The unpaired comparison could not answer the question it was asked. The
two uncle models draw independent RNG streams -- uncle_model is in the
config key, which is what makes --old bit-reproduce earlier runs -- so
the arms differed in stake draw, peering graph and every lottery
outcome, each comparison paid the between-run variance twice, and the
per-cell floor (+-0.0015) sat an order of magnitude above the effect.
Only delta_max = 5 resolved, and only after pooling.
Adds `paired_streams`: the RNG root is derived from the model-
independent part of the key, so a countable cell and its --old twin get
the SAME stake, graph and lottery draws and the uncle rule is the only
difference. Each replicate is then a matched pair and the shared
variance cancels. Trajectories still diverge after epoch 0 through the
genuine feedback (a different counted density changes the next epoch's
difficulty), which is the signal.
The flag is deliberately NOT in key(): it selects which key the seed is
derived from, so including it would perturb every historical seed.
Re-verified that --old still bit-reproduces the committed 2026-07-27
rho-boundary parquet, max |delta| = 0.
Results (configs/fine-delay-paired.yaml, 40 replicates per arm):
- Negative control becomes an IDENTITY check. With U = 0 no reference is
taken, so shared streams must give bit-identical trajectories. All 200
replicate pairs differ by exactly 0.0. Unpaired, the same control only
had to agree within +-0.025 and drifted by 0.016.
- Per-cell SE shrinks by a median 1.6x (1.2-2.1x); widest 95% CI goes
+-0.0015 -> +-0.0010. 5/15 cells resolve at |t| >= 2 (0.75 expected by
chance); the largest, U=2 at delta_max=4, is t = 4.32 and clears
Bonferroni for 15 tests.
- The cost is a STEP, not the ramp the unpaired data suggested:
delta_max 1-3 unresolved (t = 1.1, 1.8, 1.4), then delta_max 4 AND 5
both resolve at -0.0011 (t = 4.7) and -0.0009 (t = 3.7). Whole-band
pooled -0.00060 +- 0.00021, t = 5.7 -- where the unpaired estimate of
the same quantity (t = 2.8) had failed correction.
So the first-fork restriction costs nothing measurable up to
delta_max = 3 and about 0.1% at 4-5 -- an order of magnitude below the
+-0.9% per-epoch sampling noise.
Two bugs found while building this, both of which would have silently
produced a wrong answer:
- paired_streams was missing from metrics._CONFIG_FIELDS, so it never
reached the parquet; plot_fine_delay.py falls back to the unpaired
test when it cannot confirm pairing, so the sweep would have completed
and quietly reported the old result. Caught before the run finished;
the sweep was restarted and a test now pins the field.
- The U=0 control check reported FAILS on a PERFECT control: paired, the
gap is exactly 0 so its SE is 0 and t is 0/0. It now checks the gap
itself when the streams are shared, and falls back to the t-test only
when there is real spread.
§3.2a is rewritten around the paired measurement; the unpaired sweep is
retained in §9 as the power comparison that motivated it. Figures 34-35
regenerated, with the control annotation and provenance reflecting the
design actually used.
Tests: 214 passed (was 209). ruff clean.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
