Bibliographic record
Abstract
Given an inductive system of spectral triples <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace left-parenthesis upper A Subscript j Baseline comma script upper H Subscript j Baseline comma upper D Subscript j Baseline right-parenthesis right-brace Subscript j"> <mml:semantics> <mml:mrow> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">H</mml:mi> </mml:mrow> <mml:mi>j</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>D</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:msub> <mml:mo fence="false" stretchy="false">}</mml:mo> <mml:mi>j</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">\{(A_j,\mathcal {H}_j,D_j)\}_j</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , we find conditions under which the triple <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis limit Underscript long right-arrow Endscripts upper A Subscript j Baseline comma limit Underscript long right-arrow Endscripts upper H Subscript j Baseline comma limit Underscript long right-arrow Endscripts upper D Subscript j Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:munder> <mml:mo form="prefix">lim</mml:mo> <mml:mo stretchy="false"> ⟶ </mml:mo> </mml:munder> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:munder> <mml:mo form="prefix">lim</mml:mo> <mml:mo stretchy="false"> ⟶ </mml:mo> </mml:munder> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:munder> <mml:mo form="prefix">lim</mml:mo> <mml:mo stretchy="false"> ⟶ </mml:mo> </mml:munder> <mml:msub> <mml:mi>D</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(\underset {\longrightarrow }{\lim } A_j,\underset {\longrightarrow }{\lim } H_j,\underset {\longrightarrow }{\lim } D_j)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a spectral triple. We also analyze and describe some classical examples of spectral triples in terms of these conditions.
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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.003 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| 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".