{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YL6X6ADFK23VBTBFJZCNDJ6M4B","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":"ebcebb453b4af6591d4bd70425c4638d1b2b08a6798cf114a8d5c4a659303d5f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-08T16:48:18Z","title_canon_sha256":"5a7877abc38dc6753cf23432c168f9544491b8e1fb70f1c8ef60d04616f7abb0"},"schema_version":"1.0","source":{"id":"1606.02633","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02633","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02633v3","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02633","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"pith_short_12","alias_value":"YL6X6ADFK23V","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YL6X6ADFK23VBTBF","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YL6X6ADF","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:ad67c4c581caddb8cd52591437cac7da24cc0d7f356124c61d7482794c3d4817","target":"graph","created_at":"2026-05-18T00:29:33Z","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":"For each simple Lie algebra $\\mathfrak{g}$ (excluding, for trivial reasons, type ${\\sf C}$) we find the lowest possible degree of an invariant second-order PDE over the adjoint variety in $\\mathbb{P}\\mathfrak{g}$, a homogeneous contact manifold. Here a PDE $F(x^i,u,u_i,u_{ij})=0$ has degree $\\le d$ if $F$ is a polynomial of degree $\\le d$ in the minors of $(u_{ij})$, with coefficients functions of the contact coordinates $x^i$, $u$, $u_i$ (e.g., Monge-Amp\\`ere equations have degree 1). For $\\mathfrak{g}$ of type ${\\sf A}$ or ${\\sf G}$ we show that this gives all invariant second-order PDEs. Fo","authors_text":"Dmitri V. Alekseevsky, Gianni Manno, Giovanni Moreno, Jan Gutt","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-08T16:48:18Z","title":"Lowest degree invariant 2nd order PDEs over rational homogeneous contact manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02633","kind":"arxiv","version":3},"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:adeba5a2c1d3717da4808ab73e94e5b0887c1c3b2e22db740670f06761289877","target":"record","created_at":"2026-05-18T00:29:33Z","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":"ebcebb453b4af6591d4bd70425c4638d1b2b08a6798cf114a8d5c4a659303d5f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-08T16:48:18Z","title_canon_sha256":"5a7877abc38dc6753cf23432c168f9544491b8e1fb70f1c8ef60d04616f7abb0"},"schema_version":"1.0","source":{"id":"1606.02633","kind":"arxiv","version":3}},"canonical_sha256":"c2fd7f006556b750cc254e44d1a7cce065ca45e83bce26ce7f0315c42eec7c82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2fd7f006556b750cc254e44d1a7cce065ca45e83bce26ce7f0315c42eec7c82","first_computed_at":"2026-05-18T00:29:33.615751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:33.615751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gg5JmiwzWu2A8KSfdKhSqf0gXUQMUwoewyf3OHWW0gL/YBy08hpx/DMPBMY78ZHy7aO/U0V5Vjt6c2mI8ChdAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:33.616350Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02633","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adeba5a2c1d3717da4808ab73e94e5b0887c1c3b2e22db740670f06761289877","sha256:ad67c4c581caddb8cd52591437cac7da24cc0d7f356124c61d7482794c3d4817"],"state_sha256":"f2b15bd80a1dc829664c9c2daeca8eeb90a18d6d7b630c50e1de460253bb8ae9"}