Code, protocols and certificates for: Graph-separator limits on third-order fluctuation information in partially observed stochastic networks

This record contains the code, protocols, parameter sets, numerical outputs and exact rank certificates supporting the preprint Graph-separator limits on third-order fluctuation information in partially observed stochastic networks (H. Karimov and R. Z. Alekberli, preprint DOI: 10.5281/zenodo.23044203). The study asks when joint third-order fluctuations in a stochastic gradient network carry information about the nonlinear coefficients that node-level statistics do not, under full and partial observation. No experimental, observational or third-party data are used; all data are generated from the model defined in the preprint. Contents Protocols frozen before computation, with SHA-256 hashes (one-dimensional quadrature protocol v1.0/v1.1; population-level protocol v0.3; superseded drafts v0.1–v0.2). Population-level study (1800 partially observed instances): generation script, stored input parameters (exact IEEE-double representation), raw outputs and run information. Post hoc audit of the population results, including documentation of a rank-rule error in the original summary and its correction. Exact certificates: rational-arithmetic and high-precision checks, local-separator certificates, and modular-arithmetic generic-rank certificates for every instance. Scripts for the examples in the preprint (exact rational witness, K₂,₂ case, 18-node counterexample, independent-hidden-set rank checks) and for the symbolic one-dimensional coefficients. One-dimensional quadrature check (verdict file only; script and outputs were executed in a separate environment). Exploratory Gaussian Monte Carlo control (not pre-registered). Source data and script for Fig. 1. Reproducibility. README.md lists the pre-registration status of each protocol, the execution order and which file supports which part of the preprint. ENVIRONMENT.txt records software versions. MANIFEST.sha256 gives the SHA-256 hash of every file. All scripts run unchanged from the top-level directory. Post hoc scripts were re-executed from the stored inputs before deposit, and their outputs were reproduced bit-for-bit.