{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:MOO7RNMWC2DQJZ3IM2DUP2P7KP","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":"eb5e53f798bab5e282777cfb2507bc4441bb11af100ab19a7b65321a0cb876e1","cross_cats_sorted":["cond-mat.other","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2006-11-23T14:46:28Z","title_canon_sha256":"9eaaccba5d6306f228bef989f91458a9c9363ac3ae6c447500043c31bccd5fd3"},"schema_version":"1.0","source":{"id":"math-ph/0611061","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0611061","created_at":"2026-05-18T04:37:21Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0611061v4","created_at":"2026-05-18T04:37:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0611061","created_at":"2026-05-18T04:37:21Z"},{"alias_kind":"pith_short_12","alias_value":"MOO7RNMWC2DQ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"MOO7RNMWC2DQJZ3I","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"MOO7RNMW","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:87b691aeec96d77a8525de032578d1e2fb68efae5d64f37984ea84c7bac413a1","target":"graph","created_at":"2026-05-18T04:37:21Z","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 theory of group classification of differential equations is analyzed, substantially extended and enhanced based on the new notions of conditional equivalence group and normalized class of differential equations. Effective new techniques are proposed. Using these, we exhaustively describe admissible point transformations in classes of nonlinear (1+1)-dimensional Schroedinger equations, in particular, in the class of nonlinear (1+1)-dimensional Schroedinger equations with modular nonlinearities and potentials and some subclasses thereof. We then carry out a complete group classification in t","authors_text":"Homayoon Eshraghi, Michael Kunzinger, Roman O. Popovych","cross_cats":["cond-mat.other","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2006-11-23T14:46:28Z","title":"Admissible Transformations and Normalized Classes of Nonlinear Schroedinger Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0611061","kind":"arxiv","version":4},"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":"sha256:48b3316965c82a7b56eedd8c9e7d0681a05f9c79a6dd0a192f917e34ae6a8f70","target":"record","created_at":"2026-05-18T04:37:21Z","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":"eb5e53f798bab5e282777cfb2507bc4441bb11af100ab19a7b65321a0cb876e1","cross_cats_sorted":["cond-mat.other","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2006-11-23T14:46:28Z","title_canon_sha256":"9eaaccba5d6306f228bef989f91458a9c9363ac3ae6c447500043c31bccd5fd3"},"schema_version":"1.0","source":{"id":"math-ph/0611061","kind":"arxiv","version":4}},"canonical_sha256":"639df8b596168704e768668747e9ff53d7486450523b2e2b6424e2db28e61b9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"639df8b596168704e768668747e9ff53d7486450523b2e2b6424e2db28e61b9e","first_computed_at":"2026-05-18T04:37:21.008719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:21.008719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xJg4UfANfOBi5HY7c5t9DdEoZZWp+PVeTsfqNzIVzB3DWaa2PfiR8XdnNmXWrfO8rWNgJQ4TALAL+b2h6aHXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:21.009166Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0611061","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48b3316965c82a7b56eedd8c9e7d0681a05f9c79a6dd0a192f917e34ae6a8f70","sha256:87b691aeec96d77a8525de032578d1e2fb68efae5d64f37984ea84c7bac413a1"],"state_sha256":"b12aec93c04f0d279df04ed0c99cb144b2bdd1a846a7a63a5dcaabc595b25391"}