{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LEEVRTPNKGXRISWW7GOYVYJYIO","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":"3365d8816f864be6d5dc146cd277cb7517437cbbe285f376a74428094bf29260","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-12-04T03:15:12Z","title_canon_sha256":"c30043672a658bb02265e4c070f942fadb9360c7f789321df76aa42fc2cc1aa2"},"schema_version":"1.0","source":{"id":"2312.01591","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.01591","created_at":"2026-07-05T09:37:33Z"},{"alias_kind":"arxiv_version","alias_value":"2312.01591v2","created_at":"2026-07-05T09:37:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.01591","created_at":"2026-07-05T09:37:33Z"},{"alias_kind":"pith_short_12","alias_value":"LEEVRTPNKGXR","created_at":"2026-07-05T09:37:33Z"},{"alias_kind":"pith_short_16","alias_value":"LEEVRTPNKGXRISWW","created_at":"2026-07-05T09:37:33Z"},{"alias_kind":"pith_short_8","alias_value":"LEEVRTPN","created_at":"2026-07-05T09:37:33Z"}],"graph_snapshots":[{"event_id":"sha256:9cf5c03ffaf1d43c74b49d5a2614baac7c8d074bdb04f8b636315f65007730a1","target":"graph","created_at":"2026-07-05T09:37:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2312.01591/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be a reductive group over a local field $F$ of characteristic $0$. By Harish-Chandra's regularity theorem, the character $\\Theta_{\\pi}$ of an irreducible, admissible representation $\\pi$ of $G$ is given by a locally integrable function $\\theta_{\\pi}$ on $G$. It is a natural question whether $\\theta_{\\pi}$ has better integrability properties, namely, whether it is locally $L^{1+\\epsilon}$-integrable for some $\\epsilon>0$. It turns out that the answer is positive, and this gives rise to a new singularity invariant of representations $\\epsilon_{\\star}(\\pi):=\\sup\\left\\{ \\epsilon:\\theta_{\\p","authors_text":"Itay Glazer, Julia Gordon, Yotam I. Hendel","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-12-04T03:15:12Z","title":"Integrability and singularities of Harish-Chandra characters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.01591","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":"sha256:931f7152c5991563abd7105e5e99cd252b238e72b89b4be65bde65489e175ecf","target":"record","created_at":"2026-07-05T09:37:33Z","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":"3365d8816f864be6d5dc146cd277cb7517437cbbe285f376a74428094bf29260","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-12-04T03:15:12Z","title_canon_sha256":"c30043672a658bb02265e4c070f942fadb9360c7f789321df76aa42fc2cc1aa2"},"schema_version":"1.0","source":{"id":"2312.01591","kind":"arxiv","version":2}},"canonical_sha256":"590958cded51af144ad6f99d8ae1384395dd2e2c911323028dc06acd8efa0506","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"590958cded51af144ad6f99d8ae1384395dd2e2c911323028dc06acd8efa0506","first_computed_at":"2026-07-05T09:37:33.963620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:37:33.963620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8ajr69C4v3Ak1+D3yLIi+mEaeCcZKjyfROraIyhWm3R1sLTbi7We6Nw4xZXLXFvwE6VxLoHPvw0abjQoe9HmBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:37:33.964214Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.01591","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:931f7152c5991563abd7105e5e99cd252b238e72b89b4be65bde65489e175ecf","sha256:9cf5c03ffaf1d43c74b49d5a2614baac7c8d074bdb04f8b636315f65007730a1"],"state_sha256":"1779bd9c0b620829e6a3725faba5defda3062338bdc2ff471633ac3b37550da3"}