Bibliographic record
Abstract
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -adic Lie group associated to a connected reductive group over <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper Q Subscript p"> <mml:semantics> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">Q</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> <mml:annotation encoding="application/x-tex">\mathbb {Q}_{p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P"> <mml:semantics> <mml:mi>P</mml:mi> <mml:annotation encoding="application/x-tex">P</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a parabolic subgroup of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a Levi quotient of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P"> <mml:semantics> <mml:mi>P</mml:mi> <mml:annotation encoding="application/x-tex">P</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . In this paper, we define a <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="delta"> <mml:semantics> <mml:mi> δ </mml:mi> <mml:annotation encoding="application/x-tex">\delta</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -functor <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H Superscript star Baseline upper J Subscript upper P"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo> ⋆ </mml:mo> </mml:mrow> </mml:msup> <mml:msub> <mml:mi>J</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>P</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">H^{\star }J_{P}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> from the category of admissible locally analytic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -representations to the category of essentially admissible locally analytic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -representations that extends the Jacquet-Emerton module functor <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper J Subscript upper P"> <mml:semantics> <mml:msub> <mml:mi>J</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>P</mml:mi> </mml:mrow> </mml:msub> <mml:annotation encoding="application/x-tex">J_{P}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> defined in Emerton [Ann. Sci. École Norm. Sup. (4) <bold>39</bold> (2006), pp. 775–839].
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How this classification was reachedexpand
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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".