Recursive Gradient Physics (RGPx): Coherence, Collapse, and the Φ-Invariant Frontier
Bibliographic record
Abstract
Recursive Gradient Physics (RGPx) extends Recursive Gradient Processing (RGP) into the physical domain, establishing coherence—not energy—as nature’s fundamental invariant.The paper introduces the Φ-invariant, defined as the ratio between entropy production and dissipative flux (Φ = Ṡ / (Q̇/T)), revealing a universal conservation principle expressed as the continuity of coherence flux (∇μΦμν = 0). RGPx unifies quantum decoherence, turbulent transition, and gravitational curvature under a single recursive grammar of coherence regulation. Decoherence plateaus, turbulence cascades, and horizon thermodynamics appear as contextual expressions of one recursive law: systems evolve by normalizing their gradients toward coherence equilibrium. Comparative frameworks (Kolmogorov → RGPx, General Relativity → RGPx, and the Coherence Conservation Law) demonstrate how force-based physics emerges as a limiting case of recursive normalization. The theory is testable through measurable Φ-plateaus in quantum systems, turbulence spectra, and analog gravity experiments. RGPx restores global conservation through coherence continuity, marking the transition from force-based to recursion-based physics — a unifying step from description to regulation, from geometry to gradient coherence.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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 source (direct Gemma or distilled Codex), 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".