{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:E477HBO33KI5BM3KBSP343Y5VO","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":"7ffb7a3b7edfb9c63e34030265c99ec631d84851f7fa3627fef210ebe939aab9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-02T23:04:26Z","title_canon_sha256":"edb69779fb7a30298dd186d8434e2d5e6700cd14fb76bafd36d7a42ce36f9fce"},"schema_version":"1.0","source":{"id":"1003.0704","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.0704","created_at":"2026-05-18T04:12:10Z"},{"alias_kind":"arxiv_version","alias_value":"1003.0704v2","created_at":"2026-05-18T04:12:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.0704","created_at":"2026-05-18T04:12:10Z"},{"alias_kind":"pith_short_12","alias_value":"E477HBO33KI5","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"E477HBO33KI5BM3K","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"E477HBO3","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:8186d3de575cb8b303839bed6d27ca327827713d84f6a93aebdf5197a900ab56","target":"graph","created_at":"2026-05-18T04:12:10Z","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":"Let $G$ be a non-compact simple Lie group with Lie algebra $\\mathfrak{g}$. Denote with $m(\\mathfrak{g})$ the dimension of the smallest non-trivial $\\mathfrak{g}$-module with an invariant non-degenerate symmetric bilinear form. For an irreducible finite volume pseudo-Riemannian analytic manifold $M$ it is observed that $\\dim(M) \\geq \\dim(G) + m(\\mathfrak{g})$ when $M$ admits an isometric $G$-action with a dense orbit. The Main Theorem considers the case $G = \\widetilde{\\mathrm{SO}}_0(p,q)$ providing an explicit description of $M$ when the bound is achieved. In such case, $M$ is (up to a finite ","authors_text":"Gestur Olafsson, Raul Quiroga-Barranco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-02T23:04:26Z","title":"On low-dimensional manifolds with isometric $\\mathrm{SO}_0(p,q)$-actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0704","kind":"arxiv","version":2},"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:b161b9fc94ac91b3028e8ce87345f880510911cc6fc8b4e84db3721aafcee3bd","target":"record","created_at":"2026-05-18T04:12:10Z","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":"7ffb7a3b7edfb9c63e34030265c99ec631d84851f7fa3627fef210ebe939aab9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-02T23:04:26Z","title_canon_sha256":"edb69779fb7a30298dd186d8434e2d5e6700cd14fb76bafd36d7a42ce36f9fce"},"schema_version":"1.0","source":{"id":"1003.0704","kind":"arxiv","version":2}},"canonical_sha256":"273ff385dbda91d0b36a0c9fbe6f1daba9fc87995bfe2627666be4bb1c5a6bef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"273ff385dbda91d0b36a0c9fbe6f1daba9fc87995bfe2627666be4bb1c5a6bef","first_computed_at":"2026-05-18T04:12:10.689151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:10.689151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rfbpWk+CsF1SikAi7YihlWW6ZXySdQx8mIpndDX4cDftjUNlNnRCFCK8kS+W2FhZAakG7TwerDjKjNO6TpZhDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:10.689593Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.0704","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b161b9fc94ac91b3028e8ce87345f880510911cc6fc8b4e84db3721aafcee3bd","sha256:8186d3de575cb8b303839bed6d27ca327827713d84f6a93aebdf5197a900ab56"],"state_sha256":"8df97de3c530aa3a85cf544a2a83aa9392ab1bb2a9827a069b81810c0f616b0b"}