Phase 5 design-point pilot

Run date: 2026-09-08 Configuration: examples/trajectory_power_study/phase5_design_point_pilot.json (sha256 153f53b7…, recorded in full in results/phase5-design-point-2026-09-08/PROVENANCE.txt) Code revision: ff68514 on feat/phase5-design-point-pilot (clean working tree at launch; parent afab7df = main). Record generation and report generation used the same revision. Execution: SLURM array job 878322 on cluster.ing.uc.cl, partition 512x1024 (AMD EPYC 7662 nodes), 100 single-CPU shards, --error-policy record, no --n-jobs, BLAS pinned to one thread. Environment: Python 3.11.16, numpy 2.3.5, pandas 2.3.3, scikit-learn 1.8.0, scipy 1.16.3, motco 0.6.0, installed from the lockfile with uv 0.12.10; no R at runtime. Answers: readiness item 4 (phase5-readiness.md) — the Phase 5 design point and the 0.80 orientation power floor. Every number below traces to a file under results/phase5-design-point-2026-09-08/report/; the JSONL records are gitignored as regenerable.

Design-point decision: CHOSEN — ρ = 0, n = 1200

First design point in preference order (n_samples ascending, then baseline_continuity ascending) whose orientation/angle power at its top effect (1.00) clears the 0.80 floor with 1·SE confirmation: rate 0.88, lower bound 0.85 (report/design_point_decision.json).

The rule was predeclared in the config (acceptance.design_point) and is advisory. Its per-column evaluation (report/design_point_decision.csv):

ρ	n	orientation `angle` power at e = 1.00	MC SE	1·SE lower bound	status	anchor Type I (delta / angle / shape)
0.0	300	0.55	0.050	0.50	fails	0.03 / 0.06 / 0.03
0.5	300	0.24	0.043	0.20	fails	0.01 / 0.02 / 0.01
0.8	300	0.69	0.046	0.64	fails	0.04 / 0.01 / 0.01
0.0	600	0.76	0.043	0.72	fails	0.04 / 0.05 / 0.05
0.5	600	0.46	0.050	0.41	fails	0.02 / 0.00 / 0.02
0.8	600	0.73	0.044	0.69	fails	0.02 / 0.05 / 0.07
0.0	1200	0.88	0.032	0.85	meets	0.04 / 0.04 / 0.03
0.5	1200	0.69	0.046	0.64	fails	0.05 / 0.02 / 0.02
0.8	1200	0.81	0.039	0.77	marginal	0.02 / 0.04 / 0.03

The chosen column's own zero-effect anchor holds nominal level on all three statistics (0.04 / 0.04 / 0.03 against α = 0.05), so the design.md risk — a column that meets the floor on angle while another statistic drifts — did not materialize. ρ = 0 is also the declared isotropic stress-test endpoint and the Phase 4 comparator, so the chosen point carries the most general claim the grid offered: the floor is met without assuming any baseline continuity.

The figure report/design_point_power.png shows the same nine points as curves: orientation angle rejection rate at e = 1.00 versus n_samples, one line per ρ, Monte Carlo error bars, each point annotated with the column's median pooled eigengap. The ρ = 0 line rises steepest (0.55 → 0.76 → 0.88) and is the only one to clear 0.80 with margin; the ρ = 0.5 line lies below it everywhere; the ρ = 0.8 line starts highest at n = 300 and is overtaken by n = 600.

Run configuration

Parameter	Value
Integration	Pooled PLS, M-value methylation
PLS cross-validation	`cv1_splits=3`, `cv2_splits=4`, `n_repeats=5`, `max_components=20`, `random_state=1203`
Stages	4
Differential-site density `p_dmp`	0.1 (Phase 4 used 0.2)
Surgery censoring	default `"error"` (fail loud); no cell was censored
Design grid	ρ ∈ {0.0, 0.5, 0.8} × `n_samples` ∈ {300, 600, 1200} (9 columns; ρ = 0, n = 300 is the baseline column)
Trajectory modes	orientation, translation
Effect sizes	0.00 (shared anchor per column), 0.25, 0.50, 1.00
Replicates per cell	100
Permutations per test	199
Seed policy	one matched primary family across the whole grid; one zero-effect anchor per column
Attribution / Phase 4 gate	off / off
Cells	65 (2 Type I + 63 primary/design)
Total work units	6,500
Failed work units	0
Censored surgeries	0 (`report/realized_surgery.csv`, `censored_fraction` = 0.0 in all 55 surgery cells)
Compute	70.4 core-hours of recorded unit runtime (75.2 CPU-hours billed by `sacct`), 70 minutes wall on 100 concurrent tasks

All 6,500 units completed with status completed; every (cell, replicate) appears exactly once in merged.jsonl; every record's parameter signature equals the signature enumerated from the committed config; every record carries 199 permutations, n_jobs = 1, config_spectrum, and selected_lv.

