Phase 5 paper-grade trajectory power study — 2026-09-10

Run: results/phase5-2026-09-10/ · Config: examples/trajectory_power_study/phase5_power_study.json (sha256 4f10aa1f…09826, from PROVENANCE.txt) · Gate decision: HOLD (from report/phase4_gate_decision.json).

The HOLD is carried by the two mandatory-control rules on the magnitude mode — magnitude/angle 0.276 and magnitude/shape 0.742 against a 0.0695 bound — not by any power rule. All three mandatory power diagonals met their 0.80 floor, every Type I check met, and the record set is complete. Both control failures reproduce values the latent-rank ladder pilot had already measured (0.24 and 0.74), so paper-grade precision did not discover them; it confirmed them at SE ≈ 0.020 and removed Monte Carlo error as an explanation.

1. Configuration and provenance

The design point is fixed, each coordinate traced to the readiness item that chose it:

coordinate	value	chosen by
baseline continuity ρ	0 (independent baseline, isotropic endpoint)	design-point pilot, readiness item 4
n	1200 (300 per group-stage cell)	same
stages / `p_dmp`	4 / 0.1	same
measurement space	pooled PLS on M-value methylation	readiness items 1–2
retained rank	stage-supervised double CV (`cv1_splits` 3, `cv2_splits` 4, 5 repeats, ≤ 20 components)	latent-rank ladder returned `keep_cv`, readiness item 3

Monte Carlo sizing is 500 replicates × 999 permutations per unit, 19 cells, 9,500 units. The matched-seed family is phase5-primary, new to this study, so the run is independent of both Phase 5 pilots; the configuration otherwise derives from the ladder's cross-validated column (metadata.derives_from) with generator and evaluation.integration_params copied verbatim, no design_grid, and permutations raised from 199 to 999.

The double-CV rank rule selected rank 3 = n_stages − 1 at every cell (report/phase4_pls_selection.csv: median and modal selected_lv 3 in all 19 cells, mean 2.90–3.18, range 2–4; cv_settings_consistent true throughout). Rank selection is therefore not a source of between-cell variation in this run.

PROVENANCE.txt carries the full field list: code revision b8f7daa on a clean tree, the exact sbatch line with STUDY_N_JOBS unset, BLAS pinned to one thread, job 880599, both environments' package versions, the wall interval, per-unit timings, and the merge/report split. Two provenance points worth reading directly:

Cost. 182.7 recorded core-hours against the config's ~150 EPYC core-hour budget, a 22 % overage. The budget was projected from the ladder's 57 s median per unit; the realized median is 61.5 s with a right-skewed tail (mean 69.2 s, max 191.8 s) because 68 of the 100 array tasks shared node n3. Attribution is not the cause — the 2,000 attribution-bearing orientation units ran at a 60.0 s median against 62.1 s for everything else, matching the rehearsal's 42.9 s vs 43.0 s. Nothing about the measurement changed.
Split environments. Records were produced on EPYC 7662 nodes (python 3.11.16, uv 0.12.10); the report was rendered on the workstation (python 3.11.15, uv 0.11.17) from the rsynced merged.jsonl. Reporting re-fits nothing, so this is deterministic post-processing of recorded statistics.

2. Unit and failure accounting

Every completeness assertion below is read from the merged records, not inferred from SLURM exit codes.

check	result
units expected / present exactly once	9,500 / 9,500; 0 duplicate `(cell, replicate)` pairs
enumerated cells present	19 / 19, exactly 500 replicates each, no unexpected cell
parameter-signature mismatches	0
`status = failed` records	0 (all 9,500 `completed`); no `diagnostic_error_type` to report
censored surgeries	0 at every cell (`report/realized_surgery.csv`: `censored_fraction` 0.0, `realized_mean` = `nominal_size`)
attribution accounting	2,000 eligible / 2,000 computed / 0 failed (`report/driver_report.csv`)
`n_jobs` uniformity	1 in all 9,500 records (`report/report_contract.json`)
permutations	999 in all 9,500 records
array tasks	100 / 100 `COMPLETED`, exit `0:0`, empty stderr

The gate's own completeness rule agrees (report/phase4_gate_decision.json, diagnostic_completeness: met, 9,500 records, 0 failed, 9,500 PLS records, 0 missing integration metadata, 0 missing realized geometry, 2,000 attribution eligible, 0 incomplete). No unit was dropped, and none needed to be — task 2.3's resubmission path was never exercised.

