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June 13, 20262 citationsOpen Access

No Stationary Entropy-Production Attractor in Frozen de Sitter Wright–Fisher Coarsening: A Null Result Closing the σ→μD Route

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ACArturo Cerezo

Key Points

  • To test whether the stationary entropy-production rate can fix the disformal coupling scale μ_D in the context of radial coherential dynamics.
  • Conducted a pre-registered null test (KS-B1) on the σ*→μ_D hypothesis.
  • Measured medium entropy using a pathwise T-odd functional with boundary singularity artifact removal.
  • Analyzed data from frozen de Sitter regime with approximately 97% lattice site saturation.
  • Found σ_ss = 0.030 ± 0.152 in lattice units, indicating a lack of positive σ source.
  • Confirmed that a stationary state exists in a frozen equilibrium, but no positive stationary entropy-production attractor could fix μ_D.
  • Closed the route of σ*→μ_D in red, indicating necessary future conditions for reopening.

Abstract

We report a pre-registered null test (KS-B1) of the σ*→μD hypothesis within the Radial Coherential Dynamics (RCD) program: the conjecture that the stationary entropy-production rate of the sealed Allen–Cahn/Wright–Fisher kernel fixes the disformal coupling scale μD — the last remaining route by which that scale could be derived rather than calibrated. We measure the medium entropy production with a pathwise T-odd functional (Stratonovich midpoint), which, unlike Schnakenberg-type estimators, requires no stationary density and therefore evades the failure mode of an earlier attempt. We identify and remove a boundary-singularity artifact: with ~97% of lattice sites saturated, the raw estimator returns σᵣaw ≈ −1. 1e5 driven entirely by the 1/C (1−C) singularity; the active-site estimator collapses this by four orders of magnitude. In the frozen de Sitter regime (≥7 tH, five seeds) we find σₛs = 0. 030 ± 0. 152 in lattice units (2-SEM bound |σₛs| < 0. 33), suppressed by ≈2. 0e3 relative to the active coarsening epoch (σₐct (1 tH) ≈ +657), with an instrumental floor of order 1e−1 compatible with a decreasing O (dt) -like bias. A stationary state does exist in de Sitter — correcting an earlier non-existence claim — but it is an effective frozen equilibrium, not a positive-σ source. Within the sealed kernel and tested backgrounds, no positive stationary entropy-production attractor exists from which μD can be fixed. The σ*→μD route is closed in red; the only reopening requires a field–horizon noise bridge (Gibbons–Hawking-type sourcing), explicitly identified as Obstruction 1 and not derived here. Deposit contents: main preprint (PDF + Markdown source), standalone abstract, reproducibility checklist, figure plan, CITATION. cff, README, and the KS-B1 script chain with preserved console outputs (files. zip). Pre-registered gates, seeds, and parameters are documented in the checklist; verdict-logic corrections and executor autocorrections are recorded in Appendix B of the preprint.

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Cite This Study

Arturo Cerezo (2026) studied this question.

synapsesocial.com/papers/6a2cf688faef96ed7f05848chttps://doi.org/10.5281/zenodo.20635561
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