Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
In this paper we investigate the zeros of the Eisenstein series <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E 2"> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:annotation encoding="application/x-tex">E_2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . In particular, we prove that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E 2"> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:annotation encoding="application/x-tex">E_2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has infinitely many <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S upper L 2 left-parenthesis double-struck upper Z right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>SL</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo> </mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\operatorname {SL}_2(\mathbb {Z})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -inequivalent zeros in the upper half-plane <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German upper H"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">H</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {H}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , yet none in the standard fundamental <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German upper F"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">F</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {F}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . Furthermore, we go on to investigate other fundamental regions in the upper half-plane <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German upper H"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">H</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {H}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for which there do or do not exist zeros of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E 2"> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:annotation encoding="application/x-tex">E_2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . We establish infinitely many such regions containing a zero of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E 2"> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:annotation encoding="application/x-tex">E_2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and infinitely many which do not.
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 | 0.000 | 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 it