companion code for The singular fluctuation is a tensor: an equation of state and the field germ of a singular neuromanifold

# The singular fluctuation is a tensor: replication package Author: Vincent Looten (ORCID 0000-0002-9897-1539).License: CC BY 4.0 (see LICENSE). DOI: to be assigned on deposit. This package contains the manuscript, its Supplementary Material, and self-contained scriptsthat regenerate every reported number and figure. It is organised so a reviewer can check anyspecific claim quickly. ## Contents fluctuation_tensor_germ.pdf the article fluctuation_tensor_germ_supp.pdf the Supplementary Material reproduce_all.sh one command to regenerate the main numbers and figures LICENSE CC BY 4.0 code/ verification and figure scripts (+ requirements.txt, README_scripts.md) ## Quick reproduction bash reproduce_all.sh This installs the pinned dependencies (numpy, scipy, mpmath, matplotlib) and runs the shortverifications and the two figures. Each script is deterministic given its fixed seed. The twolonger runs (the A4 n-scaling and the panel-(g) scale experiment) are optional and printed at theend of the script; the panel-(g) experiment additionally needs PyTorch and benefits from a GPU. ## Which script checks which claim Claim / object Section Script ------------------------------------------------ ----------- ------------------------------------- tensor equals the gap, scalar nu does not 7(b), S7 code/verif_A5_scaling_deterministic.py (exact quadrature, no Monte Carlo) closed-form density of states; (lambda,m) S15 code/verif_audit_response.py recovery; temperature-scan bias structural-closure reduction on a second, S11 code/verif_A9_second_base.py non-exponential base fluctuation tensor on a trained singular 7(f), S16 code/verif_A4_real_network.py network under covariate shift (panel f) finite-n scaling of the tensor remainder S16 code/verif_A4_scaling.py scale experiment, ~5.4e5-parameter network 7(g), S16 code/verif_H2_scale.py (panel g) Figure 1 (angular fluctuation; gap under - code/fig_tensor_vs_watanabe.py anisotropic test) Figure 2 (coordinate-free estimator) - code/fig_covariate_shift.py A per-script manifest with dependencies, run commands and expected runtimes is incode/README_scripts.md. ## Recompiling the manuscript The LaTeX uses the Elsevier CAS class (cas-sc.cls, provided by TeX Live texlive-publishers). Fromlatex/: pdflatex manuscript && bibtex manuscript && pdflatex manuscript && pdflatex manuscript The same four commands with "supplementary" rebuild the Supplementary Material. ## Notes for reviewers - Every number in the paper is regenerable by a deposited script; there are no hand-entered values.- For singular targets the package prefers exact deterministic computation (Gauss-Hermite or high-precision mpmath quadrature) over Monte Carlo; Monte Carlo is reserved for quantities that are irreducibly stochastic and is always seeded. Scripts that use posterior sampling print a mixing diagnostic.- The panel-(f) reference run uses five seeds; the panel-(g) run uses six. Increasing the seed count tightens the reported intervals without changing the conclusions. ## Citation Looten, V. "The singular fluctuation is a tensor: an equation of state and the field germ of asingular neuromanifold." Zenodo (DOI to be assigned).