What question did this study set out to answer?

The aim is to verify the new universal invariant in gravitational wave dispersion and its implications in causal dynamical triangulations.

June 27, 2026Open Access

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The Causal Spine of Discrete Spacetime: Gravitational Wave Dispersion and LISA Falsifiability in Causal Dynamical Triangulations (GRU v2.3)

Key Points

The aim is to verify the new universal invariant in gravitational wave dispersion and its implications in causal dynamical triangulations.
Analyzed gravitational wave injection experiment using GRU causal mesh with N=20 shells and 2560 nodes.
Conducted several tests across 5 independent seeds to verify the universal invariant εA and its scaling law.
Corrected previous CMB quadrupole calculation and introduced new scripts and results for enhanced analysis.
Confirmed εA = 4.1816% ± 0.0006% as a universal invariant with a scaling law εA ∝ 1/√N at slope -0.500.
CMB bug corrections improved Dℓ to 6.34 µK², indicating a better match with Planck data (+0.67σ from 5.77±0.85 µK²).
Fisher analysis updates showed a σn improvement to 0.0027 with a single SMBHB event remaining unchanged.

Abstract

Version 2. 3 of GRU (Geometría Radial Unitaria). New central results: εA = 4. 1816% ± 0. 0006% — universal invariant, verified across 5 independent seeds and scaling law εA ∝ 1/√N confirmed with slope = −0. 500 exact. CMB quadrupole bug corrected. What's new in v2. 3: εA = 4. 1816% ± 0. 0006% — Universal Invariant: Measured by gravitational wave injection experiment on GRU causal mesh (N=20 shells, 2560 nodes). CV = 0. 015% across 5 seeds. Zero frequency dependence → purely geometric effect. Scaling law εA ∝ 1/√N verified: slope log-log = −0. 500 exact (N=10→5. 91%, N=20→4. 18%, N=50→2. 65%, N=100→1. 87%, N=200→1. 32%). Confirms analytic Mewes formula. CMB bug corrected: v2. 2 used spurious denominator 1+ (κ/2. 5) ² with no physical derivation, giving Dℓ=3. 78 µK² (34% tension). v2. 3 canonical formula R2 (κ) = (1−e−√6·κ/2) ² gives Dℓ=6. 34 µK² (+0. 67σ from Planck 5. 77±0. 85 µK²) ✅ Fisher updated: σn=0. 0027 (1. 13× improvement), N=1 SMBHB event for 5σ unchanged. 12 new files in GRUᵥ2₃ₛcripts. zip: 3 scripts (MESHBUILDER, WAVEINJECTOR, EPSILONA) + 9 results. 3 new references: Ambjørn & Loll 2026 (arXiv: 2604. 05641), Gong et al. 2023 (PRD 107, 124015), Wang et al. 2025 (PRD 111, 084064). v2. 2 results confirmed: λcorr=2. 14±0. 79 (21/32 CDT in LISA window), Afinal=1. 46×10−16 ✅, nGRU=0. 0564, factiva=1. 0, ηint=0. 169±0. 038. Concept DOI (always latest): 10. 5281/zenodo. 20352929

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The Causal Spine of Discrete Spacetime: Gravitational Wave Dispersion and LISA Falsifiability in Causal Dynamical Triangulations (GRU v2.3)

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Abstract

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