Bibliographic record
Abstract
Let $W(t)=\tfrac12\sum_ρ\exp\{(ρ-\tfrac12)^2t\}$ be the Xi heat trace, with zeros counted with multiplicity. We prove that verification of the zeros through height $T_N=20\,000N\sqrt{1+\log N}$ suffices for positive definiteness of both leading $N\times N$ heat trace Hankel blocks at every positive time. For the three by three blocks, height $10\,000$ suffices. Published rigorous zero verification makes the conclusion unconditional for $N\le30\,000\,000$. A separate Cauchy estimate for the prime kernel proves $(-1)^kW^{(k)}>0$ through order $10^{17}$ and yields positive finite order integral representations of $W$. A quantitative perturbation estimate constructs functions with off line zeros preserving both these finite blocks and all the stated derivative signs. The reciprocal Xi clock is infinitely divisible and self decomposable, and the sine squared lemma gives a regularised arithmetic formula for its Thorin functional. Positivity of the full functional and the generalised gamma convolution property are reformulations of RH; for the latter it suffices to establish the transform identity for real $0
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.013 | 0.002 |
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".