Generalized causal set d’Alembertians
Bibliographic record
Abstract
We introduce a family of generalized d’Alembertian operators in D-dimensional Minkowski spacetimes $ {\mathbb M} $ D which are manifestly Lorentz-invariant, retarded, and non-local, the extent of the nonlocality being governed by a single parameter ρ. The prototypes of these operators arose in earlier work as averages of matrix operators meant to describe the propagation of a scalar field in a causal set. We generalize the original definitions to produce an infinite family of “Generalized Causet Box (GCB) operators” parametrized by certain coefficients {a, b n }, and we derive the conditions on the latter needed for the usual d’Alembertian to be recovered in the infrared limit. The continuum average of a GCB operator is an integral operator in $ {\mathbb M} $ D , and it is these continuum operators that we mainly study. To that end, we compute their action on plane waves, or equivalently their Fourier transforms g(p) [p being the momentum-vector]. For timelike p, g(p) has an imaginary part whose sign depends on whether p is past or future-directed. For small p, g(p) is necessarily proportional to p · p, but for large p it becomes constant, raising the possibility of a genuinely Lorentzian perturbative regulator for quantum field theory in $ {\mathbb M} $ D . We also address the question of whether or not the evolution defined by the GCB operators is stable, finding evidence that the original 4D causal set d’Alembertian is unstable, while its 2D counterpart is stable.
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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".