{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6JAVMY6NFZLK3CWU5LMHG2WQSK","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":"a6a4ce7be9186b65d8f4a2edab284991326d244a343e72a45a72ee95da2aa89d","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-24T10:02:31Z","title_canon_sha256":"e32f7e23d4eed22e6bf236f8edd45ac08e565f549a4381203a73ec673b51e183"},"schema_version":"1.0","source":{"id":"1901.08318","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.08318","created_at":"2026-05-17T23:55:37Z"},{"alias_kind":"arxiv_version","alias_value":"1901.08318v1","created_at":"2026-05-17T23:55:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.08318","created_at":"2026-05-17T23:55:37Z"},{"alias_kind":"pith_short_12","alias_value":"6JAVMY6NFZLK","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6JAVMY6NFZLK3CWU","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6JAVMY6N","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:ecd5375fffd87c0268748b08b04e8176fe19bd516268ca7b456d6287c53881c1","target":"graph","created_at":"2026-05-17T23:55:37Z","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":"Pseudo $H$-type Lie groups $G_{r,s}$ of signature $(r,s)$ are defined via a module action of the Clifford algebra $C\\ell_{r,s}$ on a vector space $V \\cong \\mathbb{R}^{2n}$. They form a subclass of all 2-step nilpotent Lie groups and based on their algebraic structure they can be equipped with a left-invariant pseudo-Riemannian metric. Let $\\mathcal{N}_{r,s}$ denote the Lie algebra corresponding to $G_{r,s}$. A choice of left-invariant vector fields $[X_1, \\ldots, X_{2n}]$ which generate a complement of the center of $\\mathcal{N}_{r,s}$ gives rise to a second order operator \\begin{equation*} \\D","authors_text":"Andr\\'e Froehly, Irina Markina, Wolfram Bauer","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-24T10:02:31Z","title":"The fundamental solution of a class of ultra-hyperbolic operators on Pseudo $H$-type groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08318","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:b92dc75466a8bb826d0140d614505c336747c17e03093bda47438e0b47bfeaec","target":"record","created_at":"2026-05-17T23:55:37Z","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":"a6a4ce7be9186b65d8f4a2edab284991326d244a343e72a45a72ee95da2aa89d","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-24T10:02:31Z","title_canon_sha256":"e32f7e23d4eed22e6bf236f8edd45ac08e565f549a4381203a73ec673b51e183"},"schema_version":"1.0","source":{"id":"1901.08318","kind":"arxiv","version":1}},"canonical_sha256":"f2415663cd2e56ad8ad4ead8736ad092bcf60340c1d638f6b36c4ca0f03db683","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2415663cd2e56ad8ad4ead8736ad092bcf60340c1d638f6b36c4ca0f03db683","first_computed_at":"2026-05-17T23:55:37.364163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:37.364163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BUfwvG90k4TThu1bSQ1DJvMMjdaLn6lvHnk7mVWrokP5CHIRuEGZT3XQ7E2AtlHDrD0kpLREz1XM6lMeY3OBBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:37.364608Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.08318","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b92dc75466a8bb826d0140d614505c336747c17e03093bda47438e0b47bfeaec","sha256:ecd5375fffd87c0268748b08b04e8176fe19bd516268ca7b456d6287c53881c1"],"state_sha256":"cda517fec4feb0ebb1ee73c874da42a3bf9ac58af29329bde117401bc322f89e"}