Bibliographic record
Abstract
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German upper T"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">T</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {T}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denote the full Toeplitz algebra on the Bergman space of the unit ball <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper B Subscript n"> <mml:semantics> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">B</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">\mathbb {B}_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . For each subset <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> of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript normal infinity"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal"> ∞ </mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">L^{\infty }</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="German upper C German upper I left-parenthesis upper G right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">C</mml:mi> <mml:mi mathvariant="fraktur">I</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>G</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {CI}(G)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denote the closed two-sided ideal of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German upper T"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">T</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {T}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> generated by all <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T Subscript f Baseline upper T Subscript g minus upper T Subscript g Baseline upper T Subscript f"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>f</mml:mi> </mml:msub> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mo> − </mml:mo> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>f</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">T_fT_g-T_gT_f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f comma g element-of upper G"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>,</mml:mo> <mml:mi>g</mml:mi> <mml:mo> ∈ </mml:mo> <mml:mi>G</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">f,g\in G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . It is known that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German upper C German upper I left-parenthesis upper C left-parenthesis double-struck upper B overbar Subscript n Baseline right-parenthesis right-parenthesis equals script upper K"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">C</mml:mi> <mml:mi mathvariant="fraktur">I</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>C</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mover> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">B</mml:mi> </mml:mrow> <mml:mo accent="false"> ¯ </mml:mo> </mml:mover> <mml:mi>n</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">K</mml:mi> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {CI}(C(\overline {\mathbb {B}}_n))=\mathcal {K}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , the ideal of compact operators, and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German upper C German upper I left-parenthesis upper C left-parenthesis double-struck upper B Subscript n Baseline right-parenthesis intersection upper L Superscript normal infinity Baseline right-parenthesis equals German upper T"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">C</mml:mi> <mml:mi mathvariant="fraktur">I</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>C</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvarian
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.000 | 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".