Bibliographic record
Abstract
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper G comma upper E right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(G,E)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a graph with weights <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace a Subscript x y Baseline right-brace"> <mml:semantics> <mml:mrow> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:msub> <mml:mi>a</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>x</mml:mi> <mml:mi>y</mml:mi> </mml:mrow> </mml:msub> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\{a_{xy}\}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for which a parabolic Harnack inequality holds with space-time scaling exponent <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="beta greater-than-or-equal-to 2"> <mml:semantics> <mml:mrow> <mml:mi> β </mml:mi> <mml:mo> ≥ </mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">\beta \ge 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . Suppose <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace a prime Subscript x y right-brace"> <mml:semantics> <mml:mrow> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>x</mml:mi> <mml:mi>y</mml:mi> </mml:mrow> <mml:mo>′</mml:mo> </mml:msubsup> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\{a’_{xy}\}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is another set of weights that are comparable to <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace a Subscript x y Baseline right-brace"> <mml:semantics> <mml:mrow> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:msub> <mml:mi>a</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>x</mml:mi> <mml:mi>y</mml:mi> </mml:mrow> </mml:msub> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\{a_{xy}\}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . We prove that this parabolic Harnack inequality also holds for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper G comma upper E right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(G,E)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with the weights <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace a prime Subscript x y right-brace"> <mml:semantics> <mml:mrow> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>x</mml:mi> <mml:mi>y</mml:mi> </mml:mrow> <mml:mo>′</mml:mo> </mml:msubsup> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\{a’_{xy}\}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . We also give stable necessary and sufficient conditions for this parabolic Harnack inequality to hold.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.020 | 0.003 |
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 source (direct Gemma or distilled Codex), 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".