Reproducibility archive: Ricci-curvature recovery in the Sverdlov–Bombelli nested-interval construction (four-geometry causal-set sprinkling study)

This archive contains the manuscript, supplementary material, complete analysis code, sampler versions, and raw per-replicate simulation output for a preregistered four-geometry test of the Sverdlov–Bombelli nested-interval construction for recovering Ricci curvature from a causal set. The Sverdlov–Bombelli construction (Class. Quantum Grav. 26, 075011, 2009) recovers the Ricci scalar R and the timelike Ricci component R00 from interval volumes measured at a family of nested scales. A companion paper (doi:10.5281/zenodo.22137975) established the bias and noise properties of its auxiliary nested sum in flat spacetime. This work is the curved-space test: whether the construction separates the two curvature components in geometries where they are actually present. Four geometries are sprinkled — radiation and dust FLRW, de Sitter and anti-de Sitter — with acceptance bands frozen in advance. Structure. Maximally symmetric backgrounds satisfy R00 = -R/4 and therefore explore only one direction in curvature-parameter space; the de Sitter and anti-de Sitter arms measure only that combination, which is detected against zero at 61σ and 64σ and reverses sign correctly. Independent validation of the two component responses falls to the FLRW arms. The 2x2 inversion is algebraically invertible but strongly ill-conditioned throughout the tested range: the design rows are 4.4 degrees apart in the production dust arm, closing to 2.0 degrees as the cutoff rises, with corr(R,R00) = +0.997. Registered outcome. All six registered marginal and sign-gate criteria pass, and a dedicated unbanded R arm returns R T^2 = 0.13235 +/- 0.02734 against truth 0.13038. The preregistered global closure nonetheless fails, with lambda_00 lying 3.39σ from unity against a registered 3σ limit. Diagnosis. The miss is a finite-size model discrepancy: the registered design is first order in curvature while the observable is the unexpanded finite-diamond continuum volume, a 4.4% difference invisible in marginal bands but decisive along the covariance's stiff direction. An oracle intervention using converged continuum volumes returns lambda_R = 1.0000 +/- 0.0238 and lambda_00 = 1.0020 +/- 0.0091. A first-order sampler defect found and corrected during the programme is also documented here, with both the historical and corrected sampler versions retained. Contents manuscript/ — the paper and supplementary material (LaTeX source and PDF), the four figures, and the Figure 4 eigenvector loadings. scripts/ — the frozen preregistration, both design modules, the arm-scoring and global-fit analyses, the dedicated-R ratio analysis, the oracle truncation-corrected fit, the proper-time sensitivity study, the figure generator, and the manifest tooling. scripts2/ — the sampler chain (historical and corrected), the sampler unit suite, and the inverse-CDF convergence suite with its machine-readable results. shards/ — raw per-replicate output: the four registered arms, the flat-gate ensemble, and the 7.7 million replicate dedicated-R arm. MANIFEST.json — SHA-256 hash, size, role and provenance for every artifact, plus the command reproducing each table and figure. Notes on reproducibility Every artifact is hashed in MANIFEST.json, and verify_manifest.py re-checks every hash and exits nonzero on any mismatch. Each shard additionally carries its own recorded provenance — geometry, curvature parameter, seed, replicate count, density and code version — read from the file itself rather than inferred from its filename. The dedicated-R shard is identified by that recorded content and hash-checked against the file the published Section 4.2 numbers were computed from, so a renamed or substituted shard cannot silently enter the archive; this guard caught exactly that error during assembly. Both the defective and corrected sampler versions are retained, with distinct code-version strings, and the analysis refuses to pool shards across them. The convergence suite regenerates the sampler-defect evidence from a fresh seed and enforces, rather than assumes, that the two sampler versions consume identical random streams. Requires Python 3 with NumPy, SciPy and Matplotlib. CuPy is optional and used only for GPU acceleration of the sprinklers, which fall back to NumPy.