By: ValentinHirschi <valentin.hirschi@gmail.com>
solve threshold projections with a shared dimensionless scale Use the existing radial root owner on unnormalized active displacements, retain alpha as the authoritative projection, and derive physical rstar and radial derivatives from it. Align dual bases to the actual native representative and share reconstruction between ordinary and mixed raised-cut paths. The existing implicit-function evaluator now differentiates alpha(t). Correct its Taylor/raw-partial factorial conversions, after an independent old-owner analytic regression reproduced a second-order error (2.446370096 vs 1.991231474). Keep the same generated evaluator and saved-state layout. This is a prerequisite for certified CT-star sampling. It does not yet add sampling/physical geometry handoff, stable star branches or a joint normal map. All six frozen GL638 cuts have max_occurrence1, so the higher-order IFT defect was not dispatched in the recorded pilots. User prompt: "Just a status question—please continue your current orchestration unchanged: where does the joint two-normal density sit in the implementation sequence, and what prerequisites remain before you reach it? (direct-H focusing alone is not expected to bound the previously identified corner’s weights.)" Validation: - Independent current-owner analytic regression failed before correction, passed after correction without weakening the expectation. - Three focused nextest regressions pass (--retries0): native Double/Quad/Arb alpha/null/affine/mixed geometry, generated raised derivatives/roundtrip, and conditional cut both-sides/raised-sum handling. - Native higher-order coefficients checked at1e-27 with sub-binary64 inputs. - Core --tests and API/differential dependency cargo check pass. - Core all-target clippy passes with zero changed-line warnings; formatting and git diff --check pass. - Full GL638 native replay and differential rerun remain the next validation milestone; prepared inputs preserve all936 orientations, sixcuts and fullUV.