[cailmdaley]

Full-area v2 analytic shape noise is 14–19% below measured-pair noise over 12–83′; cosmo_val now uses measured effective pairs by default.
On the fixed 2075.3 deg² B vectors, the noise-only correction changes the fiducial COSEBIs B PTE from 0.43798 to 0.64339.
Closes #431.

Mechanism and convention

For unordered TreeCorr auto 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, with per-component dispersion s.
OneCovariance c8755d6 accepts [tabulated inputs files] npair_mm_file and uses ordered counts: supply 2 W_b²/Q_b, making its 4 s⁴/N_ordered equal V_b.
The total two-component RMS is √2 s; mixing conventions gives a factor of four.

A separate cached NN rule reads only positions and weights, counts with w and w², and persists W, Q and nominal geometric centres on each exact covariance grid.
This avoids OneCovariance's unsafe rebinning of effective counts and requires no shape measurement or blind access.
covariance.shape_noise: analytic restores the old uniform-area path; other workflows and implicit tomographic targets retain analytic defaults.
No changes to blinding, signal vectors or other covariance terms.

Full-area B-only evidence

Controlled substitution, not a fresh full-area OneCovariance run: replace only the analytic ξ noise diagonal, then propagate with the original operators and fixed cached B vectors.
The analytic/pair noise ratio over 12–83′ is 0.80879–0.85565 (median 0.83931); it is 0.84051 near 30′ and 0.82209 near 60′.
The measured W reproduces the integration-ξ pair metadata to 1.13×10⁻¹³ maximum relative difference.

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

The covariance operators reproduce the cached COSEBIs/pure-B covariances to relative error 3.51×10⁻¹⁶ / zero at checked precision; all reported B sub-covariances pass Cholesky validation.
No E-mode χ²/PTE or cosmological inference was computed.
This is not catalogue acceptance or validation of mask-dependent mixed/sample-variance terms; the measured correction includes selection and weight variation as well as boundaries.

Validation and figures

• Slurm 25030338: 26 passed, 2 site-dependent skips, plus real OneCovariance analytic and tabulated-count noise-only probes matching 4 s⁴/N_ordered to its text precision.
• Full positions/weights count 25028179: 24 CPUs, 128000 MB, 1h32m41s; B-only evidence 25028544: 4 CPUs, 16 GiB, 58 s, in sp_validation-ddd58fe0.sif with checkout-first PYTHONPATH.
• Ruff check/format, git diff --check and independent static review pass.
  Derivation, interface and resource/migration notes: docs/pair-count-noise.md.

Analytic / measured-pair shape-noise variance vs θ, for the full v2 area (2075 deg², solid) and the 33.5 deg² pilot (dashed). Below ~1′ the analytic term is too large: more close pairs are measured than a uniform field predicts. Beyond ~7′ the full-area ratio settles at about 0.85 and stays nearly flat to 100′. The pilot instead falls steeply past 30′, the signature of its patch edges. A flat full-area deficit points to mask holes and weight/depth variation rather than survey edges, so the correction does not shrink with area.

B-mode PTEs at the fixed 12–83′ cut, analytic vs pair-count noise. All pass either way at full area. The correction moves each PTE up by roughly 1.3–2×, as expected for a noise term that was ~16% low.

Figures live in docs/validation/pair-noise/ on this branch. The same directory holds report.html, bmode-noise-results.json, noise-per-bin.csv, REPRODUCE.md, scripts and logs.
run/, latest/, production and #430's branch are untouched.

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