{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UYDSCXPORTOECRAZFZFSBKP56J","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":"0bb18bbab0167e1c2e67654b65b40b69efba09201471b5cab46a8d2f71cb3074","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-11-17T09:52:32Z","title_canon_sha256":"8d2234c643df61f71638e36f60b41836214bf905d3db1618e157b8fbb3e1a6ae"},"schema_version":"1.0","source":{"id":"1411.4405","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4405","created_at":"2026-05-18T02:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4405v3","created_at":"2026-05-18T02:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4405","created_at":"2026-05-18T02:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"UYDSCXPORTOE","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UYDSCXPORTOECRAZ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UYDSCXPO","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:d6cf8a993b0975c8592737ef8e02cd5587964ccd561abc7debac814e65158d82","target":"graph","created_at":"2026-05-18T02:03:50Z","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":"A general non-local point transformation for position-dependent mass Lagrangians and their mapping into a \"constant unit-mass\" Lagrangians in the generalized coordinates is introduced. The conditions on the invariance of the related Euler-Lagrange equations are reported. The harmonic oscillator linearization of the PDM Euler-Lagrange equations is discussed through some illustrative examples including harmonic oscillators, shifted harmonic oscillators, a quadratic nonlinear oscillator, and a Morse-type oscillator. The Mathews-Lakshmanan nonlinear oscillators are reproduced and some \"shifted\" Ma","authors_text":"Omar Mustafa","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-11-17T09:52:32Z","title":"Position-dependent mass Lagrangians: nonlocal transformations, Euler-Lagrange invariance and exact solvability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4405","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:acb963d835a7cf40b14edec5da31a1984acdaa0101395f8245433748b2e429b3","target":"record","created_at":"2026-05-18T02:03:50Z","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":"0bb18bbab0167e1c2e67654b65b40b69efba09201471b5cab46a8d2f71cb3074","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-11-17T09:52:32Z","title_canon_sha256":"8d2234c643df61f71638e36f60b41836214bf905d3db1618e157b8fbb3e1a6ae"},"schema_version":"1.0","source":{"id":"1411.4405","kind":"arxiv","version":3}},"canonical_sha256":"a607215dee8cdc4144192e4b20a9fdf278a17609d939447fe8a5eb627f1042fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a607215dee8cdc4144192e4b20a9fdf278a17609d939447fe8a5eb627f1042fb","first_computed_at":"2026-05-18T02:03:50.809558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:50.809558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OmzOHIZQNaRPVRWM1c80954nh12Wm/JjZ1X/KygDpJyDWPAwSWUHrL5AL3t0VZgTJATI8Oq9UZhqmytbU4ONBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:50.810193Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4405","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acb963d835a7cf40b14edec5da31a1984acdaa0101395f8245433748b2e429b3","sha256:d6cf8a993b0975c8592737ef8e02cd5587964ccd561abc7debac814e65158d82"],"state_sha256":"544146e77f032c2f76f8f2113796dc02e32803d0bb687dd9b60b33e08107d0df"}