{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:524EZKP2C6EQWALGQ2Z4OASHN3","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":"78f532e81f418f199ec94c6ce2d17c14bb279a5aafa421b8bc92ba2b8b81440c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-08-08T14:43:05Z","title_canon_sha256":"2276cf7ef839bcff57957951fff3cd959821612a2073a7a1fd2bc4f7ba4eb4a1"},"schema_version":"1.0","source":{"id":"1308.1863","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1863","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1863v3","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1863","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"524EZKP2C6EQ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"524EZKP2C6EQWALG","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"524EZKP2","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:76d79f85d8cd7e00358dfcd594956e02b174b2362f9e4e113fedf099a8d19b60","target":"graph","created_at":"2026-05-18T01:17:44Z","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":"If $G$ is a Lie group, $H\\subset G$ is a closed subgroup, and $\\tau$ is a unitary representation of $H$, then the authors give a sufficient condition on $\\xi\\in i\\mathfrak{g}^*$ to be in the wave front set of $\\operatorname{Ind}_H^G\\tau$. In the special case where $\\tau$ is the trivial representation, this result was conjectured by Howe. If $G$ is a real, reductive algebraic group and $\\pi$ is a unitary representation of $G$ that is weakly contained in the regular representation, then the authors give a geometric description of $\\operatorname{WF}(\\pi)$ in terms of the direct integral decomposi","authors_text":"Benjamin Harris, Gestur Olafsson, Hongyu He","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-08-08T14:43:05Z","title":"Wave Front Sets of Reductive Lie Group Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1863","kind":"arxiv","version":3},"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":"sha256:9f85321a535078e8c315c5ef42af4f31f6f1026bcb0795d8fe6b9474fc7db69b","target":"record","created_at":"2026-05-18T01:17:44Z","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":"78f532e81f418f199ec94c6ce2d17c14bb279a5aafa421b8bc92ba2b8b81440c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-08-08T14:43:05Z","title_canon_sha256":"2276cf7ef839bcff57957951fff3cd959821612a2073a7a1fd2bc4f7ba4eb4a1"},"schema_version":"1.0","source":{"id":"1308.1863","kind":"arxiv","version":3}},"canonical_sha256":"eeb84ca9fa17890b016686b3c702476ef52fd3618040e08b29355ab00fee47ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eeb84ca9fa17890b016686b3c702476ef52fd3618040e08b29355ab00fee47ff","first_computed_at":"2026-05-18T01:17:44.399889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:44.399889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GNw+kbiUPbYGzWaHWySqgqBoPcLyx7aaX8i7FWvssRnj3gLZ6ObaHFD2P4MSid1zWfqkXjHgEi3PC+am/vy6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:44.400854Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1863","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f85321a535078e8c315c5ef42af4f31f6f1026bcb0795d8fe6b9474fc7db69b","sha256:76d79f85d8cd7e00358dfcd594956e02b174b2362f9e4e113fedf099a8d19b60"],"state_sha256":"5106efeaacc4c553aacdf34247a895d9356cf660a3f5b0a20246f538342a8c37"}