Why this work is in the frame
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Bibliographic record
Abstract
An equivalent, but variant form of Riemann’s functional equation is explored, and several discoveries are made. Properties of Riemann’s zeta function ζ(s), from which a necessary and sufficient condition for the existence of zeros in the critical strip, are deduced. This in turn, by an indirect route, eventually produces a simple, solvable, differential equation for arg(ζ(s)) on the critical line s=1/2+iρ, the consequences of which are explored, and the “LogZeta" function is introduced. A singular linear transform between the real and imaginary components of ζ and ζ′ on the critical line is derived, and an implicit relationship for locating a zero (ρ=ρ0) on the critical line is found between the arguments of ζ(1/2+iρ) and ζ′(1/2+iρ). Notably, the Volchkov criterion, a Riemann Hypothesis (RH) equivalent, is analytically evaluated and verified to be half equivalent to RH, but RH is not proven. Numerical results are presented, some of which lead to the identification of <i>anomalous zeros</i>, whose existence in turn suggests that well-established, traditional derivations such as the Volchkov criterion and counting theorems require re-examination. It is proven that the derivative ζ′(1/2+iρ) will never vanish on the perforated critical line (ρ≠ρ0). Traditional asymptotic and counting results are obtained in an untraditional manner, yielding insight into the nature of ζ(1/2+iρ) as well as very accurate asymptotic estimates for distribution bounds and the density of zeros on the critical line.
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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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