Proof of the GM‐GR parity theorem for the two-body problem
Bibliographic record
Abstract
One loosely defines Mechanics as a physical theory that rests on the concepts of mass and force and a law of inertia. In contrast, one loosely defines General Relativity as a physical theory that describes how mass and energy curve spacetime, causing objects to move along the straightest possible paths within that curved geometry. For a long time, scientists viewed Mechanics and General Relativity as fundamentally irreconcilable theories, with neither being a mere modification of the other, but rather grounded in distinct and incompatible physical principles. This theorem reshapes that understanding by proving that a modified Mechanics, called General Mechanics, fully aligns with General Relativity in the two-body problem. The trajectories in both theories are the same, and it follows that both adopt the same physical principles. NOTE FROM THE EDITOR-IN-CHIEF: In a blinded assessment, I asked five scientists to verify the mathematics of the parity theorem presented in this article before the article would undergo a review. All of them verified the mathematics. I took this additional step because of the theorem’s potentially significant impact on the fields of Mechanics and Relativity.
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.
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 | 0.003 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.007 |
| Insufficient payload (model declined to judge) | 0.025 | 0.004 |
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".