{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BDCVYGNY44TNOEQPI2JB4N3MDB","short_pith_number":"pith:BDCVYGNY","schema_version":"1.0","canonical_sha256":"08c55c19b8e726d7120f46921e376c1856e75e76ccf0ab509f56158d0dae574d","source":{"kind":"arxiv","id":"2607.10870","version":1},"attestation_state":"computed","paper":{"title":"Loop-type geometric folding of exact solutions of shifted nonlocal NLS and MKdV equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Asl{\\i} Pekcan","submitted_at":"2026-07-12T18:22:53Z","abstract_excerpt":"Based on the notion of foldon, we introduce a geometric framework for constructing folded parametric wave representations of exact solutions of some shifted nonlocal nonlinear Schr\\\"{o}dinger and modified Korteweg-de Vries equations. Unlike the method of constructing loops in $(2+1)$-dimensional integrable models based on universal variable separation approach or hodograph transformation, we consider a simplified geometric approach of constructing loop-type folded profiles via non-monotonic parametrization of the spatial coordinate associated with the exact solution of the $(1+1)$-dimensional "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.10870","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2026-07-12T18:22:53Z","cross_cats_sorted":[],"title_canon_sha256":"db9e8dc46c2f6c955f33ddc8267d3d39db165d63b7de4d556c1f0e6bb854a821","abstract_canon_sha256":"e9721fef09a97f07618989eb9b60d035b25f97587e977f58635171bf9c747d0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T01:21:44.410795Z","signature_b64":"QQrxjXO/MCSOmR9zqlW5PxdE7siqZvvnGNgleoyMbSYytd/I+Cq6YgkSG+++PS4Xnf3hAc45xiK5qWpdFIeCBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08c55c19b8e726d7120f46921e376c1856e75e76ccf0ab509f56158d0dae574d","last_reissued_at":"2026-07-14T01:21:44.409949Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T01:21:44.409949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Loop-type geometric folding of exact solutions of shifted nonlocal NLS and MKdV equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Asl{\\i} Pekcan","submitted_at":"2026-07-12T18:22:53Z","abstract_excerpt":"Based on the notion of foldon, we introduce a geometric framework for constructing folded parametric wave representations of exact solutions of some shifted nonlocal nonlinear Schr\\\"{o}dinger and modified Korteweg-de Vries equations. Unlike the method of constructing loops in $(2+1)$-dimensional integrable models based on universal variable separation approach or hodograph transformation, we consider a simplified geometric approach of constructing loop-type folded profiles via non-monotonic parametrization of the spatial coordinate associated with the exact solution of the $(1+1)$-dimensional "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10870","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.10870/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.10870","created_at":"2026-07-14T01:21:44.410390+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.10870v1","created_at":"2026-07-14T01:21:44.410390+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10870","created_at":"2026-07-14T01:21:44.410390+00:00"},{"alias_kind":"pith_short_12","alias_value":"BDCVYGNY44TN","created_at":"2026-07-14T01:21:44.410390+00:00"},{"alias_kind":"pith_short_16","alias_value":"BDCVYGNY44TNOEQP","created_at":"2026-07-14T01:21:44.410390+00:00"},{"alias_kind":"pith_short_8","alias_value":"BDCVYGNY","created_at":"2026-07-14T01:21:44.410390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BDCVYGNY44TNOEQPI2JB4N3MDB","json":"https://pith.science/pith/BDCVYGNY44TNOEQPI2JB4N3MDB.json","graph_json":"https://pith.science/api/pith-number/BDCVYGNY44TNOEQPI2JB4N3MDB/graph.json","events_json":"https://pith.science/api/pith-number/BDCVYGNY44TNOEQPI2JB4N3MDB/events.json","paper":"https://pith.science/paper/BDCVYGNY"},"agent_actions":{"view_html":"https://pith.science/pith/BDCVYGNY44TNOEQPI2JB4N3MDB","download_json":"https://pith.science/pith/BDCVYGNY44TNOEQPI2JB4N3MDB.json","view_paper":"https://pith.science/paper/BDCVYGNY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.10870&json=true","fetch_graph":"https://pith.science/api/pith-number/BDCVYGNY44TNOEQPI2JB4N3MDB/graph.json","fetch_events":"https://pith.science/api/pith-number/BDCVYGNY44TNOEQPI2JB4N3MDB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BDCVYGNY44TNOEQPI2JB4N3MDB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BDCVYGNY44TNOEQPI2JB4N3MDB/action/storage_attestation","attest_author":"https://pith.science/pith/BDCVYGNY44TNOEQPI2JB4N3MDB/action/author_attestation","sign_citation":"https://pith.science/pith/BDCVYGNY44TNOEQPI2JB4N3MDB/action/citation_signature","submit_replication":"https://pith.science/pith/BDCVYGNY44TNOEQPI2JB4N3MDB/action/replication_record"}},"created_at":"2026-07-14T01:21:44.410390+00:00","updated_at":"2026-07-14T01:21:44.410390+00:00"}