Bibliographic record
Abstract
Corollary 3.3.Let C be a counital coalgebra and 0 -→ N -→ M -→ M/N -→ 0 be a short exact sequence of C-bicomodules.Then we have a short exact sequence of differential graded k-modules of the formProof.Since CB bar * (C) consists of co-projective C e -comodules we get a short exact sequence of the formThe result follows after Theorem 3.2.Remark 3.4.One can give a direct proof of Corollary 3.3 without appealing to • C e CB bar * (C).Indeed, for a direct proof one need not C to be counital.Definition 3.5.Let X be a left B-comodule and M be a C-bicomodule.Define X ⋊M as the C e -comodule * (C, B, X) -→ CM c * (C/K, B, X) Proof.Theorem 3.10, Theorem 4.4 and Theorem 4.6 tell us we have a homotopy cofibration sequence of the form k ⊗1) This is equivalent to saying Hopf Hochschild homology has excision.Since K, C and C/K are all Hcounital and B-projective, the differential graded k-complexes k ⊗ B (X ⊗ CB * (K)), k ⊗ B (X ⊗ CB * (C)) and k ⊗ B (X ⊗ CB * (C/K)) are all acyclic because X has finite projective dimension following Lemma 4.3.Therefore we have another homotopy cofibration sequence k ⊗ B (X ⊗ CB * (K)) -→ k ⊗ B (X
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How this classification was reachedexpand
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 | 0.001 |
| 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) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".