Fluctuation correction for the critical transition of symmetric homopolymer blends
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Bibliographic record
Abstract
Monte Carlo simulations are performed on structurally symmetric binary homopolymer blends over a wide range of invariant polymerization indices, N¯. A finite-size scaling analysis reveals that certain critical exponents deviate from the expected 3D-Ising values as N¯ increases. However, the deviations are consistent with previous simulations and can be attributed to the fact that the system crosses over to mean-field behavior when the molecules become too large relative to the size of the simulation box. Nevertheless, the finite-size scaling techniques provide precise predictions for the position of the critical transition. Using a previous calibration of the Flory-Huggins interaction parameter, χ, we confirm that the critical point scales as (χN)c=2+cN¯−1∕2 for large N¯, and more importantly we are able to extract a reliable estimate, c≈1.5, for the universal constant.
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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 | 0.000 | 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) | 0.000 | 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