Statics–dynamics exchangeability in a quenched Gaussian lattice field: an exchange-rate theorem, an aging-rate selection rule, and a residue tower
Abstract
We study a Gaussian field on a two-dimensional lattice whose drift is coupled to its equilibrium covariance through a self-consistent mobility law, and ask whether the static fixed point predicts the nonlinear response to a quench with zero fitted parameters. Two independent statics-to-dynamics channels are established. First, an exchange-rate theorem: the Riccati identity dW/db=2W2dW/db=2W2 makes the static curvature 2W∗2=0.826517…2W∗2=0.826517… the unique conversion factor between a static constraint drift and the dynamical fluctuation-dissipation-violation fingerprint; a blind, sealed prediction matches the direct simulation on the frozen 36-cell main region with 100%100% per-cell passage and a 1.06%1.06% weighted residual, while a discriminator scan of trial rates κκ (residuals 100.00%100.00%, 50.51%50.51%, 1.01%1.01%, 97.97%97.97% at κ=0,1/2,1,2κ=0,1/2,1,2) excludes circularity. Second, an aging-rate selection rule: the measured decay rate is a sensitivity-weighted mixture of lattice modes, not a single gap; the parameter-free 16-shell sum gives Yshell=2.6274Yshell=2.6274 against the measured 2.69382.6938 (2.5%2.5%). The first-order residual is certified as the second layer of a geometric residue tower with a pole at δb=1/∣2W∗∣≈0.778δb=1/∣2W∗∣≈0.778; a zero-fit second-order theorem fixes the layer coefficient α=0.931α=0.931, whose leading seat is the self-referential normalization of the observable, improving table agreement from 1%1% to ∼0.04%∼0.04%. Three machine-identified horizons—the tower pole δb≈0.778δb≈0.778, a resolution horizon tw∗∈(3,4.5]tw∗∈(3,4.5] set by the ∼10−7∼10−7 differencing floor, and the secular bound dν⋅t≤0.3dν⋅t≤0.3—delimit the validity of every claim. All results are model-internal theorems and machine-verifiable certificates; no claim about real materials is made.
ORCID: 0009-0007-1999-0293 Email: [email protected]/[email protected]
phone:+86 18278275520(china)
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BibTeX
@misc{guan2026staticsdynamics,
title = {{Statics–dynamics exchangeability in a quenched Gaussian lattice field: an exchange-rate theorem, an aging-rate selection rule, and a residue tower}},
author = {Yunlong Guan},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23592381},
url = {https://zenodo.org/records/23592381},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Statics–dynamics exchangeability in a quenched Gaussian lattice field: an exchange-rate theorem, an aging-rate selection rule, and a residue tower
AU - Yunlong Guan
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23592381
UR - https://zenodo.org/records/23592381
AB - We study a Gaussian field on a two-dimensional lattice whose drift is coupled to its equilibrium covariance through a self-consistent mobility law, and ask whether the static fixed point predicts the nonlinear response to a quench with zero fitted parameters. Two independent statics-to-dynamics channels are established. First, an exchange-rate theorem: the Riccati identity dW/db=2W2dW/db=2W2 makes the static curvature 2W∗2=0.826517…2W∗2=0.826517… the unique conversion factor between a static constraint drift and the dynamical fluctuation-dissipation-violation fingerprint; a blind, sealed prediction matches the direct simulation on the frozen 36-cell main region with 100%100% per-cell passage and a 1.06%1.06% weighted residual, while a discriminator scan of trial rates κκ (residuals 100.00%100.00%, 50.51%50.51%, 1.01%1.01%, 97.97%97.97% at κ=0,1/2,1,2κ=0,1/2,1,2) excludes circularity. Second, an aging-rate selection rule: the measured decay rate is a sensitivity-weighted mixture of lattice modes, not a single gap; the parameter-free 16-shell sum gives Yshell=2.6274Yshell=2.6274 against the measured 2.69382.6938 (2.5%2.5%). The first-order residual is certified as the second layer of a geometric residue tower with a pole at δb=1/∣2W∗∣≈0.778δb=1/∣2W∗∣≈0.778; a zero-fit second-order theorem fixes the layer coefficient α=0.931α=0.931, whose leading seat is the self-referential normalization of the observable, improving table agreement from 1%1% to ∼0.04%∼0.04%. Three machine-identified horizons—the tower pole δb≈0.778δb≈0.778, a resolution horizon tw∗∈(3,4.5]tw∗∈(3,4.5] set by the ∼10−7∼10−7 differencing floor, and the secular bound dν⋅t≤0.3dν⋅t≤0.3—delimit the validity of every claim. All results are model-internal theorems and machine-verifiable certificates; no claim about real materials is made. ORCID: 0009-0007-1999-0293 Email: [email protected]/[email protected] phone:+86 18278275520(china)
ER -