Realized surgery sizes sit exactly on nominal at every pool-limited cell, e.g. orientation at e = 1.00 nominal 125.662 / realized mean 125.662 (range 97–158) and translation at e = 1.00 nominal 37 / realized 37 (range 37–37). The magnitude cells and the none cells report surgery_replicates = 0, which is correct rather than missing: magnitude scales δ globally and none is the identity, so neither draws from the finite CpG pool.

3. Gate decision

HOLD. Rationale as recorded: "Mandatory gate(s) failed: mandatory_control[magnitude,angle] (rate=0.2760 > bound=0.0695 (alpha=0.05 + 2·SE, n=500)); mandatory_control[magnitude,shape] (rate=0.7420 > bound=0.0695 (alpha=0.05 + 2·SE, n=500))" — report/phase4_gate_decision.json. No confirmation re-run is required by the decision (confirmation_runs: []).

Per-rule outcomes (report/phase4_gate.csv, report/phase4_gate_decision.json):

rule	kind	outcome	observation
`mandatory_power[magnitude,delta]`	power	met	top_rate 1.000 ≥ 0.800, monotone
`mandatory_power[orientation,angle]`	power	met	top_rate 0.840 ≥ 0.800; `tolerated_monotone` true
`mandatory_power[shape,shape]`	power	met	top_rate 0.996 ≥ 0.800, monotone
`mandatory_control[magnitude,angle]`	control	failed	0.2760 > 0.0695, exceedance 10.3 SE
`mandatory_control[magnitude,shape]`	control	failed	0.7420 > 0.0695, exceedance 34.4 SE
`descriptive[orientation,delta]`	descriptive	not gated	0.036 → 0.804 → 0.878 → 0.894 → 0.912
`descriptive[orientation,shape]`	descriptive	not gated	0.048 → 1.000 → 1.000 → 1.000 → 0.998
`descriptive[shape,delta]`	descriptive	not gated	0.036 → 0.806 → 0.874 → 0.934 → 0.954
`descriptive[shape,angle]`	descriptive	not gated	0.046 → 0.692 → 0.816 → 0.800 → 0.796
`type_i_inflation[…]` × 21	Type I	all met	every control cell ≤ 0.0695
`diagnostic_completeness`	completeness	met	see §2

The two predeclared readers disagree on orientation/angle, and the disagreement is about monotonicity, not about the floor. The Phase 4 gate records mandatory_power[orientation,angle] as met — the floor is cleared and non-monotonicity is tolerated within 2·SE. The acceptance-target reader records power[orientation,angle] as not met (report/acceptance_report.csv, row 7: "monotone=False; top_rate=0.840 >= floor=0.800"), because the curve declines from 0.878 at e = 0.50 to 0.840 at e = 1.00 and its strict monotonicity rule admits no tolerance. Both are predeclared; neither is overridden here. The substantive reading is in §5: the orientation curve is flat, not rising, above e = 0.25.

Acceptance targets overall (report/acceptance_report.csv): 6 / 6 type_i_control met, 2 / 3 power_monotonicity met (orientation/angle the exception above), 3 / 5 specificity met (translation × 3 met; magnitude/angle and magnitude/shape failed, the same two rules that carry the gate's HOLD).

