Ti and Spi, Carrollian extended boundaries at timelike and spatial infinity
Bibliographic record
Abstract
Abstract The goal of this paper is to provide a definition for a notion of extended boundary at time and space-like infinity which, following Figueroa-O’Farril–Have–Prohazka–Salzer, we refer to as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>Ti</mml:mtext> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>Spi</mml:mtext> </mml:mrow> </mml:math> . This definition applies to asymptotically flat spacetime in the sense of Ashtekar–Romano and we wish to demonstrate, by example, its pertinence in a number of situations. The definition is invariant, is constructed solely from the asymptotic data of the metric and is such that automorphisms of the extended boundaries are canonically identified with asymptotic symmetries. Furthermore, scattering data for massive fields are realised as functions on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>Ti</mml:mtext> </mml:mrow> </mml:math> and a geometric identification of cuts of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>Ti</mml:mtext> </mml:mrow> </mml:math> with points of Minkowski then produces an integral formula of Kirchhoff type. Finally, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>Ti</mml:mtext> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>Spi</mml:mtext> </mml:mrow> </mml:math> are both naturally equipped with (strong) Carrollian geometries which, under mild assumptions, enable to reduce the symmetry group down to the BMS group, or to Poincaré in the flat case. In particular, Strominger’s matching conditions are naturally realised by restricting to Carrollian geometries compatible with a discrete symmetry of Spi.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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".