{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FVFIU2ZDGWPET6YLC3WCYHNRMX","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":"fd6c1864ecd138958005c9fce44e2bbc35e22ca86a687b4644aad57917a98425","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-10-04T09:12:32Z","title_canon_sha256":"13840fd4ea6b1039d8340d541ed109ef328d227416c96a8901d191401080e2ad"},"schema_version":"1.0","source":{"id":"2410.03247","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.03247","created_at":"2026-07-05T09:15:46Z"},{"alias_kind":"arxiv_version","alias_value":"2410.03247v1","created_at":"2026-07-05T09:15:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.03247","created_at":"2026-07-05T09:15:46Z"},{"alias_kind":"pith_short_12","alias_value":"FVFIU2ZDGWPE","created_at":"2026-07-05T09:15:46Z"},{"alias_kind":"pith_short_16","alias_value":"FVFIU2ZDGWPET6YL","created_at":"2026-07-05T09:15:46Z"},{"alias_kind":"pith_short_8","alias_value":"FVFIU2ZD","created_at":"2026-07-05T09:15:46Z"}],"graph_snapshots":[{"event_id":"sha256:c72e9c329c25b6c29feca55e1ca462546e97fe69a3b454419a93b0c75463e799","target":"graph","created_at":"2026-07-05T09:15:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.03247/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $K$ be a non-archimedean local field of residual characteristic $p\\neq 2$. Let $G$ be a connected reductive group over $K$, let $\\theta$ be an involution of $G$ over $K$, and let $H$ be the connected component of $\\theta$-fixed subgroup of $G$ over $K$. By realizing the Steinberg representation of $G$ as the $G$-space of complex smooth harmonic cochains following the idea of Broussous--Court\\`es, we study its space of distinction by $H$ as a finite dimensional complex vector space. We give an upper bound of the dimension, and under certain conditions, we show that the upper bound is sharp ","authors_text":"Chuijia Wang, Jiandi Zou","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-10-04T09:12:32Z","title":"Distinction of the Steinberg representation with respect to a symmetric pair"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.03247","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":"sha256:1a78f1a23fc3203088a16d12d7e3d5c33819220361a3710467dc6950e5fcfe15","target":"record","created_at":"2026-07-05T09:15:46Z","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":"fd6c1864ecd138958005c9fce44e2bbc35e22ca86a687b4644aad57917a98425","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-10-04T09:12:32Z","title_canon_sha256":"13840fd4ea6b1039d8340d541ed109ef328d227416c96a8901d191401080e2ad"},"schema_version":"1.0","source":{"id":"2410.03247","kind":"arxiv","version":1}},"canonical_sha256":"2d4a8a6b23359e49fb0b16ec2c1db165c31cf0c32addd895c8a3f25357651df9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d4a8a6b23359e49fb0b16ec2c1db165c31cf0c32addd895c8a3f25357651df9","first_computed_at":"2026-07-05T09:15:46.721187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:15:46.721187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Byn5AxX74TF4VuFr2ZwQY3+0anuZFbw4vRaw3jU10CeYHDdRgWbi2WDw6i9vE1YZwVG4i0ec7TXjV8EYz0iSBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:15:46.721643Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.03247","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a78f1a23fc3203088a16d12d7e3d5c33819220361a3710467dc6950e5fcfe15","sha256:c72e9c329c25b6c29feca55e1ca462546e97fe69a3b454419a93b0c75463e799"],"state_sha256":"a4346ee44f21acf1a65dcf59551c807f13e9594605879793491208c4fa850967"}