{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XLIU4CCWBPEYIJIZ2AVI25A7PH","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":"d4bc0a23adbca11bd337a08988bbe19f4a0432a79e6ffa18758eb82249eec655","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-07T18:58:12Z","title_canon_sha256":"50a3091dca460424e9d12a68155ea080aba083ebee3cc26e0743da74685ca4f8"},"schema_version":"1.0","source":{"id":"1009.1364","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1364","created_at":"2026-05-18T00:30:22Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1364v1","created_at":"2026-05-18T00:30:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1364","created_at":"2026-05-18T00:30:22Z"},{"alias_kind":"pith_short_12","alias_value":"XLIU4CCWBPEY","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XLIU4CCWBPEYIJIZ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XLIU4CCW","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:4c7aa5e4943c97d6e390252c6f202fbd32c6e83beb385751cc75f3314eb19764","target":"graph","created_at":"2026-05-18T00:30:22Z","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":"Of all real Lagrangian--Grassmannians $LG(n,2n)$, only $LG(2,4)$ admits a distinguished (Lorentzian) conformal structure and hence is identified with the indefinite M\\\"obius space $S^{1,2}$. Using Cartan's method of moving frames, we study hyperbolic (timelike) surfaces in $LG(2,4)$ modulo the conformal symplectic group $CSp(4,R)$. This $CSp(4,R)$-invariant classification is also a contact-invariant classification of (in general, highly non-linear) second order scalar hyperbolic PDE in the plane. Via $LG(2,4)$, we give a simple geometric argument for the invariance of the general hyperbolic M","authors_text":"Dennis The","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-07T18:58:12Z","title":"Conformal geometry of surfaces in the Lagrangian--Grassmannian and second order PDE"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1364","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:ff797632516322663e9b5fed25f6aef703b2510119d61778a16d8a3f2568481c","target":"record","created_at":"2026-05-18T00:30:22Z","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":"d4bc0a23adbca11bd337a08988bbe19f4a0432a79e6ffa18758eb82249eec655","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-07T18:58:12Z","title_canon_sha256":"50a3091dca460424e9d12a68155ea080aba083ebee3cc26e0743da74685ca4f8"},"schema_version":"1.0","source":{"id":"1009.1364","kind":"arxiv","version":1}},"canonical_sha256":"bad14e08560bc9842519d02a8d741f79c314f59e51ede0847a98ccd4a3ab44da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bad14e08560bc9842519d02a8d741f79c314f59e51ede0847a98ccd4a3ab44da","first_computed_at":"2026-05-18T00:30:22.938881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:22.938881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pW28c6S6srveAY8kolUrG+2oSWjrIOwBCYXZx2bP4x0HMf+jSUm/IsfQCvYN0ufAn6d9ExVCdJ/Zkv0gxo+UBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:22.939706Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1364","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff797632516322663e9b5fed25f6aef703b2510119d61778a16d8a3f2568481c","sha256:4c7aa5e4943c97d6e390252c6f202fbd32c6e83beb385751cc75f3314eb19764"],"state_sha256":"7856a27c7d74d98d31d09e1b3a27cfbb408ca1d576afad11510c5c5e557afe81"}