# Verification report

## Mathematical status

The bounded-operator version of the AIM problem is completely resolved by
the manuscript. The proof was independently reconstructed from four
components:

1. diagonal unitary conjugation and the sharp endpoint obstruction;
2. an explicit Hilbert--Schmidt comparison with a weighted Carleman kernel;
3. scalar Wiener--Hopf Fredholm theory with a directly recomputed Fourier
   symbol;
4. Hill's complete latent-eigenvector classification and independently
   recomputed coefficient asymptotics.

The zero spectral point is handled separately by a moment argument, so the
infinite-dimensional zero summand used in the compact comparison is not
silently ignored.

## Executable falsification checks

Run:

`python3 reproducibility/check.py`

The checker verifies:

- `A_alpha^* = A_-alpha` on finite sections;
- the numerical Fourier transform of the Wiener--Hopf kernel;
- the quartic equation of the Fredholm curve;
- Hill's moment eigen-equation for a non-real parameter;
- the weighted membership exponent and nonvanishing leading constant;
- the endpoint p-series obstruction.

Current output:

`PASS: adjoint, Fourier symbol, Fredholm curve, Hill identity, weighted threshold, and endpoint checks`

## Literature and novelty status

Primary and current sources were searched through 2026-09-02. Magnus,
Rosenblum, Hill, Aleman--Montes-Rodriguez--Sarafoleanu,
Montes-Rodriguez--Virtanen, Silbermann, and Jin cover the principal
ingredients or close analogues. No source giving the exact spectrum for the
pair `(m+n+1)^-1` and `(n+1)^alpha` was located.

Novelty confidence is moderate-low: the synthesis appears to answer the AIM
record, but the compact comparison is natural and may occur in older
Wiener--Hopf or projection-method literature under other notation. The paper
therefore makes no absolute priority claim.

## Build and PDF QA

`PASS`: Tectonic 0.17.0 and BibTeX produced a six-page letter-size PDF with
zero LaTeX errors, undefined references/citations, overfull boxes, or
underfull boxes. All six pages were rendered at 144 DPI and directly
inspected; no clipping, margin, formula, bibliography, or legibility defect
was found. `arxiv_source.zip` contains only the English TeX/BibTeX sources and
the reproducibility material. The author approved public release on 2026-09-02 under CC BY 4.0. The manuscript remains unrefereed.

## Public release and license

The author approved public release on 2026-09-02. This paper, its source files, and this verification report are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0): https://creativecommons.org/licenses/by/4.0/