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Two findings from re-reviewing the fine-delay section. 1. The rho values I put in s3.2a were wrong. The report derives rho = f*D_vis with D_vis = hops*delta_max/2 + (hops+1)*ell_mean from a MEASURED ell_mean (1.211 slots at N=1000/degree=6), not from the link_latency_mean parameter (0.5). Hand-substituting a guessed 1.5 inflated every value by ~0.04: the band is rho 0.21-0.41, not 0.25-0.45. To stop that recurring, graph_ell_mean moves out of rho_boundary_analysis.py into figures_pernode.py, joined by a new rho_for() that both scripts and any future quotation go through; plot_fine_delay.py now prints the derived rho per delay. This also exposed an inconsistency in the existing s3.2 table, which rounded delta_max=4 to "rho ~ 0.4" while s3.2a called the same cell 0.36 and prose elsewhere already used 0.56 for delta_max=8. The s3.2 column now carries the derived values (0.36/0.56/0.96/1.76). 2. Testing each cell against the exact target 1.0 -- the same question the gap test asks, without reference to the other model -- corroborates the first-fork onset independently. Unrestricted: 1/15 cells below 1 (t=-2.09, chance). Countable: 4/15, and not scattered -- delta_max=4 at U=1, and ALL THREE caps at delta_max=5 (-0.0012 to -0.0019, t=-2.5..-3.7). A shortfall appearing at every cap at once, only at the top of the band, only under the restricted model, is the first-fork cost seen absolutely. That makes "one uncle slot is sufficient -- not approximately, exactly" too strong as I had written it. s3.2a now states the residual (0.1-0.2% at the top of the band, zero below delta_max=3), reconciles it with the s1 headline, and notes that since all three caps show the same shortfall the residual is not a capacity limit. The bound quoted in s1 moves from "below 0.15%" to "<= 0.2%". Also adds the new run directories to s9's canonical list, which covered every other study but not these. Tests: 209 passed. ruff clean. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>