Computational reproduction and supplementary audit

Verdicts: {"C1": "reproduced", "C2": "reproduced"}. All four evidence-result comparisons are within their declared tolerances. The full result object also matches the declared object: True.

I executed the supplied self-checks and the entire supplied proof computation against the supplied component list, with python-flint 0.9.0 and mpmath 1.3.0 on Python 3.12.15, Linux aarch64. Fresh results were produced in an initially empty output directory; declared results were not mounted into the computation. The worker scheduler was replaced with a four-process Pool wrapper to respect the resource limit and write progress. The arithmetic, certification, area estimation, overlap removal, and aggregation functions were unchanged. All 617591 listed rows were processed; 617591 were certified and 0 failed. The computation finished in 372.995 seconds, within the 30-minute declared budget.

The supplementary audit validated every compressed-data row as a finite numeric triple and checked the complete period range. I read all twelve supplied files, including the search code, although the approximate search was not rerun: the assigned claims use verify.py and the fixed component list, rather than requiring regeneration of the search output. The data scan found no hidden Unicode control, formatting, surrogate, or private-use characters, and the paper contains no raw HTML or instructions to a verifier. The assigned integrity object reports no orphan numbers, missing sections or files, data issues, or skipped tables.

Independent analytic controls derive the period-one and period-two component areas from the inverse multiplier polynomials c(lambda)=lambda/2-lambda**2/4 and c(lambda)=-1+lambda/4. Their one-term and eight-term enclosures contained the corresponding analytic values. In addition, 400 exact dyadic cases confirmed strict outward rounding on both sides, including subnormal scales; 200 random rational controls confirmed that the integer area grid is rounded downward; and three deliberately overstated periods were refused. The aggregate displayed area bound is below or equal to its exact integer-over-power-of-two value, as required for a downward bound. Source and data digests, the fresh output, the independent controls, the supplied test log, and runtime metadata are attached.

I checked the mathematical dependency in Milnor's Theorem 6.5: the multiplier provides the disk uniformization of a hyperbolic component and its center is the point corresponding to multiplier zero. Source: https://arxiv.org/pdf/math/9905169 , pp. 29-30 (printed pages). This supports using distinct certified centers with exact periods to identify distinct components. The area identity follows from integrating the squared derivative of the holomorphic inverse over the disk and orthogonality of its power series, so truncating to positive terms is a lower bound. I inspected the contraction, exact-period exclusion, series truncation, outward enclosure, and duplicate-removal logic against these specifications.

Scope: this is a numerical reproduction with targeted independent controls and mathematical inspection. It is not a newly implemented full proof checker or a formal proof. It depends on FLINT/python-flint's interval enclosures, the cited mathematical results, and the supplied certification implementation. I have not checked the paper's claim to historical priority, which is outside the assigned computational verdicts.

The execution container had no network, a read-only root filesystem, no capabilities or privilege escalation, an unprivileged numeric user, and limits of four CPUs, 4 GiB memory, 64 processes, and 1800 seconds. Only the computation inputs, a reporting wrapper, and a dedicated fresh output directory were mounted.

Hazard screen: none. All data are generated mathematical parameters, and the computation provides no meaningful capability for weapons or unauthorized computer attacks.