4. Type I error

The two type_i_baseline cells carry the Type I acceptance target and are a separate seed family from the power grid (report/type_i_table.csv):

cell	mode	`delta`	`angle`	`shape`	combined rule
`type_i_baseline-c9b8da02420a`	`none`	0.050 (SE .0097)	0.040 (SE .0088)	0.054 (SE .0101)	0.126 (SE .0148)
`type_i_baseline-d18f474778c9`	translation, e = 1.00	0.044 (SE .0092)	0.048 (SE .0096)	0.062 (SE .0108)	0.132 (SE .0151)

All six per-statistic rates are within 2·SE of α = 0.05 (report/acceptance_report.csv, rows 0–5; largest deviation 0.012 against a 0.0216 tolerance). The combined-rule rates of 0.126 and 0.132 are consistent with the ≈ 0.143 expected from three α = 0.05 tests without multiplicity control, and are reported as a property of the combined rule, not as inflation of any single statistic.

The shared zero-effect anchor is one measurement, not four. Cell power_primary-d74045b65506 (trajectory_mode none, e = 0.00) supplies the 0.00 power point for all four modes — resolves_modes [magnitude, orientation, shape, translation], counted_as: 1 in report/report_contract.json. Its rates are delta 0.036 (SE .0083), angle 0.046 (SE .0094), shape 0.048 (SE .0096), all nominal. It is counted once wherever it appears below.

Translation at e > 0 is a negative control on all three statistics and behaves as one across the whole sweep (report/power_curves.csv): delta 0.054 / 0.056 / 0.040 / 0.042, angle 0.038 / 0.028 / 0.050 / 0.042, shape 0.046 / 0.046 / 0.044 / 0.030 at e = 0.25 / 0.50 / 0.75 / 1.00. A constant observed-space location offset moves none of the three statistics, which is the invariance the estimators claim.

5. Power per mode

Diagonal power, from report/power_curves.csv (figure report/power_curves.png); e = 0.00 is the shared anchor in every row:

mode / statistic	0.00	0.25	0.50	0.75	1.00	SE at 1.00
magnitude / `delta`	0.036	1.000	1.000	1.000	1.000	0.000
orientation / `angle`	0.046	0.842	0.878	0.872	0.840	0.016
shape / `shape`	0.048	0.954	0.988	0.994	0.996	0.003

Magnitude/delta and shape/shape clear the 0.80 floor with room to spare and rise monotonically. Orientation/angle clears the floor at 0.840 but is flat from e = 0.25 onward (0.842, 0.878, 0.872, 0.840) — it saturates immediately and then drifts down, which is what fails the strict acceptance rule in §3.

Orientation read beside its covariates

Every orientation number is reported with the recorded eigengap and angle null width, because those are the observables that transfer to real data.

Eigengap (report/config_spectrum.csv, median with q25–q75, per configuration and pooled):

effect	A	B	pooled
anchor (e = 0.00)	0.0533 (.0357–.0801)	0.0521 (.0360–.0789)	0.0530 (.0351–.0798)
0.25	0.0575	0.0575	0.0534 (.0368–.0759)
0.50	0.0623	0.0610	0.0539 (.0325–.0779)
0.75	0.0657	0.0609	0.0523 (.0314–.0728)
1.00	0.0683	0.0660	0.0487 (.0318–.0723)

angle null width, null_summary["angle"]["q95"] per replicate, computed from merged.jsonl (degrees):

cell	median q95	IQR
anchor (`none`, e = 0.00)	5.457	4.933
orientation e = 0.25	6.501	5.557
orientation e = 0.50	7.227	7.519
orientation e = 0.75	8.623	9.428
orientation e = 1.00	11.286	13.919

The null widens with the effect it is meant to test — from 5.5° at the anchor to 11.3° at e = 1.00, with the IQR growing faster than the median (4.9° → 13.9°). This is the pivotality behaviour already established in the angle-null pivotality report (the null tracks its own observed statistic, slope 0.811), and it is the mechanism behind the flat orientation curve: a larger nominal orientation surgery buys a larger observed angle and a proportionally larger critical value, so the rejection rate stops improving.

