{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7GYEHI7EEQD57575JQ6CWBJL3G","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":"27b390fa8136f66c7ddf4dcf61212985f509ae9b2a4a08980c285b7fe53fe253","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-27T14:38:45Z","title_canon_sha256":"62d9ff40e398ea4cc0d7f141a200a53e971e4456173dc41b2a7e239f0235b7c4"},"schema_version":"1.0","source":{"id":"1009.5274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5274","created_at":"2026-05-18T02:47:06Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5274v1","created_at":"2026-05-18T02:47:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5274","created_at":"2026-05-18T02:47:06Z"},{"alias_kind":"pith_short_12","alias_value":"7GYEHI7EEQD5","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7GYEHI7EEQD57575","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7GYEHI7E","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:c602d16475a9f5f6505de81e4c537c124e26623f2604c23eb0cb9e231c013546","target":"graph","created_at":"2026-05-18T02:47:06Z","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 define a transformation on harmonic maps from a Riemann surface into the 2-sphere which depends on a complex parameter, the so-called mu-Darboux transformation. In the case when the harmonic map N is the Gauss map of a constant mean curvature surface f and the parameter is real, the mu-Darboux transformation of -N is the Gauss map of a classical Darboux transform f. More generally, for all complex parameter the transformation on the harmonic Gauss map of f is induced by a (generalized) Darboux transformation on f. We show that this operation on harmonic maps coincides with simple factor dre","authors_text":"A. Quintino, F. E. Burstall, J. F. Dorfmeister, K. Leschke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-27T14:38:45Z","title":"Darboux transforms and simple factor dressing of constant mean curvature surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5274","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:f6790796027fe50d7bdf9d6660a90143286c01d32072e4cd818e3cf1ad689d06","target":"record","created_at":"2026-05-18T02:47:06Z","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":"27b390fa8136f66c7ddf4dcf61212985f509ae9b2a4a08980c285b7fe53fe253","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-27T14:38:45Z","title_canon_sha256":"62d9ff40e398ea4cc0d7f141a200a53e971e4456173dc41b2a7e239f0235b7c4"},"schema_version":"1.0","source":{"id":"1009.5274","kind":"arxiv","version":1}},"canonical_sha256":"f9b043a3e42407dff7fd4c3c2b052bd9a3d3a8c62eeb05fcdac89c408595583c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9b043a3e42407dff7fd4c3c2b052bd9a3d3a8c62eeb05fcdac89c408595583c","first_computed_at":"2026-05-18T02:47:06.013985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:06.013985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IRGI+su6g6ccbf9dJ8XTexQDUOZYZJaELmrziryLCKFK8awPIDqLDtVasGCqnnBxyn0rbavZmrR7HnN88lD6Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:06.014410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6790796027fe50d7bdf9d6660a90143286c01d32072e4cd818e3cf1ad689d06","sha256:c602d16475a9f5f6505de81e4c537c124e26623f2604c23eb0cb9e231c013546"],"state_sha256":"8f8c71d4a0d7bf1943821df3e3d522da443c1702f2ab92ef323099a3a1f2ead6"}