Symptom
Homogenizing a system whose functions include a product of linears (the two-step sphere-cap regeneration's L1 * L2 start, and linear-product start structures generally) fails with
ExpandToFunctionTree: products-of-linears variable count mismatch
Why it matters
The cellular-decomposition reliability work established that complex-gamma moves must track projectively (homogenize + patch) so paths only go to infinity at the end, never mid-path (mid-path affine poles were diagnosed as pre:GoingToInfinity divergence). That fix was applied to the regeneration witness moves and collapsed mid-path divergence — but the product-to-sphere deformation cannot be projectivized because its products-of-linears start system will not homogenize, so that one move family still tracks affinely.
The measurable consequence: the residual preimage-curve cap losses in the whitney gauntlet (1–2 truncated paths per dirty run, SecurityMaxNormReached/pre:GoingToInfinity during regen-slicemove/regen-linprod: sphere-cap), each of which costs a critpointset a genuine point and produces mis-assembled faces downstream. Raising the security ceiling (max_norm/path_truncation 1e14) recovers most, but the principled fix is projective tracking for this move family, which is blocked here.
Ask
Make homogenization handle products-of-linears function structures (or provide an expansion path so the homogenizer sees plain polynomials), so the sphere-cap deformation can join the projective-move policy.
🤖 Generated with Claude Code
Symptom
Homogenizing a system whose functions include a product of linears (the two-step sphere-cap regeneration's
L1 * L2start, and linear-product start structures generally) fails withWhy it matters
The cellular-decomposition reliability work established that complex-gamma moves must track projectively (homogenize + patch) so paths only go to infinity at the end, never mid-path (mid-path affine poles were diagnosed as
pre:GoingToInfinitydivergence). That fix was applied to the regeneration witness moves and collapsed mid-path divergence — but the product-to-sphere deformation cannot be projectivized because its products-of-linears start system will not homogenize, so that one move family still tracks affinely.The measurable consequence: the residual preimage-curve cap losses in the whitney gauntlet (1–2 truncated paths per dirty run,
SecurityMaxNormReached/pre:GoingToInfinityduringregen-slicemove/regen-linprod: sphere-cap), each of which costs a critpointset a genuine point and produces mis-assembled faces downstream. Raising the security ceiling (max_norm/path_truncation 1e14) recovers most, but the principled fix is projective tracking for this move family, which is blocked here.Ask
Make homogenization handle products-of-linears function structures (or provide an expansion path so the homogenizer sees plain polynomials), so the sphere-cap deformation can join the projective-move policy.
🤖 Generated with Claude Code