You read the files correctly, and I reproduced all of it before answering. Every share value matches to four decimals, the mean is +0.2635, the tuning step is +0.0244, the ratio comes out 10.81. The consensus.json figures check out and so does your retraction: the 30-arm and 36-arm sets are used consistently and nothing is quoted across them.
The word "same" is a real error and is now corrected. Chasing your count also explained the 30 versus 31: code_select.py globbed every json in the generation directory, so task_ids.json was read as an arm. It has one entry per problem, so it passed the length check, and slicing its task-id strings produced 11 single-character "candidates", which is the k = 11 and the all-zero row. The glob now requires an arm tag. The published artifact is left alone and Section 12 documents the entry, because silently rewriting a result file mid-thread is worse than labelling it.
On the substance, your objection to raw headroom is right and your normalization is where I part company.
share = floor / oracle is very close to a function of competence alone. Regressed on floor_pass1 across the 30 arms it gives r = 0.9840. Holding competence fixed, the format-specific residual is +0.0223 against your headline +0.2635, so competence accounts for 92% of the movement. Per rung, chat minus raw: 0.5B +0.0968, 1.5B +0.0434, 3B +0.0085, 7B −0.0118, 14B −0.0254. Monotone decreasing, sign change at 7B, largest where floor_pass1 is 0.026 and the ratio is least stable.
You suggested matched-competence arms, so I ran it rather than leaving it as a suggestion. Pairs differing in framing with |Δfloor| < 0.03: 42 pairs, mean share difference for the more-formatted arm +0.0010, median +0.0018, 23 of 42 positive. At |Δfloor| < 0.02 it is −0.0003 over 30 pairs, at 0.05 it is +0.0102 over 64.
One caveat against that null. The framings barely overlap in competence, weak framings spanning floor 0.021 to 0.109 and strong ones 0.156 to 0.540, so most matched pairs are cross-rung. Same-rung pairs number 9 to 20 depending on threshold and give +0.0085 to +0.0151. Thin, and not zero.
So the honest range for a format-specific effect on share is 0.00 to 0.02, against your +0.2635. Within-pool convergence is a different claim from 5.4 and this evidence does not establish it. 5.4 says text similarity across models does not imply agreement on correctness, and nothing here touches that. What these numbers show is that the chat template makes the model better, and competence mechanically raises the fraction of pool coverage a single sample captures.
The mechanism underneath your reading is real. The selector eats residual disagreement, so anything that raises competence shrinks the room. We measured that on a separate banked set this week, on a different axis to your ladder. The selector's edge over a pool's own pass rate is +0.44 when two candidates agree and +0.04 when eight do. The format closes the room the same way scale does, by making the model right more often rather than by making it agree with itself.