{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JMVBA7BC5IYBXH54QL4IFG2J7K","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":"f2bcafa2202284e23863df0d407282064412d1040839e00830f8441a35a0de56","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-21T20:19:06Z","title_canon_sha256":"9f54f42549cd16f601474407ed64c436a8c753fd6c3220951fba67e99e80def0"},"schema_version":"1.0","source":{"id":"1607.06486","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06486","created_at":"2026-05-18T01:10:41Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06486v1","created_at":"2026-05-18T01:10:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06486","created_at":"2026-05-18T01:10:41Z"},{"alias_kind":"pith_short_12","alias_value":"JMVBA7BC5IYB","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JMVBA7BC5IYBXH54","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JMVBA7BC","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:92177215f8c50c44a9dc5da5bb917c0702adebea560ae14a22fc4309d56b0c91","target":"graph","created_at":"2026-05-18T01:10:41Z","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":"We have shown that a Lagrangian for a torus surface can yield second order nonlinear differential equations using the Euler-Lagrange formulation. It is seen that these second order nonlinear differential equations can be transformed into the nonlinear quadratic and Mathews-Lakshmanan equations using the position dependent mass approach developed by Mustafa for the classical systems. Then, we have applied the quantization procedure to the nonlinear quadratic and Mathews-Lakshmanan equations and found their exact solutions.","authors_text":"Ozlem Yesiltas","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-21T20:19:06Z","title":"Position Dependent Mass Approach and Quantization for a Torus Lagrangian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06486","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:e8707ff7049c67a1f5dfc7cd769f20b617fcdfa997436ddce328ab171fe985db","target":"record","created_at":"2026-05-18T01:10:41Z","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":"f2bcafa2202284e23863df0d407282064412d1040839e00830f8441a35a0de56","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-21T20:19:06Z","title_canon_sha256":"9f54f42549cd16f601474407ed64c436a8c753fd6c3220951fba67e99e80def0"},"schema_version":"1.0","source":{"id":"1607.06486","kind":"arxiv","version":1}},"canonical_sha256":"4b2a107c22ea301b9fbc82f8829b49fa9d660f8a5be36ac1e1ec2202c847f202","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b2a107c22ea301b9fbc82f8829b49fa9d660f8a5be36ac1e1ec2202c847f202","first_computed_at":"2026-05-18T01:10:41.632762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:41.632762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d0FkrAD1sH4VOyyhDAN/G15R3nJ6UbPVYpyMFeOpMh4CyjQJV7g8w9ubqdkAjGdXEzLGq5k/gqnj3BSfwdPcAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:41.633235Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06486","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8707ff7049c67a1f5dfc7cd769f20b617fcdfa997436ddce328ab171fe985db","sha256:92177215f8c50c44a9dc5da5bb917c0702adebea560ae14a22fc4309d56b0c91"],"state_sha256":"0d83bb6e4ad986eb905ecb5bc9fc6abcc7b0e6323c992eacab3a131696ae268f"}