Note 23. Discrete Number Count Quadrupole in Schwarzschild: Agreement with the Continuum Contrast in a Causal Set
Year: 2026
Type: article
Abstract: We present the results of the Number Count Quadrupole (NCQ) session within thetemporal scale invariance hypothesis, aimed at measuring the angular anisotropy of thenumber of events in the causal diamond of a static observer in Schwarzschild spacetime.We report three main results.Result I (Geometric): The continuum calculation establishes the unsubtractedSchwarzschild contrast CSchw(4.5M) = −0.710% ± 0.01% and the contrast after subtractingthe Rindler acceleration background CSchwtidal (4.5M) = −1.11% ± 0.01%. (Hereand below, ± reflects the estimate of numerical integration convergence and does notinclude all systematic interpolation errors). Similarly for 6M: CSchw(6M) = −0.139%,CSchwtidal (6M) = −0.246% ± 0.02%.Result III (Discrete): The discrete realization at Ngen = 2·108 for r0 = 4.5M yieldsa result that is statistically consistent with the continuum unsubtracted contrast CSchwwithin 0.40σ. The measured sector observable is ˆ CSchw = −0.8059% ± 0.2376%. Thisconfirms the compatibility of the discrete measurement with the continuum prediction inthe studied regime. The Rindler subtraction is established in the continuum calculation,but has not yet been reproduced by a separate discrete comparison.Result II (Open): The comparison with the Fermi-Walker (FW) code on a Rindlerbackground remains methodologically open, as the compared calculations use differentoperational constructions. The 0.39 pp gap currently has no unambiguous physical interpretation.Additionally, we report a control run at r0 = 6M. The discrete NCQ yields ˆ CSchw =+0.0043% ± 0.2276%. This result is statistically consistent with both the unsubtracted(−0.139%) and the subtracted (−0.246%) continuum values, but resolves neither of thesesmall signals. The control serves as a statistical consistency check, not a proof of scaling.
Author: Gromov, Alexey
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225616126
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