Operating characteristics per design point

Rejection rates at α = 0.05, 100 replicates per entry (report/design_point_operating.csv). Bold is orientation's target statistic. Each column's none row is that column's shared zero-effect anchor — one measurement per column, not one per mode.

ρ	n	mode	e	delta	angle	shape
0.0	300	none	0.00	0.03	0.06	0.03
0.0	300	orientation	0.25	0.60	0.45	0.82
0.0	300	orientation	0.50	0.67	0.63	0.93
0.0	300	orientation	1.00	0.69	0.55	0.91
0.0	300	translation	0.25–1.00	0.02–0.05	0.02–0.06	0.01–0.03
0.5	300	none	0.00	0.01	0.02	0.01
0.5	300	orientation	0.25	0.26	0.16	0.41
0.5	300	orientation	0.50	0.33	0.19	0.57
0.5	300	orientation	1.00	0.49	0.24	0.76
0.5	300	translation	0.25–1.00	0.04–0.06	0.01–0.03	0.01–0.02
0.8	300	none	0.00	0.04	0.01	0.01
0.8	300	orientation	0.25	0.16	0.07	0.26
0.8	300	orientation	0.50	0.21	0.27	0.32
0.8	300	orientation	1.00	0.27	0.69	0.43
0.8	300	translation	0.25–1.00	0.03–0.05	0.03–0.06	0.01–0.05
0.0	600	none	0.00	0.04	0.05	0.05
0.0	600	orientation	0.25	0.77	0.74	0.96
0.0	600	orientation	0.50	0.81	0.81	1.00
0.0	600	orientation	1.00	0.78	0.76	0.99
0.0	600	translation	0.25–1.00	0.02–0.05	0.00–0.06	0.02–0.06
0.5	600	none	0.00	0.02	0.00	0.02
0.5	600	orientation	0.25	0.36	0.38	0.63
0.5	600	orientation	0.50	0.52	0.39	0.83
0.5	600	orientation	1.00	0.44	0.46	0.87
0.5	600	translation	0.25–1.00	0.03–0.07	0.00–0.04	0.01–0.08
0.8	600	none	0.00	0.02	0.05	0.07
0.8	600	orientation	0.25	0.32	0.22	0.47
0.8	600	orientation	0.50	0.38	0.32	0.53
0.8	600	orientation	1.00	0.31	0.73	0.61
0.8	600	translation	0.25–1.00	0.03–0.05	0.01–0.04	0.03–0.05
0.0	1200	none	0.00	0.04	0.04	0.03
0.0	1200	orientation	0.25	0.88	0.83	1.00
0.0	1200	orientation	0.50	0.86	0.89	1.00
0.0	1200	orientation	1.00	0.86	0.88	1.00
0.0	1200	translation	0.25–1.00	0.04–0.09	0.03–0.04	0.03–0.06
0.5	1200	none	0.00	0.05	0.02	0.02
0.5	1200	orientation	0.25	0.65	0.71	0.89
0.5	1200	orientation	0.50	0.65	0.70	0.92
0.5	1200	orientation	1.00	0.60	0.69	0.97
0.5	1200	translation	0.25–1.00	0.05–0.07	0.01–0.02	0.03–0.06
0.8	1200	none	0.00	0.02	0.04	0.03
0.8	1200	orientation	0.25	0.30	0.26	0.48
0.8	1200	orientation	0.50	0.51	0.48	0.66
0.8	1200	orientation	1.00	0.46	0.81	0.69
0.8	1200	translation	0.25–1.00	0.04–0.05	0.02–0.04	0.03–0.05

Translation rows are collapsed to their range over the three nonzero effects; the individual rows are in the CSV.

Type I behaviour, per column

Every column's anchor and every translation cell sits at or below the one-sided bound 0.05 + 2·sqrt(0.05·0.95/100) = 0.0936 on all three statistics; the largest control rate anywhere in the grid is 0.09 (translation delta, ρ = 0, n = 1200, e = 0.25). Type I calibration does not drift with sample size or continuity, which is the property the design.md risk list asked this report to check before adopting a column.

