7818ffcb

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

certify the alternate endpoint of an exhausted radial bracket

Preserve existing accepted solves, then test the other represented endpoint
with the same residual allowance and fresh candidate-specific consistency
checks. Retain the original error/history when that candidate is rejected.
The actual GL638 regression pins the prior strict failure and original-equation
bounds, including an inconsistent-derivative negative case.

Validation: 35 broader tests plus the final strengthened overlapping fixture;
format/check/clippy pass with no changed-line warnings. Optimized build7 passes.
The exact previously failing complete Sample now returns stable Double and Arb
results with six cuts and identical canonical point/J/partition; all 25 native
accuracy checks pass. Preserve the tiny cut-2 component underflow diagnostic,
original interrupted confirmation and deliberately interrupted build6 evidence.
No proposal/tolerance change, further performance optimization, partial pooling
or completed-confirmation estimate is claimed.

User requests:
Continue as planned, but after this current round of optimisation completes for the joint advanced sampling, stop optimizing further; we will accept current advanced sampling performance as-is for now. Instead focus on verifying that the physics expectation are met. That is:

i) The integrand weight in the HZ corner are now bounded.

ii) The variance of at least the absolute value of the integrand, but hopefully also of the integrand itself, is improved. (compare the MC error at a) fixed sample counts without advanced sampling, b) with only combinations of channels with simpler non-joint advanced maps, c) with the full optimal combination involving also joint advanced sampling maps)

iii) For a reasonable number of sample gain confidence of the fact that the case c) above leaves a bounded maximum weight, and at least smaller than the one found in b) and c). Also analyze what is the origin and cause of the remaining max weight point in b) and c) setups.

iv) Provide you current best estimate (central value + error) you current have now on GL638 cross-section. You can use up to 30 cores and 300 GB of RAM; but use less if you don't see performance scale linearly with number of cores until 30.

Continue as planned, but did you already do a local instpect/approach of the HZ corner to establish that the new joint map makes the GL638 weight bounded there now?

(
continue as planned, but also consider different combination of channels which you think are optimal,e.g. something like:

| ChannelTarget | |
| --------------- | ----------------------------------------------- |
| Cut 0 | `cut(2,6,12,13)` |
| **Cut 1 + H/Z** | `cut(2,6,10)` combined with joint H/Z focusing |
| Cut 2 | `cut(2,6,7,13,14)` |
| Cut 3 | `cut(2,4,12)` |
| Cut 4 | `cut(2,4,10,13)` |
| Cut 5 | `cut(2,4,7,14)` |
| Soft coverage | One LMB: `[6,12,13,14]`, containing both gluons |

Although the soft channel may not even be necessary.

Experiment with different combinations.

So toggling on/off the join mapping should not be by itself, but rather always in the presence of cut channels.

but of course also compare against the baseline of just the optimized LMBs (which is what we had before).

)

Timeline