The metric from energy-momentum non-conservation: Generalizing Noether and completing spectral geometry
Bibliographic record
Abstract
Abstract The conventional picture is that of a dichotomy of (a) a spacetime that hosts (b) matter fields. We show that this picture can emerge from an underlying reality in which all degrees of freedom are of the same kind: abstract correlators, G (n) Regarding the G (n) , we merely assume that they are operators on n tensor factors of a Hilbert space. We say that a spacetime and matter emerges from the G(n) if the G(n) can be represented as the n-point correlation functions of a QFT on a curved spacetime. Our main finding here is that the locality inherent in interactions allows the identification of position bases for the basis-independent abstract correlators: position bases are bases in which the G(n) for n > 2 are singular at coincidence of their arguments. If such bases exist, we can write the correlators G(n) for n ≥ 2 in a coordinate system and we can then use the prior result that the metric, gμν(x), can be derived from the 2-point function G(2)(x, y). This implies a generalization of Noether’s theorem: the specific pattern of energy-momentum non-conservation that is encoded in the interaction vertices G(n) for n > 2 as measured in the eigenbasis of G(2) (as in an S-matrix), directly determines the spacetime metric g μν(x) It also completes spectral geometry, in the sense that the metric can be derived from the ‘sound’ (the spectrum of G(2)) if we add knowledge of the ’anharmonicities’ (G(n), n > 2) of quantum fluctuations. At sufficiently high energies, such as the Planck scale, the abstract G(n) for n > 2 may turn out not to be singular at coincidence. In such a regime, the abstract correlators G(n) are no longer representable as QFT correlation functions on a curved spacetime, transcending the picture of a spacetime stage hosting matter actors. Since abstract correlators are the foundation of information theory, this points towards a fundamentally information-theoretic description of nature.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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 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".