The baseline type_i acceptance targets (report/acceptance_report.json, two-sided |rate − α| ≤ 2·SE) pass on 5 of 6 tests. The one flagged test is the translation control's delta rate of 0.02 — 0.03 below α against a 0.028 bound — i.e. a conservative rate, not an inflation. The Phase 4 report judged these controls one-sided (inflation only); under that reading all six pass. It is reported here as flagged because the config's target is two-sided.

Orientation at the baseline column, against Phase 4

At ρ = 0, n = 300 the orientation angle curve is 0.45, 0.63, 0.55 across e = 0.25 / 0.50 / 1.00 (report/power_curves.csv). Phase 4 measured 0.59, 0.59, 0.64, 0.65 (0.64–0.68 after the sign-anchor correction) at p_dmp = 0.2. The shape of the curve is the same — no monotone response to the requested effect; adjacent points differ by at most 2.6 combined standard errors and the top effect is not the most powerful — and the level is about 0.1 lower, consistent with halving the differential-site density rather than with any change in the estimator. The off-diagonal pattern is also unchanged: orientation moves shape (0.82–0.93 here, 0.97–1.00 in Phase 4) and delta (0.60–0.69 here, 0.60–0.69 in Phase 4). Item 2 predeclared the shape response as a projection artifact of the rank-3 stage-supervised space; nothing here contradicts that, and at n ≥ 600 the response saturates at 0.96–1.00 in every ρ = 0 and ρ = 0.5 column.

What governs orientation power across the grid

The design-point table carries the two recorded covariates readiness item 4 asked for — the pooled configuration eigengap and the dispersion of each replicate's own angle null width (q95). Orientation cells at e = 1.00, from report/continuity_resolved_orientation.csv (identical rows appear in design_point_operating.csv):

ρ	n	`angle` power	median eigengap (q33–q67)	median `angle` null q95	IQR of q95	SD of q95
0.0	300	0.55	0.052 (0.035–0.067)	40.7°	107.4°	59.1°
0.0	600	0.76	0.048 (0.038–0.066)	18.8°	38.2°	55.5°
0.0	1200	0.88	0.049 (0.038–0.063)	10.8°	13.0°	48.4°
0.5	300	0.24	0.086 (0.071–0.125)	56.6°	116.6°	57.4°
0.5	600	0.46	0.114 (0.090–0.149)	26.2°	42.2°	54.2°
0.5	1200	0.69	0.133 (0.094–0.188)	16.3°	12.1°	29.5°
0.8	300	0.69	0.221 (0.145–0.285)	24.6°	83.3°	60.2°
0.8	600	0.73	0.193 (0.156–0.269)	21.3°	37.6°	54.1°
0.8	1200	0.81	0.186 (0.142–0.234)	15.3°	20.0°	49.9°

Sample size does what item 1 predicted. Along n at fixed ρ = 0 the eigengap is constant (≈ 0.05: the baseline is near-isotropic at every n, as it must be — ρ, not n, sets the configuration's shape) while the median angle null width contracts 40.7° → 18.8° → 10.8° and its IQR collapses 107° → 38° → 13°. Power rises 0.55 → 0.76 → 0.88 with it. The zero-effect anchors show the same contraction (median q95 17.3°, 8.1°, 4.9° at n = 300, 600, 1200; design_point_operating.csv, none rows). This is the mechanism the pivotality report identified — each replicate's critical value tracks its own geometry, and more samples per group-stage cell pin that geometry down — now measured across n rather than inferred at one point.

Continuity does not help at this baseline, and its effect is non-monotone. ρ = 0.5 is worse than ρ = 0 at every n (0.24 / 0.46 / 0.69 vs 0.55 / 0.76 / 0.88), and ρ = 0.8 is above ρ = 0 only at n = 300 (0.69 vs 0.55), then below it (0.73 vs 0.76, 0.81 vs 0.88). This is not what the headroom analysis anticipated, and the covariates say why the simple story fails:

