{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RCOSOLE243B7JTVBAHYUUKNNGI","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":"40b9352e15b8ec7861f7aeafa86a3fe256fcafc6f724742139bb8eedce041dfe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-30T10:26:17Z","title_canon_sha256":"fbd3e3d6a7d1e37bf21c154a6b9153e1f4b19ea7cda9f9a62a174a4be1f171b1"},"schema_version":"1.0","source":{"id":"1110.6596","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6596","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6596v1","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6596","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"pith_short_12","alias_value":"RCOSOLE243B7","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RCOSOLE243B7JTVB","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RCOSOLE2","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:509934da2f6c3cca1fb4e4838e421861d4d747795a75aad556618b63445e00f2","target":"graph","created_at":"2026-05-18T04:09:55Z","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":"The geometric conjecture developed by the authors in [1,2,3,4] applies to the smooth dual Irr(G) of any reductive p-adic group G. It predicts a definite geometric structure - the structure of an extended quotient - for each component in the Bernstein decomposition of Irr(G).\n  In this article, we prove the geometric conjecture for the principal series in any split connected reductive p-adic group G. The proof proceeds via Springer parameters and Langlands parameters. As a consequence of this approach, we establish strong links with the local Langlands correspondence.\n  One important feature of","authors_text":"Anne-Marie Aubert, Paul Baum, Roger Plymen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-30T10:26:17Z","title":"Extended quotients in the principal series of reductive p-adic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6596","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":"sha256:2b9ea235e87e6e14b1ba6a9f350d6ebd82af06d1afdff1b1c3c655668497184e","target":"record","created_at":"2026-05-18T04:09:55Z","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":"40b9352e15b8ec7861f7aeafa86a3fe256fcafc6f724742139bb8eedce041dfe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-30T10:26:17Z","title_canon_sha256":"fbd3e3d6a7d1e37bf21c154a6b9153e1f4b19ea7cda9f9a62a174a4be1f171b1"},"schema_version":"1.0","source":{"id":"1110.6596","kind":"arxiv","version":1}},"canonical_sha256":"889d272c9ae6c3f4cea101f14a29ad3218eb07f317e2eed3bda668af582e70ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"889d272c9ae6c3f4cea101f14a29ad3218eb07f317e2eed3bda668af582e70ba","first_computed_at":"2026-05-18T04:09:55.124126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:55.124126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XLPCcvvrc6IlX1y1Un5oTofeLIDe3Hr2gDrJqcc17SnSTKWB96A9C4qYzlQi3IJU7efpKL0lUnYHjaoE5NHWAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:55.124815Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6596","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b9ea235e87e6e14b1ba6a9f350d6ebd82af06d1afdff1b1c3c655668497184e","sha256:509934da2f6c3cca1fb4e4838e421861d4d747795a75aad556618b63445e00f2"],"state_sha256":"559f564f4590abdd707316d8d960993c3a07c999a577d57b8dad8f2cf31ac022"}