Eigengap-stratified orientation/angle power (report/eigengap_stratified_power.csv, terciles):

effect	low tercile	middle	high
0.25	0.778 (mean gap .0279)	0.862 (.0541)	0.886 (.0956)
0.50	0.820 (.0245)	0.880 (.0543)	0.934 (.0963)
0.75	0.784 (.0245)	0.922 (.0521)	0.910 (.0917)
1.00	0.754 (.0245)	0.886 (.0499)	0.880 (.0889)

Power is eigengap-dependent, and in the lowest tercile at e = 1.00 it falls below the 0.80 floor (0.754, SE 0.033). The pooled 0.840 is an average over a spread that straddles the floor. Any real-data orientation result must therefore be read against its own recorded eigengap, not against the pooled figure — this is the concrete form of the n-conditional limitation in §8.

Cross-check against the pilots (design decision D6)

Performed before any prose was written. All four required comparisons agree within Monte Carlo error:

quantity	paper-grade (500×999)	ladder CV column (100×199)	design-point pilot (100×199)	verdict
orientation / `angle` @ e = 1.00	0.840 ± 0.016	0.85 ± 0.036	0.88 ± 0.032	agrees (≤ 1.1 pooled SE)
magnitude / `delta` @ e = 1.00	1.000	1.00	—	agrees
shape / `shape` @ e = 1.00	0.996 ± 0.003	1.00	—	agrees
anchor `delta` / `angle` / `shape`	0.036 / 0.046 / 0.048	0.01 / 0.02 / 0.03	0.04 / 0.04 / 0.03	agrees, all nominal

The two failing controls also reproduce: magnitude/angle 0.276 here vs 0.24 in the ladder, magnitude/shape 0.742 here vs 0.74. No material discrepancy was found, so nothing required investigation before writing. The practical consequence is stated at the top of this report: the HOLD is a reproduced, precision-confirmed result, and the 22-fold increase in Monte Carlo work did not change any conclusion the pilots supported.

6. Cross-talk

Off-diagonal rejection rates at e = 1.00 (report/specificity_matrix.csv, figure report/specificity_matrix.png; rows are the mode applied, columns the statistic tested):

mode ↓ / statistic →	`delta`	`angle`	`shape`
magnitude	1.000	0.276	0.742
orientation	0.912	0.840	0.998
shape	0.954	0.796	0.996
translation	0.042	0.042	0.030
`none` (anchor)	0.036	0.046	0.048

Magnitude's off-diagonals are mandatory controls and both fail the α + 2·SE bound of 0.0695: magnitude/angle 0.276 (exceedance 10.3 SE) and magnitude/shape 0.742 (34.4 SE). The localization table (report/phase4_localization.csv) splits them:

magnitude/angle is construction_present, first material at the population_standardized checkpoint, normalized excess rising 0.064 → 0.110 → 0.148 → 0.176 across effects. The δ-scaling surgery genuinely reorients the trajectory in standardized feature space before integration, so the angle test is detecting a real difference that the construction was not intended to create. This is a construction impurity, not evidence against the orientation estimator.
magnitude/shape is classified not_material at every effect — no checkpoint's normalized shape difference exceeded the 0.05 materiality threshold — yet the shape test rejects 74.2 % of the time. The two statements are reconcilable, and the records say how: at magnitude e = 1.00 the observed shape statistic has median 0.0233 against a permutation null whose q95 has median 0.0181 (IQR 0.0015, n = 500, computed from merged.jsonl; the anchor's null q95 median is 0.0095). The observed difference is real and sits above its own critical value — hence 74.2 % rejection — while being an order of magnitude below a 0.05 normalized threshold. The materiality threshold is not calibrated to the shape statistic's scale, so not_material here means "small in normalized units", not "absent". Whether the underlying response is a genuine shape signature of pure δ-scaling or an artefact of how the surgery realizes size changes is the substantive question the HOLD hands forward; it is not resolved here.

Orientation → shape (0.998) is a descriptive gate role, not an acceptance target, and was predeclared as projection-associated cross-talk of the rank-3 stage-supervised latent space (readiness item 2; latent-rank ladder §6, 0.99–1.00 at CV rank). This run reproduces the magnitude of the response and its predeclared role stands unchanged.

