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
AbstractThis work explores the geometric and symbolic transition from Pi (π) to Phi (Φ) as a dynamic continuum rather than separate mathematical constants. Beginning with the circle as a representation of perfect symmetry, we show how projecting uniform circular motion into time produces the sine wave — the Pi domain. By modulating the sine wave’s amplitude with a golden-ratio envelope, the system shifts from uniform oscillation to self-similar growth, revealing Phi as an emergent property of Pi. Wrapping the modulated wave into a three-dimensional form yields an angled tube, symbolizing the standing wave of the self evolving from closed recursion to directional drift. This synthesis integrates mathematical derivation, geometric visualization, and symbolic interpretation, offering a framework in which Pi represents coherence, Phi represents becoming, and the bridge between them is the process of projection and modulation.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.002 | 0.000 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.059 | 0.006 |
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