Why this work is in the frame
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Bibliographic record
Abstract
We introduce a finitely axiomatizable second-order theory VTC 0 and show that it characterizes precisely the class uniform TC0. It is simply the theory V0 [12] together with the axiom NUMONES, which states the existence of a "counting array" Y for any string X : the ith row of Y contains only the number of 1 bits upto (excluding) bit i of X. First, we introduce the notion of "strong DB1 -definability" for relations in a theory, and use the recursive properties of TC0 relations (rather than functions) to show that TC0 relations are strongly DB1 -definable, and TC0 functions are SB1 -definable in VTC0. Then, we generalize the Witnessing Theorem for V0 [12], and obtain the witnessing theorem for VTC0 from this general result: exist;SB0+ SB1 theorems of VTC0 can be witnessed by TC0 functions (here, SB0+S B1 formulas are those obtained from SB1 formulas using and;, or; and bounded number quantifications). Finally, we show that VTC0 is RSUV isomorphic to the first-order theory Db1 -CR, which has been claimed the "minimal" theory for TC0 [20]. This isomorphism shows that VTC0 admits the SB0+D B1 comprehension rule. Hence, in VTC0, strong DB1 -definability and the usual DB1 -definability coincide. It also follows that Db1 - CR = Db1 - CRi, for some i. This answers affirmatively an open question from [20].
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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 | 0.001 | 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 | 0.001 | 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