Magnitude-construction diagnostic — 2026-09-10

Run: results/magnitude-construction-2026-09-10/ · Driver: scripts/magnitude_construction_diagnostic.py · Records read: results/phase5-2026-09-10/merged.jsonl (the paper-grade run, 9,500 units)

The paper-grade Phase 5 run returned gate decision HOLD on the two magnitude mandatory controls (magnitude/angle 0.276, magnitude/shape 0.742 against a 0.0695 bound). This diagnostic establishes what causes those responses and whether they are fixable, so the Phase 5 exit review can choose between a method revision and a claim revision on evidence.

Both verdicts point the same way: method revision. The magnitude surgery's off-target response is entirely an artefact of scaling one omic block's δ and not the others, and a construction that scales all three together is exactly size-pure in the measurement space. Nothing about the angle or shape estimators is implicated.

1. Mechanism: the response exists only in the concatenation

magnitude_kind='all' (semisynthetic.py) scales delta_methyl alone and leaves delta_expr and delta_protein at baseline, while the measurement space standardizes and concatenates all three omic blocks (evaluation.py). The per-omic scopes recorded in the paper-grade run show the consequence directly (block_decomposition.csv, checkpoint population_standardized, median over 500 replicates):

statistic	scope	e = 0.25	0.50	0.75	1.00
`angle`	methylation / expression / proteomics	0.0000	0.0000	0.0000	0.0000
`angle`	joint	6.6978	12.1199	16.5890	20.3293
`shape`	methylation / expression / proteomics	0.0000	0.0000	0.0000	0.0000
`shape`	joint	0.0076	0.0138	0.0187	0.0226
`delta`	methylation	9.9148	18.1365	24.8473	30.3300
`delta`	expression / proteomics	0.0000	0.0000	0.0000	0.0000

block_localization_summary.csv records the verdict as joint_only = True for magnitude/angle and magnitude/shape at population_standardized: every individual block is flat while the joint scope moves.

Within each omic block the surgery is exactly size-pure. The zeros are analytic, not small — angle is 0.0000 and shape lands at 8.4e-18, floating-point dust from the Procrustes routine. Only delta moves, and only in the block whose δ was scaled. The off-target response is created by concatenation: lengthen one component of a vector and leave the others, and the vector rotates. That is ordinary geometry, not a defect in any estimator.

Across all four checkpoints the causal chain is fully attributable:

checkpoint	per-block `angle`	joint `angle`
`population_native`	0.0000 at every effect	(no joint scope recorded)
`population_standardized`	0.0000 at every effect	6.70 → 20.33
`observed_standardized`	constant in effect (7.91 expression, 6.24 proteomics — a sampling floor)	10.70 → 21.96
`pls_latent`	(joint only)	3.30 → 7.59

Two things follow that correct beliefs recorded in the repository:

It is not the methylation rev.logit nonlinearity. specificity.py previously stated that magnitude bends shape through that nonlinearity. At population_native — before any standardization and before any sampling — the per-omic angle and shape are 0.0000 at every effect, so the nonlinearity does not bend the methylation trajectory at all. The module docstring is corrected in this change.
The PLS projection attenuates the rotation rather than creating it. Joint angle is 20.33° at population_standardized and 7.59° at pls_latent. Whatever the latent space does here, it reduces the off-target geometry it is handed.

2. Constructibility: a size-pure magnitude change is realizable

The open question was whether scaling every omic's δ together survives per-block standardization, which z-scores each block on pooled data and so divides back out part of what the scaling adds. It does (uniform_delta_comparison.csv, population-standardized geometry, n_stages = 4):

construction	e	joint `delta`	joint `angle`	joint `shape`	max block `angle`
production (`delta_methyl` only)	0.25	5.9456	6.2898	1.095e-02	0.000e+00
production	1.00	18.1360	18.9097	3.288e-02	0.000e+00
uniform probe (all three δ)	0.25	14.9623	8.538e-07	9.558e-16	8.538e-07
uniform probe	1.00	44.7980	2.561e-06	9.995e-16	1.479e-06
anchor (e = 0, either)	0.00	0.0000	0.000e+00	1.008e-15	0.000e+00

The uniform-δ construction grows the trajectory strongly (joint delta 14.96 → 44.80) while holding joint angle at 8.5e-07 → 2.6e-06 and joint shape at ~1e-15 — the anchor's own floating-point floor — at every effect. Per-block standardization does not defeat it. A genuinely size-only magnitude change is constructible in this measurement space.

One calibration caveat for whoever adopts it: the effect axis is not comparable between constructions. At e = 1.00 the uniform probe reaches joint delta 44.80 against production's 18.14, because three blocks grow instead of one. A corrected mode needs its own effect-size calibration before its power curve can be read beside the existing one.

3. Shape-free confirmation

At two stages the trajectory is a single step and Procrustes shape is undefinable, so the orientation response can be observed with no possibility of shape contaminating it (uniform_delta_comparison.csv, n_stages = 2):

n_stages	construction	e	joint `delta`	joint `angle`	joint `shape`
2	production	1.00	5.4250	19.0470	(undefinable)
2	uniform probe	1.00	12.9072	1.000e-06	(undefinable)
4	production	1.00	18.1360	18.9097	3.288e-02
4	uniform probe	1.00	44.7980	2.561e-06	9.995e-16

The production construction's joint angle is 19.05° at two stages against 18.91° at four — indistinguishable. The rotation is real and independent of the shape-removal step; it is not an artefact of Procrustes alignment in the four-stage design. This was a confirmation of an already-analytic finding and it confirmed it.

