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Research . 2025
License: CC BY
Data sources: Datacite
ZENODO
Research . 2025
License: CC BY
Data sources: Datacite
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De-patching the TUCSL–CST bridge Diagnostics, scaling limits, and parameter discipline for the BD/BDG sum-over-causal-sets programm

Authors: Villa, Thomas Emilio;

De-patching the TUCSL–CST bridge Diagnostics, scaling limits, and parameter discipline for the BD/BDG sum-over-causal-sets programm

Abstract

We address critical "patch-susceptible" junctions in the Transactional Unimodular CSL (TUCSL) synthesis with Causal Set Theory (CST) introduced our previous papers. Four potential vulnerabilities are converted into falsifiable diagnostics: (i) the diffusion/semigroup bridge between BD/BDG causal-set dynamics and the TUCSL q-heat kernel is reformulated as explicit convergence criteria with computable error functionals E_diag(s) and spectral dimension flow d^C_s(s); (ii) the Poisson-to-Gaussian passage is proven as Theorem 4.1 via cumulant expansion, with the dimensionless control parameter χ := kV_cell tracking the high-intensity/small-mark scaling limit; (iii) the apparent freedom in event density k and transactional energy E_⋆ is eliminated by operational definitions tying k to the semigroup diagonal and bounding E_⋆ through laboratory CSL constraints; (iv) the sum-over-causal-sets measure is implemented as a microcanonical admissibility prior Ω^TUCSL_N (support restriction) rather than phenomenological weighting, avoiding new continuous couplings. We provide an explicit assumption ledger (A1–A5), a "no-hidden-knobs" parameter accounting (Table 1), and four decisive failure modes (F1–F4) that would falsify the bridge. The correlation cell volume V_cell(s;x) := [K_2s(x,x)]^(-1) emerges as the unique non-geometric operational notion linking TUCSL coarse-graining to causal-set sprinkling density. A roadmap to "hard results" specifies: numerical computation of BDG diagnostics on manifoldlike causal-set ensembles, extraction and comparison of discrete vs continuum V_cell, and propagation of experimental bounds through the Paper XIV closure formula to derive tight E_⋆ intervals.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green