Realized Generator Geometry — Phase 2 Findings
Decision
The Phase 2 gate is resolved at the construction level. MOTCO now records four geometry checkpoints for every generated replicate, which separates exact construction, pooled preprocessing, finite sampling, and PLS projection:
population_native
↓ pooled observed-fitted block scaling
population_standardized
↓ finite-sample cell-mean error
observed_standardized
↓ fitted PLS projection
pls_latent
The generator modes are not required to form a perfectly diagonal mode-by-statistic matrix. Their revised contracts are:
- Orientation is a pure coordinate relocation in native methylation M-space. The biological CpG→gene→protein cascade makes it a joint multi-omic program relocation with expected magnitude and shape co-movement.
- Shape/relocate is a free biological bend. It changes the interior-stage program and may also change path length and principal orientation.
- Shape/magnitude is an interior-stage amplitude perturbation and is intrinsically mixed; retain it as a stress-test construction, not a shape-specific positive control.
- Magnitude/all is pure within native methylation but scales only one of three omic blocks, so joint standardization can introduce orientation and shape co-movement even though the established production test remains empirically specific.
- Translation remains the negative geometry control: its exact population delta, angle, and shape stay at numerical zero before and after standardization.
These interpretations replace the assumption that requested mode alone identifies the realized pre-integration geometry. All subsequent operating-characteristic studies must report the realized checkpoint diagnostics alongside rejection rates.
Small matched-seed characterization
This implementation check used two matched seeds and three effects. It is sufficient to validate the decomposition and locate construction cross-talk, but it is not a power study and its noisy observed/PLS values must not be treated as stable operating characteristics.
Parameters:
- seeds:
0,1 - effects:
0,0.5,1 n_samples=80,n_stages=4,p_dmp=0.2- PLS CV: one repeat, two inner and outer folds, at most three components
- no permutations
Orientation
Native methylation preserves equal path length and shape while rotating direction. At effects 0.5 and 1.0, its mean realized angles were 57.89° and 73.40°, with delta 0 and shape at numerical zero.
The cascade is the first source of cross-talk. At effect 0.5, native expression showed angle 64.99°, delta 1.12, and shape 0.066; native proteomics showed angle 59.32°, delta 1.36, and shape 0.037. Consequently, standardized joint population geometry was already mixed before sampling or PLS:
| Effect | Joint population angle | Joint population delta | Joint population shape |
|---|---|---|---|
| 0.00 | 0.00° | 0.00 | 0.000 |
| 0.50 | 67.41° | 1.43 | 0.029 |
| 1.00 | 85.35° | 1.78 | 0.052 |
The requested effect maps monotonically to the exact joint angle in this check. The nonzero joint delta and shape are construction/cascade behavior, not PLS leakage.
Shape
Both constructions were mixed at the exact-population checkpoint.
For shape_kind=relocate, joint standardized population geometry increased as follows:
| Effect | Angle | Delta | Shape |
|---|---|---|---|
| 0.00 | 0.00° | 0.00 | 0.000 |
| 0.50 | 53.88° | 1.97 | 0.050 |
| 1.00 | 85.45° | 7.61 | 0.081 |
The relocation affects all three native omic layers through the cascade, confirming that it is a free multi-omic bend rather than an isolated Procrustes-shape intervention.
For shape_kind=magnitude, only native methylation changes because the binary cascade indicators remain unchanged. The interior-stage amplitude change nevertheless produces large angle and delta responses in that layer. Joint standardized population geometry was:
| Effect | Angle | Delta | Shape |
|---|---|---|---|
| 0.00 | 0.00° | 0.00 | 0.000 |
| 0.50 | 63.54° | 4.99 | 0.064 |
| 1.00 | 75.26° | 8.99 | 0.112 |
This construction is useful for sensitivity analysis but cannot support a claim of shape specificity.
Controls and sampling
The exact none and translation checkpoints remained invariant. Observed standardized statistics were nonzero even for these controls because the two groups are independent finite samples. At n_samples=80, the PLS null angles were particularly unstable, so this run does not update the medium-pilot power conclusions.
Magnitude was pure in native methylation (effect 0.5/1.0 delta 31.97/63.94, angle and shape approximately zero) but became mixed in standardized joint population space (angle 13.56°/22.14°, shape 0.012/0.019). This occurs because methylation is scaled while expression and proteomics retain their baseline trajectories.
Reproduction
Run from the repository root:
uv run python scripts/realized_geometry_characterization.py \
--seeds 0,1 \
--effects 0,0.5,1 \
--n-samples 80 \
--n-stages 4 \
--pls-repeats 1 \
--pls-cv1 2 \
--pls-cv2 2 \
--pls-max-components 3 \
--out-dir /tmp/motco-phase2-small
The driver writes config.json, replicate-level JSONL, a long-form summary CSV, and a monotonicity CSV. For the medium pilot, use the roadmap sample size and effect grid with more matched seeds and the production PLS CV settings.
Gate to Phase 3 and the medium pilot
Phase 3 orientation-driver attribution can proceed using the revised interpretation: it should explain the joint molecular-program direction captured by PLS, not claim a pure methylation-only rotation. Before the medium pilot, retain all four checkpoint diagnostics and predeclare interpretation against realized geometry rather than requested mode labels alone.