An Operational Bridge from Central-Regime Responses in Causal Update Cosmology to a 2D Critical Finite-Size Susceptibility Class

This work presents an operational bridge between central-regime responses in Causal Update Cosmology (CUC) and a two-dimensional critical finite-size susceptibility class.

In previous CUC response studies, a structured perturbation profile (P(u)) was found to induce a cumulative central-regime response of the approximate form

[
R_{\mathrm{CUC}}(u;L) \simeq A_{\mathrm{CUC}}(L) CP + B_{\mathrm{CUC}},
]

where (CP) denotes the cumulative form associated with the perturbation profile. That earlier result established the response shape, but it did not yet identify the physical interpretation of the scale-dependent coefficient (A_{\mathrm{CUC}}(L)), or of the associated central-regime front-response observables.

The present study addresses that missing step. It tests whether the audited CUC central-regime front response can be connected to a known statistical-physics response class: the finite-size susceptibility of a two-dimensional critical crossing event. The external comparison model is critical site percolation, where a small structured perturbation of the occupation probability changes the probability of a left-right crossing. The corresponding crossing susceptibility is expected to scale with the inverse two-dimensional percolation correlation-length exponent, (1/\nu = 3/4).

Using regenerated CUC raw front-response data and independent physical/statistical-side crossing-susceptibility simulations, this work finds that the CUC front-quantile response is compatible with a scaling class near (L^{3/4}). On the physical side, critical crossing susceptibility exhibits robust small-amplitude scaling consistent with the same (3/4) finite-size susceptibility class. The physical-side result survives profile variation, small-amplitude validation, seed-split robustness checks, leave-one-(L) prediction, and (L)-range stability tests.

The spatial response shape on the physical side also remains strongly compatible with the earlier cumulative (C[P]) response form. Thus, the present result does not replace the previous CUC response-function result; rather, it extends it from a shape-level law to a coefficient-scaling and response-class bridge.

The main conclusion is deliberately restricted: the audited CUC central-regime front-quantile response admits an operational and numerical bridge to a two-dimensional critical finite-size susceptibility class near exponent (3/4). This work does not claim SI-unit calibration, a direct derivation of gravity, quantum mechanics, or electromagnetism, nor an identity between the internal mechanisms of CUC and percolation. Instead, it establishes a reproducible intermediate bridge from CUC central-regime response behavior to a known class of critical statistical physics.

The accompanying data packages include the regenerated CUC-side and physical/statistical-side all-in-one handoff outputs, figures, scripts, tables, and supplementary negative-result documentation.

Acknowledgement

This work was conducted with substantial assistance from artificial intelligence tools, particularly ChatGPT (OpenAI), which supported code generation, data processing workflows, figure generation, and manuscript drafting. The author directed the research design, conceptual framework, and interpretation of results.