A `Numbers' Approach to Astronomical Correlations I: Introduction and Application to galaxy Scaling Relations
Bibliographic record
Abstract
We propose a new systematic method of studying correlations between parameters that describe an astronomical (or any) physical system. We recall that behind Dimensionless scaling laws in complex, self-interacting physical objects lies a rigorous theorem of Dimensional analysis, known widely as the Buckingham theorem. Once a {\it catalogue} of properties and forces that define an object or physical system is established, the theorem allows one to select a complete set of Dimensionless quantities or {\it Numbers} on which structure must depend. The internal structure takes the form of a functionally defined manifold in the space of these Numbers. Simple and familiar examples are discussed by way of introduction. Correlations in properties of astronomical objects can be sought either through the constancy of these Numbers or between pairs of the Numbers. In either case, within errors, the functional dependences take on an absolute numerical character. As our principal application, we study a well defined sample of galaxies in order to reveal the implied Tully Fisher and Baryonic Tully Fisher relations. We find that $L\,\propto\,v_{rot}^4$ for the former and $M_b\,\propto\,v_{rot}^3$ for the latter, suggesting that these relations may have different causal origins.
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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 | 0.000 | 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 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".