Note 23. Discrete Number Count Quadrupole in Schwarzschild: Agreement with the Continuum Contrast in a Causal Set

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.