Bibliographic record
Abstract
A new approach to information-theoretic converses is proposed based on Shannon’s original sphere-packing argument. Typical sequence arguments are hardened with decoding sets to include structured codewords. Each decoding set is shown to have a minimum volume of 2nH(Y|X)typical y-sequences in the point-to-point discrete-memoryless channel if the probability of decoding error vanishes. Since a codebook of type p(x) generates at most 2nH(Y)typical y-sequences, the error probability is non-vanishing when R > maxp(x)I(X;Y). Kolmogorov’s zero-one law is applied to prove the error probability also goes to one, unifying the weak and strong converses. In preparation for the capacity of the relay channel, i.i.d codebooks are shown via the zero-one law and a sphere-absorption argument, to exhibit a clustering property where their orbits in the y-space asymptotically coincide or separate into clusters of indistinguishable codewords. The capacity of the relay channel is shown to be ${\max _{p\left({{x_s},{x_r}}\right)}}\min \left\{ {I\left({{X_s},{X_r};{Y_d}}\right),I\left({{X_s};{Y_r}{Y_d}\mid {X_r}}\right) - \delta } \right\}$ where $\delta : = \min \left\{ {{{\left| {I\left({{{\hat Y}_r};{Y_r}\mid {X_r}{Y_d}}\right) - {C_0}} \right|}^ + },I\left({{X_s};{Y_d}\mid {X_r}{Y_r}}\right)} \right\}$, C0:= I(Xr;Yd), and ${\hat Y_r}$ emulates Xsin a virtual source-relay channel.
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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 | 0.008 | 0.019 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.003 | 0.009 |
| Scholarly communication | 0.006 | 0.011 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.009 | 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".