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According to the semicontinuity conjecture of the first author, there should exist a positive natural number $m$ such that, for any weight function $L' : W \\to \\NM$ such that $L(s^+)=L'(s^+) > m L'(s^\\circ)$ for all $s^+ \\in S^+$ and $s^\\circ \\in S^\\circ$, $C$ is a union of Kazhdan-Lusz"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1103.4025","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-21T14:18:21Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"4a917181189699248e054270db5207369d11a5bc26d56c16299b83e09d9a1a07","abstract_canon_sha256":"fa02613b423f5bde0d0fdd720d068b561463acede4763eeb7716b7d93f286245"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:56.017893Z","signature_b64":"CSaH+fHRxB702ouqhsz0N2bIG0AJQLzEXkH5O52mtQhFZzZX+y3mGaWjuEO5/N73Lp/Q/I5X80qTYSKvR3lSAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08bc31bcfa4fcf92910e8ac0b70cb0806eb2d696bad8e092f4409ba2839694a4","last_reissued_at":"2026-05-18T04:23:56.017482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:56.017482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic lowest two-sided cell","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"C\\'edric Bonnaf\\'e (I3M), J\\'er\\'emie Guilhot","submitted_at":"2011-03-21T14:18:21Z","abstract_excerpt":"To a Coxeter system $(W,S)$ (with $S$ finite) and a weight function $L : W \\to \\NM$ is associated a partition of $W$ into Kazhdan-Lusztig (left, right or two-sided) $L$-cells. 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