cb4e82dd

By: ValentinHirschi <valentin.hirschi@gmail.com>

validate threshold overlap centers before interpreting solver status

GL638 point 5586 produced seven overlap subsets under the identity probe
and one full seven-surface overlap after a z rotation. Both SOCP candidates
were over 70 GeV inside every physical surface, but the previous whitelist
discarded NumericalError while accepting InsufficientProgress.

Check actual surface energies first in both overlap implementations. Return
no overlap only after PrimalInfeasible without a valid center; propagate
unresolved solves through pair and maximal-subset discovery. Keep existing
subspace, native-complement, mass and strict-interior checks unchanged.
Add structured SOCP diagnostics and an exact seven-instance GL638 routing
fixture that checks identity, z and Euler rotations without a generated state.

Validation: cargo fmt; locked workspace/all-targets cargo check; 21 focused
overlap/localization nextest tests; clippy with warnings denied. The focused
fixture's matrices reproduce the captured NumericalError/InsufficientProgress
statuses while retaining the full overlap. No serialized state/schema change.

All 71 full-state replays completed. Point 5586's explicit z/Euler complex
rotation differences fall to 3.01e-12/3.34e-12 (largest per-cut 3.62e-12).
Both maxima, 48 soft-limit controls and 11 finite portable controls are
bit-identical to their frozen references. The two known exact A/P invalid
cases persist; forced Arb at point 5586 still reports finite instability
against its strict 1e-12 target. This does not claim an A/P residue cure.

User prompts:

Continue as planned, but look into the current implementation, it should already offer such flexibility.
But feel free to add some if you need be (but make sure it's steered through runtime integrand toml parameters so the user can easily access it). And it's only weakly tested, so if you find any bug there you can also adjust it.

Ok commit+push what you got here?
Then us there anyway you can think of improving the situation regarding the remaining integrable singularity here? What kind of sampling would be needed, can you experiment with various solutions to see if something can further improve the situation? Especially around max weights found?
You can now do longer integration run to monitor the behaviour, on 20 cores. Make sure you don't waste tokens though when waiting for the outcome.

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