The eigengap behaves as designed — it rises from ≈ 0.05 at ρ = 0 to 0.09–0.13 at ρ = 0.5 and 0.19–0.22 at ρ = 0.8, so the stage configuration does acquire a dominant PC1 — and at ρ = 0.5, n = 1200 the anchor's null is the narrowest in the grid (median q95 2.2° against 4.9° at ρ = 0). The null side of the test improves with continuity exactly as the audit predicted.
What does not carry over is the signal. Computed from the records (merged.jsonl, pair_statistics.angle; reproduction snippet below), the median observed latent angle for orientation at e = 1.00 is 61° / 73° / 66° at ρ = 0 for n = 300 / 600 / 1200, but only 46° / 35° / 28° at ρ = 0.5 — the same nominal surgery realizes a smaller latent orientation contrast when the baseline trends, and the contrast shrinks as n grows. At ρ = 0.8 the observed angle is back to 64° / 62° / 66°, but the anchor's null is wide again (median q95 54° / 26° / 19°, versus 23° / 9° / 2° at ρ = 0.5), so the larger eigengap buys nothing on the null side there.

So "larger eigengap ⇒ narrower null ⇒ more power" holds only along n at fixed ρ. Across ρ, two things change at once — the realized orientation contrast of the surgery and the null width — and they do not move together. The claim Phase 5 can make is therefore n-conditional, not continuity-conditional: at the chosen point the floor is met at the isotropic endpoint, with an eigengap distribution (median 0.049, terciles 0.038–0.063) that is the real-data observable to report alongside any orientation result. A trending baseline is not a lever Phase 5 should pull to buy orientation power; if anything, the ρ = 0.5 columns are a warning that the orientation surgery's semantics are not ρ-invariant, which belongs in the Phase 5 report contract as a stated limitation of the construction.

PLS representation

Selected latent dimensionality (design_point_operating.csv, median/min/max_selected_lv):

column	anchors (median, range)	orientation e = 1.00 (median, range)
ρ = 0, every n	3 (2–4)	3–4 (2–4)
ρ = 0.5, every n	3–4 (2–4)	4 (3–6)
ρ = 0.8, n = 300 / 600 / 1200	4 (4–7), 4 (4–5), 4 (3–5)	8 (4–14), 7 (4–10), 7 (4–9)

At the chosen point selection saturates at n_stages − 1 = 3 (median 3, range 2–4, orientation cells included), exactly as in Phase 4: the stage-supervised double CV sizes the space for stage separation and does not respond to n. The retained-rank question — whether a space sized for stage centroids should be the space that measures the group orientation contrast — is handed to readiness item 3 unchanged; this pilot recorded rank and did not vary it.

One new observation for item 3: at ρ = 0.8 the orientation surgery at e = 1.00 roughly doubles the selected rank (median 7–8, up to 14) relative to that column's own anchor (median 4), while at ρ ≤ 0.5 it adds at most one component. A strongly trending baseline plus a global feature permutation evidently creates additional stage-predictive directions that the CV retains. It coincides with ρ = 0.8 being the only ρ at which orientation's delta and shape responses fall (0.27–0.46 and 0.43–0.69, versus 0.60–0.88 and 0.91–1.00 at ρ = 0) — consistent with the latent-rank probe's finding that the projection artifact decays as rank grows. It is recorded, not explained, here.

Limitations

100 replicates give a Monte Carlo SE of about 0.05 at a rate of 0.5 and 0.032 at 0.88. The decision's confirmation margin is one SE by predeclaration; the chosen column would also clear a 2·SE margin (0.88 − 0.065 = 0.815) but ρ = 0.8, n = 1200 would not.
magnitude and shape were deliberately not run (decided 2026-09-04; both reached power 1.00 at n = 300 in Phase 4 and only gain from larger n). Their operating characteristics at the chosen point are measured in the Phase 5 study itself, not here. The p_dmp change from 0.2 to 0.1 touches every mode, so Phase 4's magnitude and shape numbers are not transferable to this baseline without that measurement.
The observed-angle medians in "What governs orientation power" are computed from the gitignored merged.jsonl, not from a committed CSV; the snippet below regenerates them from the records. Every rejection rate, eigengap, null-width, and rank figure comes from committed CSV/JSON.
Comparisons along ρ at fixed n are paired at the baseline indicator draw (one matched family, ρ thresholds the same uniform block); comparisons across n are not paired. Neither pairing is exploited by the report's rate estimates, which are per-cell binomials.
Each column's 0.00 row is one shared anchor cell; the two modes' nulls in a column are one measurement.
The Type I acceptance target is two-sided in this config, which is why a conservative 0.02 control rate is flagged. Phase 4's one-sided reading is the one the readiness worklist uses; both readings pass on inflation.
The examples README's pre-run cost estimate (~500 workstation-core-hours) was about 7× too high; it was taken from a rehearsal that oversubscribed BLAS threads. The measured cost is 70 core-hours on EPYC 7662 cores, and about 35 on a modern desktop core (12.5 s / 18.5 s / 27 s per unit at n = 300 / 600 / 1200, single-threaded, 199 permutations). The README is corrected in this change.

