{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LXRCZGXPZ3TUI4YTJ2SQT5N4WS","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":"b43dff8da19677f1131e2d57e9687fc466b9fc33d6ba2b68368fdad78c7db8cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-02-05T05:59:19Z","title_canon_sha256":"ba850dab1a53f8a4c2f5d819bf120b54a051b8a4c7da8fd0d61a22182c20f19b"},"schema_version":"1.0","source":{"id":"1902.01558","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01558","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01558v1","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01558","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"LXRCZGXPZ3TU","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LXRCZGXPZ3TUI4YT","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LXRCZGXP","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:4dd11cbf56430087bf672b619c2787f2f4b475d43c9667a9bd009eabb11b51d6","target":"graph","created_at":"2026-05-17T23:54:47Z","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 classical result of describing harmonic maps from surfaces into symmetric spaces of reductive Lie groups states that the Maurer-Cartan form with an additional parameter, the so-called loop parameter, is integrable for all values of the loop parameter. As a matter of fact, the same result holds for $k$-symmetric spaces over reductive Lie groups. In this survey we will show that to each of the five different types of real forms for a loop group of $A_2^{(2)}$ there exists a surface class, for which some frame is integrable for all values of the loop parameter if and only if it belongs to one","authors_text":"Erxiao Wang, Josef F. Dorfmeister, Shimpei Kobayashi, Walter Freyn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-02-05T05:59:19Z","title":"Survey on real forms of the complex $A_2^{(2)}$-Toda equation and surface theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01558","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":"sha256:88c4458407eb463bfc8fcf05c129d583068cf22cb1dd17d04340b1d4a3f349cf","target":"record","created_at":"2026-05-17T23:54:47Z","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":"b43dff8da19677f1131e2d57e9687fc466b9fc33d6ba2b68368fdad78c7db8cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-02-05T05:59:19Z","title_canon_sha256":"ba850dab1a53f8a4c2f5d819bf120b54a051b8a4c7da8fd0d61a22182c20f19b"},"schema_version":"1.0","source":{"id":"1902.01558","kind":"arxiv","version":1}},"canonical_sha256":"5de22c9aefcee74473134ea509f5bcb494a45876832ed3bde0ee4edf7a0ab820","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5de22c9aefcee74473134ea509f5bcb494a45876832ed3bde0ee4edf7a0ab820","first_computed_at":"2026-05-17T23:54:47.332070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:47.332070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O5c8EozmS+gminLz1KzWL2e27B4WS6nOQ3v/n1nntb6oGcMwnw4QA2e5px5PZima1Vatqq+rk4WcmeyQKSo1Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:47.332597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.01558","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88c4458407eb463bfc8fcf05c129d583068cf22cb1dd17d04340b1d4a3f349cf","sha256:4dd11cbf56430087bf672b619c2787f2f4b475d43c9667a9bd009eabb11b51d6"],"state_sha256":"d983f42ff41084332781c62660200811f4f8f0b92bbcca8e6171fa571b2703b3"}