research: correct the circular Sersic hazard classification

[Jammy2211]

Summary

• evaluate circular Sersic behavior in the actual fitted ell_comps_0/1 coordinates
• replace the incorrect uniform axis-ratio prior mass with the analytic two-dimensional Gaussian disk mass
• prove the former q-angle structural finding is not sampler-reachable because angle is derived, not independently sampled
• add an off-centre full-FitImaging JAX gradient probe at the exact circular default-prior mean and a bounded Cartesian neighbourhood
• resolve the stale structural record and persist the real exact-origin non-finite-gradient finding under a new stable ID

Evidence

• q >= 0.99 corresponds to ||ell_comps|| <= 0.0050251 and contains 1.4028e-4 of the default independent Gaussian(0, 0.3) prior, not 1%
• the off-centre likelihood at ell_comps=(0, 0) is finite (-15.477240141252718)
• JAX returns [NaN, NaN] for its exact gradient there
• gradients at the ±1e-8 and ±1e-6 Cartesian axes are finite and have norm about 1.27892
• the explicit 1e-8 Gaussian neighbourhood contains 5.56e-16 prior mass; exact continuous prior mass is zero, but deterministic initialization at the prior mean remains reachable

Classification

Resolved:

• likelihood.imaging-sersic.circular-orientation-degeneracy

New:

• likelihood.imaging-sersic.ell-comps-origin-nonfinite-gradient

The post-change likelihood scan still contains three persistent IDs overall: conditioning, active-set kinks, and this corrected JAX-gradient finding.

Impact

Profiling and generated evidence only. This PR does not modify PyAutoGalaxy, priors, likelihood values, public API, configuration, or release behavior. The evidence recommends a bounded PyAutoGalaxy source task that preserves physical circular symmetry while making the combined Cartesian geometry path differentiable.

Validation

• ruff check .
• scoped ruff format --check
• pytest scripts/misc/test/ — 38 passed
• Python compile-all for changed modules
• full NumPy/JAX likelihood scan — 3 persistent records
• scan.py --subject likelihood --check — 3 persistent IDs, no new uncommitted IDs
• scripts/misc/tooling/build_readme.py --check
• hazards smoke path under AUTOLENS_PROFILING_SMOKE=1
• generated non-finite-gradient plot visually reviewed

Merge authorization

The user explicitly authorized merging each bounded follow-up once its required CI is green and continuing the campaign. Do not release.

Closes #121