{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AXSEHHZPSIDWHJHMTPWGCK5HCQ","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":"e9809b63c5cd175a3fa184a311f3d73da2fed6190825ee9037627acb665def17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-06T11:04:35Z","title_canon_sha256":"646d083e67fee494a1341b11f9238c6af20277e0cdaf9a8d6c3352231f74fd41"},"schema_version":"1.0","source":{"id":"1702.01564","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01564","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01564v1","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01564","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"pith_short_12","alias_value":"AXSEHHZPSIDW","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AXSEHHZPSIDWHJHM","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AXSEHHZP","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:f9f222c4bd903857d8259b3a286196ba581e9a8e67ca8876291c877bdd386f44","target":"graph","created_at":"2026-05-18T00:51:22Z","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":"We examine the asymptotics of the spectral counting function of a compact Riemannian manifold by V.G.~Avakumovic \\cite{Avakumovic} and L.~H\\\"ormander \\cite{Hormander-eigen} and show that for the scale of orthogonal and unitary groups ${\\bf SO}(N)$, ${\\bf SU}(N)$, ${\\bf U}(N)$ and ${\\bf Spin}(N)$ it is not sharp. While for negative sectional curvature improvements are possible and known, {\\it cf.} e.g., J.J.~Duistermaat $\\&$ V.~Guillemin \\cite{Duist-Guill}, here, we give sharp and contrasting examples in the positive Ricci curvature case [non-negative for ${\\bf U}(N)$]. Furthermore here the imp","authors_text":"Ali Taheri, Chalres Morris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-06T11:04:35Z","title":"On Weyl's asymptotics and remainder term for the orthogonal and unitary groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01564","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":"sha256:7432b5186ac84d30b2505eb0c213427488fe47aadd68d26ad168f317225eeac4","target":"record","created_at":"2026-05-18T00:51:22Z","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":"e9809b63c5cd175a3fa184a311f3d73da2fed6190825ee9037627acb665def17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-06T11:04:35Z","title_canon_sha256":"646d083e67fee494a1341b11f9238c6af20277e0cdaf9a8d6c3352231f74fd41"},"schema_version":"1.0","source":{"id":"1702.01564","kind":"arxiv","version":1}},"canonical_sha256":"05e4439f2f920763a4ec9bec612ba7142a6e7d72d217796fc58137accdd7dd63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05e4439f2f920763a4ec9bec612ba7142a6e7d72d217796fc58137accdd7dd63","first_computed_at":"2026-05-18T00:51:22.988087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:22.988087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZVyC9iW5CocKBYa//r5HfATRP3Dkq7+i74nfhpjKBGqGAiKeAByvP94GF1Xci41+4A0B1lSY60VppqD9tbofDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:22.988686Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.01564","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7432b5186ac84d30b2505eb0c213427488fe47aadd68d26ad168f317225eeac4","sha256:f9f222c4bd903857d8259b3a286196ba581e9a8e67ca8876291c877bdd386f44"],"state_sha256":"62b84b87bfd417609569fbc2267558f1fd4888f8d9bee5804850ef4ffdff48ec"}