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Bibliographic record
Abstract
To each submonoid <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> of a group we associate a universal Toeplitz <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper C Superscript asterisk"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">C</mml:mi> </mml:mrow> <mml:mo> ∗ </mml:mo> </mml:msup> <mml:annotation encoding="application/x-tex">\mathrm {C}^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -algebra <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper T Subscript u Baseline left-parenthesis upper P right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">T</mml:mi> </mml:mrow> <mml:mi>u</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>P</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal {T}_u(P)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> defined via generators and relations; <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper T Subscript u Baseline left-parenthesis upper P right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">T</mml:mi> </mml:mrow> <mml:mi>u</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>P</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal {T}_u(P)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a quotient of Li’s semigroup <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper C Superscript asterisk"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">C</mml:mi> </mml:mrow> <mml:mo> ∗ </mml:mo> </mml:msup> <mml:annotation encoding="application/x-tex">\mathrm {C}^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -algebra <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper C Subscript s Superscript asterisk Baseline left-parenthesis upper P right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">C</mml:mi> </mml:mrow> <mml:mi>s</mml:mi> <mml:mo> ∗ </mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>P</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathrm {C}^*_s(P)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and they are isomorphic iff <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> satisfies independence. We give a partial crossed product realization of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper T Subscript u Baseline left-parenthesis upper P right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">T</mml:mi> </mml:mrow> <mml:mi>u</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>P</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal {T}_u(P)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and show that several results known for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper C Subscript s Superscript asterisk Baseline left-parenthesis upper P right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">C</mml:mi> </mml:mrow> <mml:mi>s</mml:mi> <mml:mo> ∗ </mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>P</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathrm {C}^*_s(P)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> when <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> satisfies independence are also valid for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper T Subscript u Baseline left-parenthesis upper P right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">T</mml:mi> </mml:mrow> <mml:mi>u</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>P</
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.
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) | 0.001 | 0.002 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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