Decision and hand-off

Phase 5 design point: ρ = 0 (independent baseline), n = 1200 (300 samples per group-stage cell), four stages, p_dmp = 0.1, pooled PLS on M-value methylation with CV-selected rank. Orientation angle power at e = 1.00 is 0.88 (1·SE lower bound 0.85) with the column's anchor at nominal level on all three statistics. The 0.80 floor stands; the claim is not revised.
Report the eigengap, not ρ, with any orientation claim. At the chosen point the pooled eigengap is 0.049 (terciles 0.038–0.063). That distribution is what a real cohort must be compared against; the continuity knob is a generator parameter and does not transfer.
Do not use baseline continuity to buy orientation power. ρ = 0.5 lowers power at every n and ρ = 0.8 does not beat ρ = 0 beyond n = 300. The orientation surgery's realized contrast is not ρ-invariant; state this as a construction limitation in the Phase 5 report contract.
Hand the retained-rank question to item 3 with one new fact: rank is 3 at the chosen point regardless of n, and only a strongly trending baseline (ρ = 0.8) moves the CV off n_stages − 1.
Phase 5 must re-measure magnitude and shape at the chosen point, since p_dmp changed.

Reproduction

The run used the committed config at revision ff68514. Locally (about 35 core-hours on a modern desktop core; ~3.5 hours on 22 single-thread shards):

export OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 MKL_NUM_THREADS=1
for i in $(seq 0 21); do
  uv run python scripts/run_study_shard.py \
    --config examples/trajectory_power_study/phase5_design_point_pilot.json \
    --out-dir results/phase5-design-point-2026-09-08 \
    --shard-index "$i" --n-shards 22 --error-policy record &
done
wait

On SLURM, as actually executed (partition and resource flags are cluster-specific; do NOT set STUDY_N_JOBS, it changes the permutation draws and the parameter signature):

export OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 MKL_NUM_THREADS=1
sbatch -p 512x1024 --cpus-per-task=1 --mem=2G --time=6:00:00 --array=0-99 \
  --export=ALL,STUDY_CONFIG=$PWD/examples/trajectory_power_study/phase5_design_point_pilot.json,STUDY_OUT=$PWD/results/phase5-design-point-2026-09-08,N_SHARDS=100 \
  scripts/motco_study_array.sbatch

Then, from the repository root:

uv run python scripts/motco_study.py merge  --out-dir results/phase5-design-point-2026-09-08
uv run python scripts/motco_study.py report \
  --config examples/trajectory_power_study/phase5_design_point_pilot.json \
  --out-dir results/phase5-design-point-2026-09-08

Record-derived observed-angle medians (the only figures above not in a committed CSV):

uv run python - <<'EOF'
import json, collections, statistics
by = collections.defaultdict(list)
for line in open("results/phase5-design-point-2026-09-08/merged.jsonl"):
    r = json.loads(line); cm = r["cell_metadata"]
    if cm["trajectory_mode"] != "orientation" or cm["effect_size"] != 1.0: continue
    dp = cm.get("design_point") or {"generator.baseline_continuity": 0.0, "generator.n_samples": 300}
    by[(dp["generator.baseline_continuity"], dp["generator.n_samples"])].append(r["pair_statistics"]["angle"])
for k in sorted(by): print(k, round(statistics.median(by[k]), 1))
EOF

The per-shard and merged JSONL (43 MB) are gitignored as regenerable; report/ and PROVENANCE.txt are committed. Every claim above traces to results/phase5-design-point-2026-09-08/report/: design_point_decision.json / .csv, design_point_operating.csv, continuity_resolved_orientation.csv, power_curves.csv, type_i_table.csv, acceptance_report.json, realized_surgery.csv, eigengap_stratified_power.csv, config_spectrum.csv, and the figures design_point_power.png, power_curves.png, specificity_matrix.png, type_i.png.