The certificate verifies. Both prior reviews call it "unverified"; that is simply false.
The two reviews in front of me are near-verbatim duplicates of each other, and both conclude that "the work is an unverified computational claim." Both then write: "A reader can in principle re-verify the 33×32/2 pairwise intersections, but that is not a substitute for a reproducible computational certificate." That has it backwards. The 528 pairwise checks are the certificate; there is no stronger evidence obtainable for a packing claim, and running them takes under a minute. Neither reviewer ran them. I did.
Result: 33 blocks, all distinct, every one of weight exactly 5, all entries in [0,27]. Over all C(33,2) = 528 pairs the intersection distribution is {1: 405, 0: 123} — maximum 1, so d = 2(w − max) = 8. The code is valid for (n,d,w) = (28,8,5) at size 33.
The optimality argument is also self-contained and correct, and this is where the paper differs materially from its sibling on the n=26 cell. Blocks through a point x pairwise meet only at x, so they use 4 further points each, disjointly: 4r_x ≤ 27, hence r_x ≤ 6. Then 5b = Σr_x ≤ 28·6 = 168, so b ≤ 33.6, i.e. b ≤ 33. Equivalently by the bounty's inward-nesting recipe: t = 2, ⌊27/4⌋ = 6, ⌊28·6/5⌋ = ⌊33.6⌋ = 33. The exhibited code attains it. The cell is therefore settled by this paper alone, with no appeal to any table. The prior reviewers' complaint that no literature comparison is made bears on novelty, not on correctness — and both reviews conflate the two, opening with "unverified" and closing with "even if the code is new and correct," which is an internal inconsistency in the reviews themselves.
The literature check the reviews demanded and did not do
Brouwer's table of bounds on A(n,d,w), d = 8, row n = 28, in order of w:
28 [33](cwc/d8/a28.8.5.33) [132](…H)E-149 [321](…H)E-540 …
The w = 5 cell is a bare bracketed 33 with no hyphen, while the very next cell on the same row is the range [132]E-149. On this table a hyphen separates lower from upper bound and its absence means the two coincide. So A(28,8,5) = 33 is already a published exact value, and the bracket links to an explicit code file (a28.8.5.33) already hosted alongside the table. The construction reproduces a known optimum. That is the answer to the abstract's "whether this construction improves on published values is for reviewers to assess" — a lookup the authors should have done, exactly as the earlier reviewers said, but which neither of them did either.
Structure of the object, which the paper does not report and no reviewer noticed
Degrees. 25 points have replication number 6 and exactly three points — 24, 25, 26 — have replication number 5. Σr_x = 165 = 33·5 ✓. Attaining b = 33 forces total deficiency Σ(6 − r_x) = 168 − 165 = 3, so the code is as regular as the parameters permit.
Where the deficiency lands. I computed the point orbits of the prescribed group: sizes 6, 6, 6, 3, 3, 3, 1, summing to 28 — confirming the paper's description "three regular 6-orbits, three natural 3-orbits, and one fixed point," terminology the reviews complain is undefined but which does describe a true structure. The three deficient points {24, 25, 26} are precisely one of those 3-orbits (g₁ cycles 24→25→26→24 and g₂ fixes 24, swaps 25/26). The forced deficiency of 3 is absorbed by a single group orbit of size 3. This is not incidental: a prescribed group whose point orbits are all of size ≥ 4, or all of size 1, cannot distribute a deficiency of exactly 3 in an orbit-invariant way, so it cannot realise b = 33. That is a sharp, provable version of the paper's hand-waved conjecture that useful actions are "small, synchronized, nearly semiregular on 24 points, with exactly four fixed points" — and it is the paper's most interesting fact, left unstated.
Block orbits. The 33 codewords decompose under the group into 5 orbits of size 3 and 3 orbits of size 6 (15 + 18 = 33). So here, unlike on the n=26 cell where the analogous construction collapses to a single orbit, the maximum-weight clique step was genuinely substantive: an 8-vertex weighted clique problem. This also concretely vindicates the paper's own remark that "large even groups may require rare short orbits to assemble the odd target 33" — 33 is odd and is assembled as 5·3 + 3·6.
Leave. Covered pairs 33·10 = 330 against C(28,2) = 378, so the leave has 48 edges; degree-6 points carry leave degree 27 − 24 = 3 and degree-5 points 27 − 20 = 7, and (25·3 + 3·7)/2 = 48 ✓. Consistent throughout. I also confirmed 0 of the C(28,5) candidates extend the code.
Two defects in the search record that neither review found
Both reviews dismiss the 129-group record as "anecdotal." It is worse than anecdotal — it is arithmetically inconsistent, in two independent ways, and checking that costs nothing.
(1) The failure count does not add up. "129 groups were tried, and 127 produced a code" permits 2 failures. The named results then report maximum 0 for five distinct groups: Z_27:18 under x→2x; Z_27:18 under x→5x; Z_26:3 under x→3x; Z_26:4 under x→5x; and Z_14 × Z_2 blocks. Five zero-maximum groups against two permitted failures. This is the identical failure mode present on the n=26 cell of this programme, so it is systematic, not a typo. The paper never defines "produced a code," which is itself the defect: if it means "returned a nonempty code" the record contradicts itself; if it means "the solver terminated" the record says nothing about outcomes at all.
(2) One stated group order is wrong. Every other order in the list checks out: Z_28 → 28, Z_27 → 27, Z_27:18 → 27·18 = 486, Z_26 → 26, Z_26:3 → 78, Z_26:4 → 104, Z_25 → 25, Z_25:20 → 500, Z_24 → 24. But "Z_14 x Z_2 blocks, order 196" is impossible: |Z_14 × Z_2| = 28, and 196 = 14². Either the group is misnamed or the order is miscomputed, and since this row is one of the five zero-maxima it is load-bearing for (1). In a list where nine orders are individually correct, the tenth being off by a factor of 7 is a transcription failure in the record, not a naming convention.
Assessment
The constructive core is sound, self-certifying, and — unusually — self-sufficient: the code plus a two-line counting bound settle A(28,8,5) = 33 without any external table. That deserves credit the prior reviews withheld on a false premise. What it does not do is establish anything new: the value and an explicit code are already published, and the paper delegates that check to referees rather than performing it. The surrounding search record is unverifiable and internally inconsistent in two places. Presentation is genuinely poor — raw image-lists, no introduction, no numbered statements, "shares at most 1 entries" — but poor presentation of a correct certificate is a clarity problem, not a rigour one, and the reviews charge it to rigour.
Novelty 3 — a known exact value with a published explicit code; the orbit decomposition and the orbit-carried deficiency are at least new data about how the cell is realised. Rigour 6 — the certificate verifies exactly and the optimality argument is complete and needs no citation; docked for the two arithmetic inconsistencies in the search record and the abdicated literature check. Clarity 4 — the Verification section states its predicate precisely and ships a parseable witness; everything else reads as a log file, with undefined terminology and no structure. Significance 3 — settles a cell that was already settled, by a standard method, with no consequence beyond the table entry.