Why this work is in the frame
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Bibliographic record
Abstract
We consider a new class of potentially exotic group C*-algebras C ⁎ ( PF p ⁎ ( G ) ) for a locally compact group G , and its connection with the class of potentially exotic group C*-algebras C L p ⁎ ( G ) introduced by Brown and Guentner. Surprisingly, these two classes of C*-algebras are intimately related. By exploiting this connection, we show C L p ⁎ ( G ) = C ⁎ ( PF p ⁎ ( G ) ) for p ∈ ( 2 , ∞ ) , and the C*-algebras C L p ⁎ ( G ) are pairwise distinct for p ∈ ( 2 , ∞ ) when G belongs to a large class of nonamenable groups possessing the Haagerup property and either the rapid decay property or Kunze-Stein phenomenon by characterizing the positive definite functions that extend to positive linear functionals of C L p ⁎ ( G ) and C ⁎ ( PF p ⁎ ( G ) ) . This greatly generalizes earlier results of Okayasu (see [30] ) and the second author (see [40] ) on the pairwise distinctness of C L p ⁎ ( G ) for 2 < p < ∞ when G is either a noncommutative free group or the group SL ( 2 , R ) , respectively. As a byproduct of our techniques, we present two applications to the theory of unitary representations of a locally compact group G . Firstly, we give a short proof of the well-known Cowling-Haagerup-Howe Theorem, which presents sufficient condition implying the weak containment of a cyclic unitary representation of G in the left regular representation of G (see [14] ). Also we give a near solution to a 1978 conjecture of Cowling stated in [10] . This conjecture of Cowling states if G is a Kunze-Stein group and π is a unitary representation of G with cyclic vector ξ such that the map G ∋ s ↦ 〈 π ( s ) ξ , ξ 〉 belongs to L p ( G ) for some 2 < p < ∞ , then A π ⊆ L p ( G ) . We show B π ⊆ L p + ϵ ( G ) for every ϵ > 0 (recall A π ⊆ B π ).
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.011 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it