# Verification report

Manuscript: Sharp Induced-Norm Paving for Symmetric Weighing Matrices
Author: Alper Ferudun, Mercury Software GmbH
Problem reference: AIM-ANALYSIS-0089
Release date: 29 September 2026

The exact theorem is complete for real symmetric zero-diagonal matrices
with entries in {0,+1,-1} and W^2=dI, d>=1. General induced-norm paving
remains unresolved by this work. The original proof acceptance of
9 September 2026 is preserved without modifying its hash-bound artifacts.

## Mathematical checks

- The full norm d^(1/q) follows by interpolation and coordinate witnesses,
  then duality, including p=1 and infinity.
- For a compression B, the unit-entry identity gives ||B||_1<=||B||_2^2.
  Interpolation and symmetry give the exponent 2/q. The zero matrix is
  handled separately. No false scalar-square property of B is assumed.
- Ravichandran--Srivastava, arXiv:1706.03737v2, Theorem 1 and its
  pp. 17--18 proof, are applied to both W/sqrt(d) and its negative.
  The estimate 3 sqrt(2k/r) with k=2 gives the constant 36.
- The fixed-delta partition is common to all p. The sharper fixed-p
  count uses a p-dependent choice of delta; the two claims are separated.
- The conference lower bound uses a largest block, coordinate vectors,
  duality, and unbounded Paley orders 5^a+1. The character calculation is
  included in the paper.
- The proof is theorem-dependent and self-audited, not independently
  reviewed or formally verified. The source's arbitrary-matrix question
  is not closed. Novelty confidence is low: this may be folklore.

## Reproduction and document checks

The unchanged regression script was executed with assertions enabled in
isolated Python 3.9 and 3.13 runtimes. Both passed 15,701 exact integer or
Fraction assertions with zero failures; mathematical output agrees with
the archived reports. Runtime labels naturally differ. These finite tests
do not replace the general proof.

Native LaTeX compilation succeeded. The four-page exported PDF has no
LaTeX warnings, overfull or underfull boxes, missing glyphs, or unresolved
references. All four rendered pages were visually inspected. Only the
author name is at the top; affiliation and contacts are in a footnote,
and the AI-assistance statement is ordinary prose.

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