abstract_canon_sha256":"6b0b4895a2c2109669a4cef59fa581d20826e77a7dcf13dcc7838f5358c8af8c"},"schema_version":"1.0"},"canonical_sha256":"7ab5d8f274985e267027c759e48f7b9e2ca494b94774afde09a186fbc5415747","source":{"kind":"arxiv","id":"1712.02253","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02253","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02253v1","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02253","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"pith_short_12","alias_value":"PK25R4TUTBPC","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PK25R4TUTBPCM4BH","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PK25R4TU","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PK25R4TUTBPCM4BHY5M6JD33TY","target":"record","payload":{"canonical_record":{"source":{"id":"1712.02253","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-12-06T16:11:45Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"45abc1a6be3cebbb07d4333d191b8dc38db2049aff6cedd1b5b0f5d7b67399c7","abstract_canon_sha256":"6b0b4895a2c2109669a4cef59fa581d20826e77a7dcf13dcc7838f5358c8af8c"},"schema_version":"1.0"},"canonical_sha256":"7ab5d8f274985e267027c759e48f7b9e2ca494b94774afde09a186fbc5415747","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:09.850257Z","signature_b64":"YhoIIIkQpX5Wp9AZBSqGS56t9klNW2wOhgsjRUgeY/GxMbGkCoIxtkodqU3CQy3Ndu4nsujsQIDo4nqMyBROCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ab5d8f274985e267027c759e48f7b9e2ca494b94774afde09a186fbc5415747","last_reissued_at":"2026-05-18T00:28:09.849562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:09.849562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.02253","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":"2026-05-18T00:28:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eH1IIQVgw7OY+dL6y2OZcgy2Y8ptr18/lpwPB0Gq3zCDUBcysTXgsAAFGyrimvgJ3wcwQ1/sy+XU1g8v2tKvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:03:20.115637Z"},"content_sha256":"45980b2a9a6dccfa3e53ea15177958a8700c2352fffa61e38cd48152f0d39d5d","schema_version":"1.0","event_id":"sha256:45980b2a9a6dccfa3e53ea15177958a8700c2352fffa61e38cd48152f0d39d5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PK25R4TUTBPCM4BHY5M6JD33TY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mapping of Two-Dimensional Schr\\\"odinger Equation under the Point Transformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"D.N.Nishnianidze, M.V.Ioffe, V.V.Vereshagin","submitted_at":"2017-12-06T16:11:45Z","abstract_excerpt":"For the two-dimensional Schr\\\"odinger equation, the general form of the point transformations such that the result can be interpreted as a Schr\\\"odinger equation with effective (i.e. position dependent) mass is studied. A wide class of such models with different forms of mass function is obtained in this way. Starting from the solvable two-dimensional model, the variety of solvable partner models with effective mass can be built. Several illustrating examples not amenable to the conventional separation of variables are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02253","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":"2026-05-18T00:28:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4zIV6PqQMjm/xL7o1UeIzsxNJ/ObeL1SQHI9fdQyoGZSfKkukPDPBH9lZaB0lyLCfEhurtuySokED62znO/qDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:03:20.116406Z"},"content_sha256":"83290ba0e5eb0e27c0ec6f24085e18750ed4dee947df70b6e0beeefe7a3d9929","schema_version":"1.0","event_id":"sha256:83290ba0e5eb0e27c0ec6f24085e18750ed4dee947df70b6e0beeefe7a3d9929"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PK25R4TUTBPCM4BHY5M6JD33TY/bundle.json","state_url":"https://pith.science/pith/PK25R4TUTBPCM4BHY5M6JD33TY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PK25R4TUTBPCM4BHY5M6JD33TY/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":"2026-06-09T21:03:20Z","links":{"resolver":"https://pith.science/pith/PK25R4TUTBPCM4BHY5M6JD33TY","bundle":"https://pith.science/pith/PK25R4TUTBPCM4BHY5M6JD33TY/bundle.json","state":"https://pith.science/pith/PK25R4TUTBPCM4BHY5M6JD33TY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PK25R4TUTBPCM4BHY5M6JD33TY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PK25R4TUTBPCM4BHY5M6JD33TY","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":"6b0b4895a2c2109669a4cef59fa581d20826e77a7dcf13dcc7838f5358c8af8c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-12-06T16:11:45Z","title_canon_sha256":"45abc1a6be3cebbb07d4333d191b8dc38db2049aff6cedd1b5b0f5d7b67399c7"},"schema_version":"1.0","source":{"id":"1712.02253","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02253","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02253v1","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02253","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"pith_short_12","alias_value":"PK25R4TUTBPC","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PK25R4TUTBPCM4BH","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PK25R4TU","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:83290ba0e5eb0e27c0ec6f24085e18750ed4dee947df70b6e0beeefe7a3d9929","target":"graph","created_at":"2026-05-18T00:28:09Z","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":"For the two-dimensional Schr\\\"odinger equation, the general form of the point transformations such that the result can be interpreted as a Schr\\\"odinger equation with effective (i.e. position dependent) mass is studied. A wide class of such models with different forms of mass function is obtained in this way. Starting from the solvable two-dimensional model, the variety of solvable partner models with effective mass can be built. Several illustrating examples not amenable to the conventional separation of variables are given.","authors_text":"D.N.Nishnianidze, M.V.Ioffe, V.V.Vereshagin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-12-06T16:11:45Z","title":"Mapping of Two-Dimensional Schr\\\"odinger Equation under the Point Transformation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02253","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":"sha256:45980b2a9a6dccfa3e53ea15177958a8700c2352fffa61e38cd48152f0d39d5d","target":"record","created_at":"2026-05-18T00:28:09Z","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":"6b0b4895a2c2109669a4cef59fa581d20826e77a7dcf13dcc7838f5358c8af8c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-12-06T16:11:45Z","title_canon_sha256":"45abc1a6be3cebbb07d4333d191b8dc38db2049aff6cedd1b5b0f5d7b67399c7"},"schema_version":"1.0","source":{"id":"1712.02253","kind":"arxiv","version":1}},"canonical_sha256":"7ab5d8f274985e267027c759e48f7b9e2ca494b94774afde09a186fbc5415747","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ab5d8f274985e267027c759e48f7b9e2ca494b94774afde09a186fbc5415747","first_computed_at":"2026-05-18T00:28:09.849562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:09.849562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YhoIIIkQpX5Wp9AZBSqGS56t9klNW2wOhgsjRUgeY/GxMbGkCoIxtkodqU3CQy3Ndu4nsujsQIDo4nqMyBROCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:09.850257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.02253","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45980b2a9a6dccfa3e53ea15177958a8700c2352fffa61e38cd48152f0d39d5d","sha256:83290ba0e5eb0e27c0ec6f24085e18750ed4dee947df70b6e0beeefe7a3d9929"],"state_sha256":"f7c7c2431eaf929ad619ecce4c13fd4e8d67bace894212971399fe8decff6464"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"goqOw9aBxZzGyz21K9XctSb7/E8KAU4zfyODf2DRS+ZNgqpFSFp9vZWvSyRB32J6WyxhsoJfIzgIZmR8wSnZBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T21:03:20.120732Z","bundle_sha256":"f56d9ff09681268c2bd75f0d3519faff56589451d3121c57b9cb9695b2c6d2fc"}}