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cosmo_val: pair-count shape noise in the OneCovariance covariance #431
Description
OneCovariance's uniform-area shape noise is 14–19% below measured-pair noise across 12–83′ on the full 2075.3 deg² blinded v2 sample.
Draft PR #432 implements the default correction on branch cosmo-val-paircount-noise.
The pilot's fixed-cut COSEBIs B PTE had changed from 0.00502 to 0.0581 under the same noise-only test; the full-area comparison is below.
For unordered pairs, W_b = Σ w_i w_j and Q_b = Σ (w_i w_j)² give V_b = 2 s⁴Q_b/W_b², where s is the per-component dispersion.
OneCovariance accepts [tabulated inputs files] npair_mm_file and uses ordered counts, so supply 2 W_b²/Q_b at nominal geometric centres.
Its 4 s⁴/N_ordered then equals V_b; the total RMS is √2 s, and mixing the conventions gives a factor of four.
The workflow caches positions/weights-only NN counts on each covariance grid, with covariance.shape_noise: analytic retaining the old path.
Full-area controlled substitution
Only the analytic ξ shape-noise diagonal is replaced; cached B vectors and all other covariance terms stay fixed.
This is not a fresh full-area OneCovariance run.
The analytic/pair noise ratio across 12–83′ is 0.80879–0.85565, median 0.83931.
Measured W matches the cached integration-ξ pair metadata to maximum relative difference 1.13×10⁻¹³.
| Fixed 12–83′ statistic | dof | Analytic-noise PTE | Pair-noise PTE |
|---|---|---|---|
| COSEBIs B, 20 modes | 20 | 0.43798 | 0.64339 |
| Pure-B ξ₊ | 7 | 0.34732 | 0.48005 |
| Pure-B ξ₋ | 7 | 0.071519 | 0.12853 |
| Pure-B combined | 14 | 0.15656 | 0.29359 |
No E-mode χ²/PTE or cosmological inference was computed.
The correction includes observed selection/weight variation as well as boundaries; mixed/sample-variance mask effects and catalogue scientific acceptance remain separate questions.
Slurm 25030338 passed 26 tests, 2 site-dependent skips, plus real OneCovariance analytic/tabulated noise-only normalization probes.
The full pair measurement was job 25028179 (24 CPUs, 128000 MB); B-only propagation was 25028544 (4 CPUs, 16 GiB), both in the specified container.
Figures are local, not source-branch assets; hosting/embedding is left to the orchestrator:
/scratch/cdaley/cosmo-val-v2/pairnoise/noise-ratio-full-vs-pilot.png/scratch/cdaley/cosmo-val-v2/pairnoise/bmode-ptes-full.png
That directory also holds the self-contained report.html, numerical JSON/CSV, scripts, logs and REPRODUCE.md.
No changes to blinding, run/, latest/, production or #430's branch.
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