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We prove the following results:\n  (1) There exists a system (BT)$_{u,k}$ of non-linear ordinary differential equations for $h:R^2\\to C$ depending on $u_1, \\ldots, u_{n-1}$ in $x$ and $t$ variables such that $\\tilde L= (\\partial+h)^{-1}L(\\partial+h)$ is a solution of the $j$-th GD$_n$ flow if and only if $h$ is a solution of (BT)$_{u"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.03906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-10-13T21:35:50Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"616acc2bca750a6c9a63bd6f7e123c1247ed53df9de54bc96c2a1a99c38bf9dc","abstract_canon_sha256":"f73bcf816a2ba942c52b04b299402bc371c45b853f1ec8dcd3fc0db80bae40a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:09.855390Z","signature_b64":"hTjEL3eVB9bNTXkat+WaDSiH0BSdydCaXsaQkeHJk1litngmIYuvIB0QpORWB0OfI5xSi285btICchzu4NZABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5455114b3163c091ea744cc14a770512694824d07e29200658dd0d61bc4b0985","last_reissued_at":"2026-05-18T01:30:09.854938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:09.854938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"B\\\"acklund transformations for Gelfand-Dickey flows, revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"nlin.SI","authors_text":"Chuu-Lian Terng, Zhiwei Wu","submitted_at":"2015-10-13T21:35:50Z","abstract_excerpt":"We construct B\\\"acklund transformations (BT) for the Gelfand-Dickey hierarchy (GD$_n$-hierarchy) on the space of $n$-th order differential operators on the line. Suppose $L=\\partial_x^n-\\sum_{i=1}^{n-1}u_i\\partial_x^{(i-1)}$ is a solution of the $j$-th GD$_n$ flow. We prove the following results:\n  (1) There exists a system (BT)$_{u,k}$ of non-linear ordinary differential equations for $h:R^2\\to C$ depending on $u_1, \\ldots, u_{n-1}$ in $x$ and $t$ variables such that $\\tilde L= (\\partial+h)^{-1}L(\\partial+h)$ is a solution of the $j$-th GD$_n$ flow if and only if $h$ is a solution of (BT)$_{u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03906","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.03906","created_at":"2026-05-18T01:30:09.854999+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.03906v1","created_at":"2026-05-18T01:30:09.854999+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03906","created_at":"2026-05-18T01:30:09.854999+00:00"},{"alias_kind":"pith_short_12","alias_value":"KRKRCSZRMPAJ","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"KRKRCSZRMPAJD2TU","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"KRKRCSZR","created_at":"2026-05-18T12:29:29.992203+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/KRKRCSZRMPAJD2TUJTAUU5YFCJ","json":"https://pith.science/pith/KRKRCSZRMPAJD2TUJTAUU5YFCJ.json","graph_json":"https://pith.science/api/pith-number/KRKRCSZRMPAJD2TUJTAUU5YFCJ/graph.json","events_json":"https://pith.science/api/pith-number/KRKRCSZRMPAJD2TUJTAUU5YFCJ/events.json","paper":"https://pith.science/paper/KRKRCSZR"},"agent_actions":{"view_html":"https://pith.science/pith/KRKRCSZRMPAJD2TUJTAUU5YFCJ","download_json":"https://pith.science/pith/KRKRCSZRMPAJD2TUJTAUU5YFCJ.json","view_paper":"https://pith.science/paper/KRKRCSZR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.03906&json=true","fetch_graph":"https://pith.science/api/pith-number/KRKRCSZRMPAJD2TUJTAUU5YFCJ/graph.json","fetch_events":"https://pith.science/api/pith-number/KRKRCSZRMPAJD2TUJTAUU5YFCJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KRKRCSZRMPAJD2TUJTAUU5YFCJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KRKRCSZRMPAJD2TUJTAUU5YFCJ/action/storage_attestation","attest_author":"https://pith.science/pith/KRKRCSZRMPAJD2TUJTAUU5YFCJ/action/author_attestation","sign_citation":"https://pith.science/pith/KRKRCSZRMPAJD2TUJTAUU5YFCJ/action/citation_signature","submit_replication":"https://pith.science/pith/KRKRCSZRMPAJD2TUJTAUU5YFCJ/action/replication_record"}},"created_at":"2026-05-18T01:30:09.854999+00:00","updated_at":"2026-05-18T01:30:09.854999+00:00"}