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>
Applied the reconstructed round-4 review to the TSI parameter-selection report
set (reports/tsi) and executed the follow-ups.
Report (reports/tsi):
- Applied the must+should findings across README + parts 1-4: cross-part numeric
corrections, figure-caption fixes, spec reconciliation, and cross-file companions
(hops-degradation and notch/reward numbers, tip-agreement ordering, density-window
timing, VRF -> ZK Proof-of-Leadership, w_u window/reward gloss).
- Editorial pass for timeless voice (no "now adopted / merged / coin" narration) and
a gentle spec-safety framing (recommendations are thresholds; the protocol's
MAX_UNCLES=4 sits safely above them).
- Added the fork-rate-vs-scale table (6.10), defined "grinding gain", promoted the
clock-skew study to its own paragraph, added the correlated-latency caveat, and
moved fig27/fig28 beside their discussion.
- Documented the Blend cascade in 2: hops propagate over the shared gossip graph
(not direct links), the final broadcast comes from the last relay, relays are
blind forwarders.
Simulator (tools/simulators/tsi/tsi-sim-pernode):
- Docstring/dead-code fixes: theory.block_count_ceiling (legacy framing), measure,
reorg (catch-up reading), metrics (removed two dead helpers), config (fixed_point
10^-6; clock_skew_max/lottery_chunks documented inert), stake_vs_delay.
- Generator correctness + regenerated figures: figures_pernode.CONFIG_COLS now
exhaustive (f no longer pooled); rho_boundary_analysis SEM across replicates +
hollow floored markers + de-hardcoded ell_mean (measured from the run's graph);
appendix_fluct per-N sigma + ~18x title (figB2); bootstrap_dynamics driving
estimate so fig1 epoch-0 matches genesis.
- pytest: 186 passed; report links 528/0 dangling.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
