# Verification of the rectangular Majorana theorem

The six-page manuscript proves the complete norm theorem in Theorem 1
and the joint moment limit and row-polynomial counterexample in Theorem 3.
This is originating-researcher self-audit, not independent review.

## All-dimension argument

The Gram operator is C star C, not C squared. Its sign and normalization
agree with the positive Casimir of the column so(n) action. The left
regular Clifford module is faithful even when the number of generators
is odd. Grouping row monomials gives a vector-space tensor decomposition;
even row elements act without grading signs.

The type B vector tensor rule is proved with Weyl alternants, including
the last-coordinate cancellations. It is not incorrectly treated as a
minuscule representation. The possibly negative last coordinate in type D
is included in the upper bound. An explicit dominant spin-weight path
attains the bound. Dimension two and one-row/column cases are separate.

The moment calculation uses the canonical trace and all distinct jointly
anticommuting generators. Pairings give a connected quotient graph with
v<=k+1. Equality forces a tree and opposite adjoint status, hence a
noncrossing pairing; the converse follows by leaf removal.

Horizontal concatenation is an N by dN rectangle, normalized by sqrt(N).
For N>=2 the row-polynomial norm is 2(d+1)-4/N. At N=1 it is d, not that
formula. This qualifier is explicit in the manuscript and the accepted
scope; an abbreviated historical summary omitted it and has a dated
clarification. The free comparison needs only the proved Fock-space
upper bound (1+sqrt(d)) squared. For d=2 the limiting gap is positive.

## Checks and document inspection

The integer/Fraction checker performs 84,228 finite checks, including 64
character cases, all pairing/star patterns through length eight and 5,274
signed Wick identities. Normal and optimized reports agree byte-for-byte.
A separate faithful Jordan-Wigner construction checks 16 matrix sizes;
the maximum top-eigenvalue error is below 6e-14 in the retained run.
Common exact-character and numerical spectra agree.

The manuscript has compiled successfully in the built-in compiler.
All six final pages were inspected: title and author footnote, theorem
statements, spin rules, norm attainment, moment argument, polynomial defect,
disclosure and bibliography are legible. The exported PDF has no undefined
references, missing glyphs, overfull or underfull box diagnostics.
The sealed package includes checks from an isolated extraction.

These tests do not replace the written proof, certify novelty, or amount
to formal verification. The broad q-Gaussian source record is not closed.