Reproducibility package: Rigorous energy-condition obstructions in irrotational warp geometries

Abstract

Complete computational package behind the manuscript Rigorous energy-condition obstructions in irrotational warp geometries and reduction to a scalar inequality (submitted to Classical and Quantum Gravity). It contains every script that produced a number quoted in the paper, the console output of each one exactly as it was run, and the six figures. The setting is the irrotational class of warp geometries: unit lapse, flat spatial metric, and a shift that is the gradient of a potential, so that the extrinsic curvature is the Hessian of that potential. In this class the stress tensor reduces exactly — the quadratic terms cancel — and the question of whether the null energy condition can be satisfied collapses onto a single scalar inequality on the potential, Ω[φ] = sup ∇²|∇φ|² / (4 sup det Hess φ) ≥ 1, which the paper states as a conjecture and supports from several independent directions. The code verifies the algebra, tests the conjecture by free and constrained optimisation and by a Fourier search on the torus, reconstructs a published warp configuration from its shift function and computes its boost threshold, and measures the three-dimensional floor on a translating-bubble family. What is here a 4D Einstein-tensor engine by fourth-order centred finite differences, validated against Minkowski, Schwarzschild in Painlevé–Gullstrand form, de Sitter and Alcubierre; the numerical check of the exact stress-tensor reduction, whose residual falls from 7.40 % to 0.11 % at fourth order, and of the boost relation to eq. (3.21) of the ADM literature, satisfied to 2.6×10−15; searches for the infimum of Ω — a random scan over 2×105 Hessians, a constrained optimisation deliberately driven into the regime the paper declares uncovered, and an independent Fourier search — all of which rise above 1 once the suprema have separately converged; the three-dimensional floor χ3D = 0.2322 at η ≈ 0.63, with its refinement table and a grid drift of 0.02 %. One command python3 run_all.py runs every script in dependence order, writes each one's output to logs/, and then checks the values the manuscript quotes against what the scripts just printed — 24 named assertions with explicit tolerances, reported as a PASS/FAIL table and an exit code. A package that merely contains the code proves nothing; the question a referee asks is whether the manuscript's numbers come out of it, and that question should have a one-command answer. Expected result on the reference environment: 24 passed, 0 failed, 0 not found. Total runtime is about forty minutes on one core. Reference environment: Python 3.11.15, numpy 2.4.4, scipy 1.17.1, matplotlib 3.10.9, Linux x86_64. Every stochastic search fixes its own generator, so repeated runs give identical numbers. No data files to download and no compilation step. Three traps Section 7 of the paper lists the methodological errors made and corrected during this work. Three are encoded as active checks in the code, because they are the ones a reader is most likely to walk into: a bubble profile written with r = |x| has a conical singularity at the origin and leaves the function class, producing an apparent counterexample Ω = 0.44 that the Bochner identity detects as a membership test rather than an algebraic one; an optimiser allowed to leave the positive-definite cone reports Ω = 0.058, which is a floating-point overflow and not a counterexample; and a finite-difference step chosen too small manufactures a spurious Ω = 1.0001, because roundoff in a second derivative enters as ε/h². The README.md in the archive documents each one and where it is guarded. Declaration A large-language-model assistant (Claude, Anthropic) was used in developing these scripts, at the author's direction. The author inspected, questioned and accepted each result and is answerable for all of them.