4. Localization: the instrument, recalibrated

localize_off_diagonal normalizes delta by mean path length and angle by 180°, but passes shape through raw. At e = 1.00 the joint values normalize to angle 20.3293/180 = 0.1129 (≥ the 0.05 cut → material) and shape 0.0226 (< 0.05 → not_material) — while the RRPP shape test rejects at 0.742. A single absolute cut cannot serve a statistic whose entire response range lies below it.

The recalibrated null_dispersion rule judges each excess in units of the zero-effect null's dispersion at the same checkpoint. Where that dispersion is degenerate — zero or dust, as it is at every population checkpoint for an analytically null construction (measured: delta sd exactly 0.0, angle sd 8.7e-07, shape sd 3.5e-16) — it falls back to "excess exceeds the dust tolerance", the limit of the rule as the null variance goes to zero. Each row records which path decided it.

Classifications under both rules (localization_by_rule.csv); 12 of 32 pairs change:

mode / statistic	e	absolute rule	null-dispersion rule
magnitude / `angle`	0.25–1.00	`construction_present`	`construction_present`
magnitude / `shape`	0.25–1.00	`not_material`	`construction_present`
orientation / `delta`	0.25–0.75	`not_material`	`construction_present`
orientation / `delta`	1.00	`projection_associated`	`construction_present`
orientation / `shape`	0.25	`not_material`	`construction_present`
orientation / `shape`	0.50–1.00	`construction_present`	`construction_present`
shape / `angle`	0.25–1.00	`construction_present`	`construction_present`
shape / `delta`	0.25–0.75	`not_material`	`construction_present`
shape / `delta`	1.00	`construction_present`	`construction_present`
translation / `angle`	0.25–1.00	`not_material`	`not_material`
translation / `shape`	0.25–1.00	`not_material`	`not_material`

Two properties of that table matter more than the individual rows:

The negative control is preserved. Translation stays not_material on all eight rows under the recalibrated rule. The rule is calibrated, not merely permissive — its population off-target geometry is exactly zero, so nothing promotes it.
No response anywhere remains projection_associated. The paper-grade run's single such classification, orientation/delta at e = 1.00, becomes construction_present. Under the absolute rule its population-standardized excess fell below the 0.05 cut, so localization skipped forward to pls_latent; once the population checkpoint is judged against its own (degenerate) null, the response is seen where it actually first appears.

Interpretive shift this implies, stated plainly. Because population checkpoints carry analytically zero nulls, the recalibrated rule makes them very sensitive: any non-dust population-level off-target geometry now localizes as construction_present. That is the right standard for a localization instrument — a construction with any real off-target population geometry is impure, by definition, and the old cut was hiding real impurity behind an arbitrary threshold. But it answers "is this construction exactly pure?", not "is the impurity large enough to matter". The latter is read from the response magnitude, which the same tables carry. The exit review should not read construction_present as a severity claim.

5. What this hands the exit review

deviation from the paper-grade run	what this diagnostic establishes	revision implied
`mandatory_control[magnitude,angle]` 0.276	Block-asymmetric δ scaling; exactly size-pure within every block; rotation confirmed shape-free at two stages; a uniform-δ construction is exactly pure in the joint space	Method revision. Correct the magnitude construction to scale all omics' δ together, recalibrate its effect axis, and re-measure. The `angle` estimator is not implicated.
`mandatory_control[magnitude,shape]` 0.742	Same mechanism; and the response was real all along — the 0.05 absolute materiality cut mis-reported it as `not_material`	Method revision, same fix. The diagnostic prerequisite the paper-grade report named is discharged: the threshold is recalibrated and the pair now classifies.
orientation/`shape` predeclared "projection-associated"	Not supported. Orientation's response is present within each omic block (max block `angle` 90.08° against joint 89.93°; max block `shape` 0.108 against joint 0.059), and under the recalibrated rule no pair in the study is `projection_associated`	Claim revision. Drop the projection-associated framing for orientation; it is construction-present cross-talk of a per-omic feature permutation. No gate impact — both orientation off-diagonals are descriptive roles.
`power[orientation,angle]` monotonicity	Untouched by this diagnostic — it is a property of the `angle` null's pivotality, not of a construction	Claim revision, as the paper-grade report stated. Out of scope here.

Nothing here adopts a revision. The uniform-δ construction is reachable only from the diagnostic entry point (generate_semisynthetic_trajectory(..., _probe_uniform_delta=True)); it is not a magnitude_kind value, and a study configuration naming it is refused at load time. Adopting it as the production magnitude mode is the exit review's decision.

6. Reproduction

export LD_LIBRARY_PATH=/nix/store/61a1nwx3w6rqyaisj5rn1sal1981apm7-zlib-1.3.2/lib:$LD_LIBRARY_PATH
python scripts/magnitude_construction_diagnostic.py \
    --merged results/phase5-2026-09-10/merged.jsonl \
    --out-dir results/magnitude-construction-2026-09-10

Steps 1 and 2 read committed records only. Step 3 generates data but computes analytic population geometry — no sampling, no RRPP, no PLS fit — so the whole diagnostic runs on a workstation in minutes with no cluster and no R runtime. The LD_LIBRARY_PATH export is the local numpy/zlib workaround, not a project requirement.