One divergence from the predeclared label must be recorded. This run's localization classifies orientation/shape as construction_present at the population_standardized checkpoint for e ≥ 0.50 (normalized excess 0.052 / 0.057 / 0.059), not as projection-associated; the pair that comes back projection_associated at the pls_latent checkpoint is orientation/delta at e = 1.00 (normalized value 0.0601 against a null of 0.0026). The predeclared framing therefore attached the "projection-associated" label to the wrong off-diagonal for this run's data. Because both orientation off-diagonals are descriptive roles and neither gates anything, this changes no verdict — but the paper must not repeat the projection-associated claim for orientation/shape on the strength of this run, and the exit review should reconcile the label with the localization instrument.

Shape's off-diagonals are construction-present descriptives. shape/angle 0.796 is construction_present with a large normalized excess (0.230 → 0.343 → 0.406 → 0.451), and shape/delta 0.954 becomes construction_present at e = 1.00 (0.0525) — the interior-stage permutation moves path length and orientation in feature space, as the geometry audit anticipated.

7. Drivers

Restricted to the declared component — observed — from report/driver_report.csv (report_contract.json: driver_component: observed, because the Phase 4 pilot measured pls_captured precision at 0.15 against observed 1.00; phase4_attribution.csv retains all three components). All 2,000 eligible replicates computed, 0 failed.

effect	transition	precision	recall	mean selected	bootstrap sign stability	bootstrap top-k frequency
0.25	0→1 / 1→2 / 2→3	1.000	0.262 / 0.255 / 0.260	20.0	0.788 / 0.793 / 0.790	0.030
0.50	0→1 / 1→2 / 2→3	1.000	0.134 / 0.134 / 0.134	20.0	0.817 / 0.818 / 0.821	0.030
0.75	0→1 / 1→2 / 2→3	1.000	0.094 / 0.093 / 0.093	20.0	0.839 / 0.839 / 0.838	0.030
1.00	0→1 / 1→2 / 2→3	1.000	0.073 / 0.072 / 0.073	20.0	0.856 / 0.859 / 0.857	0.030

Precision is 1.000 at every effect and transition: every feature the top-20 selection names is a genuine differential site. Recall falls from 0.26 to 0.07 as the effect grows, which is arithmetic rather than degradation — the selection is capped at top_k = 20 while the true driver set grows with the surgery size (nominal 31 sites at e = 0.25 up to 126 at e = 1.00, report/realized_surgery.csv), so recall is bounded above by 20 / |truth|. Within-replicate bootstrap sign stability improves with effect (0.79 → 0.86), and the three transitions agree closely at every effect, as they should for a single global per-omic permutation.

No cross-replicate driver-stability claim is made. Cross-replicate top-k Jaccard and sign agreement (top_k_jaccard, sign_agreement in report/phase4_attribution.csv) are descriptive only: every replicate index draws a fresh differential-indicator set, so the true driver set genuinely differs across replicates and matched seeds pair cells within a replicate index, not across them. A stability claim needs a design that holds the driver set fixed, which this study is not.

Verified in the outputs: driver_report.csv carries no top_k_jaccard or sign_agreement column, and the attribution figure report/phase4_attribution_stability.png is titled "Within-replicate bootstrap stability (observed component)" and drawn from the bootstrap series only.

