By: ValentinHirschi <valentin.hirschi@gmail.com>
extend sampling plan with amplitude and infrared benchmarks Record reproducible UV-finite two-loop kite and double-box amplitude candidates, real threshold/orientation witnesses and the missing production amplitude surface registration. Require actual graph-backed correctness and fair physical variance comparisons, independent of Cutkosky rescaling. Add independently reviewed LU h-matched radial profiles, raised-residue and reference-tail requirements, and portable numerical comparisons. Preserve a future collinear extension with exact cylindrical/prolate maps, normalized profiles, soft-endpoint analysis, and typed frame/precision requirements. Update the active goal's referenced plan and implemented-architecture status. Validation: independently reproduced h-profile output, pinched-map finite difference determinants, boosted kite intersection residuals and normal rank; reviewed local links and git diff --check. Generation timings are not physical advanced-sampling integration results or evidence of a GL638 improvement. User requests: Continue as planned, but now that you'll have a sampling density with a variable aligned directly with the "distance to the cutkosy cut", then it'd be natural to choose a sampling density for that variable whose jacobian is the inverse of the Cutkosky cut h-function! Of course, the CDF arising from the h-function is not exactly invertible, but one can use a density for that variable which yields a jacobian close to that requirement (i.e. approximates it "well enough"). Continue your orchestration as planned, but launch a subagent on that topic and based on its findings, edit the goal / plan and research documents to include that element too. Also launch a subagent to consider the possibility to add a sampling for IR-pinched surfaces (i.e. given a cutkosky cut, some surfaces are then pinched, i.e correspond to collinear segment). In that case the corresponding optimal sampling would be a light-code decomposition along that segment, exposing in the measure (k_perp)^2 for the normal variables to that segment. This is not immediately useful or necessary to add, but it would be interesting for the agent to study how the current architecture could make this possible at a later point. I.e. make sure to steer the architecture of the implementation so that such a later extension may be possible (but not do it right now, unless it seems like it would be simple, the agent must establish this too). Continue as planned, but also add that the advanced sampling implementation should also be tested for amplitude multiloop graphs (not just the cross-section ones), where it is of course simpler as there are no cuksosky cuts. Spawn a subagent to propose good candidates, but the 6-photons 2-loop graphs in the presence of thresholds is an idea, but it may be slow to generate, I would then rather consider some UV finite scalar 2-loop amplitude topologies. Let a subagent what would be best. This allows to not only test the implementation of advanced sampling on amplitude, but also test the new advanced surface maps in a simpler context with not cutkosky cut rescaling, and also monitor the impact on the variance for these cases.