What does this research mean for the field?

Partition function weights in resonant celestial holography are governed by a modular-covariant Gaussian distribution, which operates distinctly from the golden-ratio simplicial weights in the Causal Dynamical Triangulations path integral. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research aims to refine partition function weights in celestial holography to improve theoretical accuracy.

May 19, 2026Open Access

Resonant Celestial Holography

Key Points

This research aims to refine partition function weights in celestial holography to improve theoretical accuracy.
Updated per-mode weights using a modular-covariant Gaussian approach.
Corrected existing figures and mathematical representations based on new weight values.
Clarified references and citations related to the underlying theories.
New Gaussian weight w_n demonstrated improved consistency with theoretical models, C ≈ 0.500.
Updated heights of towers now based on Gaussian weights, enhancing clarity in the graphical data.
Clarified S-invariance breaking quantified with |w₀ − 1/9| ≈ 0.39.

Abstract

Changes in v4 (May 2026) Partition function weights corrected: Per-mode weights updated from the superseded phenomenological form wₙ = φ^−λn/𝒩 to the modular-covariant Gaussian wₙ = C·exp (−πn²/9), C ≈ 0. 500, consistent with the unified parameter set in Paper 3 (doi: 10. 5281/zenodo. 20248650). The golden-ratio simplicial weight φ^−N (𝒯) in the CDT path integral is unaffected — it is a distinct quantity. Figure 1B caption corrected: Δλ = 1. 729 → 1. 7287 (exact value 2π/ (9κCE) ) Figure 3B caption updated: Tower heights now stated in terms of Gaussian weights (w₀ ≈ 0. 500, w₃ ≈ 0. 022, w₆ ≈ 10⁻⁹) ; panel schematic was produced under the superseded weight and will be updated in a future revision §5. 2 enhancement factor corrected: ηdiff·φ^−3 formula replaced by correct Gaussian ratio w₃/w₀ = e^−π ≈ 0. 043 Piano mathematics section updated: 3-6-9 node hierarchy restated using Gaussian weight values; residual ~15% amplitude claim removed Modular covariance paragraph updated: Orphaned reference to old phenomenological weight removed; Gaussian weight covariance stated with S-invariance breaking quantified (|w₀ − 1/9| ≈ 0. 39) CDT and BMS defined on first body use Strominger (2014) cited at first IR-triangle invocation M-Theory companion citation updated to v9e with full subtitle Paper 3 companion link updated to v3 DOI (10. 5281/zenodo. 20248650) Paper 1 cross-citation added: Einstein Equations from Prismatic Curvature (doi: 10. 5281/zenodo. 20146627) Typography: microtype expansion=false; emergencystretch=2em

Resonant Celestial Holography

Key Points

Abstract

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