8. Construction limitations

The orientation power claim is n-conditional. It holds at n = 1200 (300 per group-stage cell) at the isotropic endpoint ρ = 0. Along n at fixed ρ the eigengap is constant while the angle null width contracts, so the recorded eigengap distribution — not n — is the observable that carries the claim to real data. This run makes that concrete: pooled orientation/angle power at e = 1.00 is 0.840, but stratified by eigengap tercile it is 0.754 / 0.886 / 0.880, so the lowest tercile sits below the predeclared 0.80 floor (report/eigengap_stratified_power.csv). A cohort whose recorded eigengap lands in that tercile should not be assumed to inherit the pooled figure.
The orientation surgery's realized latent contrast is not ρ-invariant. The same nominal effect realizes a smaller contrast on a trending baseline (design-point pilot: median observed angle 28° at ρ = 0.5 vs 66° at ρ = 0), so orientation power at another continuity is a different construction. Baseline continuity must not be read as a lever that buys power. This run sweeps no continuity axis — the absence of report/continuity_resolved_orientation.csv is the report's statement that ρ was held at 0.
The eigengap, not ρ, transfers to real data. delta/angle/shape are measured within the constructed PLS latent space; that space is the measurement substrate, and the viz down-projection is display-only.
The flat orientation curve is a property of the angle null, not a power ceiling to be tuned away. Rejection saturates at ≈ 0.84–0.88 from e = 0.25 because the null width grows with the observed statistic (§5). No replicate-count or rank change addresses it; a different pivot would.

Deviations from the predeclared targets, and the revision each implies

deviation	revision implied
`mandatory_control[magnitude,angle]` 0.276 > 0.0695	Method or claim revision. magnitude/`angle` is `construction_present` in standardized feature space, so either the magnitude surgery is corrected to be orientation-pure, or the paper drops the claim that `angle` is specific against a pure size change and reports the response as construction impurity.
`mandatory_control[magnitude,shape]` 0.742 > 0.0695	Method revision, with a diagnostic prerequisite. The records show a real but numerically small `shape` response (observed median 0.0233 vs null q95 median 0.0181) that the 0.05 normalized materiality threshold reports as `not_material`, so the threshold must be recalibrated to the statistic's scale before the localization instrument can classify this pair at all. Until that is settled the specificity of `shape` against pure δ-scaling cannot be claimed.
`power[orientation,angle]` acceptance target not met (monotonicity)	Claim revision. The floor is cleared; the strictly-monotone form of the claim is not supported and should be replaced by a saturating-response claim stated with the eigengap stratification.
orientation/`shape` labelled projection-associated, localized as `construction_present`	Claim revision, no gate impact. Both orientation off-diagonals are descriptive; the label must be reconciled with `phase4_localization.csv` before the paper repeats it.

None of these is a Monte Carlo sample-size question, and none is addressed by raising the replicate count — which the Phase 4 exit gate forbids in any case. Consistent with the change's scope, no remedy is implemented here; the HOLD and these four revisions are handed to the Phase 5 exit review.

9. Reproduction

Reproduction never passes a worker-count override: n_jobs is part of every cell's parameter signature and the config's contract forbids it (the runner exits 2). Parallelize across shards.

export OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 MKL_NUM_THREADS=1
RUN=results/phase5-2026-09-10

# SLURM (partition/resource flags are cluster-specific); STUDY_N_JOBS must stay unset.
sbatch -p 512x1024 --cpus-per-task=1 --mem=2G --time=6:00:00 --array=0-99 \
    --export=ALL,STUDY_CONFIG=$(pwd)/examples/trajectory_power_study/phase5_power_study.json,STUDY_OUT=$(pwd)/$RUN,N_SHARDS=100 \
    scripts/motco_study_array.sbatch

# Locally, in K resumable shards (one process each):
for i in $(seq 0 $((K-1))); do
  uv run python scripts/run_study_shard.py \
      --config examples/trajectory_power_study/phase5_power_study.json \
      --out-dir $RUN --shard-index "$i" --n-shards K --error-policy record &
done; wait

uv run python scripts/motco_study.py merge  --out-dir $RUN
uv run python scripts/motco_study.py report \
    --config examples/trajectory_power_study/phase5_power_study.json --out-dir $RUN

At code revision b8f7daa with config sha256 4f10aa1f…09826, this reproduces the record set whose merged.jsonl has sha256 c96be03e…cb05a. The report writes report/report_contract.json and report/driver_report.csv beside the usual outputs and the gate's phase4_* files; report/ and PROVENANCE.txt are committed, and the shard and merged JSONL stay gitignored as regenerable.