Self-referential discs and the light bulb lemma
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We show how self-referential discs in 4-manifolds lead to the construction of pairs of discs with a common geometrically dual sphere which are homotopic rel \partial , concordant and coincide near their boundaries, yet are not properly isotopic. This occurs in manifolds without 2-torsion in their fundamental group, e.g. the boundary connect sum of S^2\times D^2 and S^1\times B^3 , thereby exhibiting phenomena not seen with spheres. On the other hand we show that two such discs are isotopic rel \partial if the manifold is simply connected. We construct in S^2\times D^2\natural S^1\times B^3 a properly embedded 3-ball properly homotopic to a z_0\times B^3 but not properly isotopic to z_0\times B^3 .
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 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 | 0.004 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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