Topological Observability Gap in Precision Cosmology — Reproducibility Tests, Exact Certificates, and Tomographic Benchmarks

Abstract

This archive contains the public computational material supporting the reproducibility of the results reported in The Topological Observability Gap in Precision Cosmology: Stable Expansion Histories, Non-Identifiable Dark-Energy Phase Structure, and Tomographic Closure Criteria. The package includes exact-symbolic and numerical reproduction scripts, public DESI DR2 BAO input data, frozen result files, a standard pytest regression suite, dependency specifications, and documentation describing the governing equations, data provenance, verification strategy, and claim boundaries. The principal reproduced results are: exact rational certification that the cubic DESI DR2 reconstruction of (u(z)=D_H(z)/r_d) satisfies (u'(z)<0) on (0\le z\le2.33) throughout the declared (\Delta\chi^2\le16.25) coefficient ellipsoid; explicit positive dark-energy-density histories realizing topology counts (K=0,1,2,3,4) within (\Delta\chi^2<2) at fixed (\Omega_m=0.313); an independent floating-point reconstruction and held-out (D_V/r_d) prediction; reproduction of the single-ratio topology-resolution thresholds; reproduction of the correlated tomographic-bank benchmark, including[N_T=3.063137195536,\qquad\Delta\chi_T^2=9.382809478675,]together with numerical agreement between the direct covariance and Schur/Woodbury formulations; reproduction of[N_T=5.013450073397]when the mean-redshift calibration scale is improved to (0.001(1+z)). The archive is intended as a standalone reproducibility record. It does not include the main paper PDF and does not contain private research software or unpublished general-purpose solver infrastructure. All public tests can be run with: pytest -q and python code/run_all_tests.py The expected terminal result is: ALL PUBLIC REPRODUCTION TESTS PASS