Four points and modular methods

The predecessor reports resource failures on a 15\,GB machine, multi-gigabyte ghost-box expressions, stopped symbolic or numerical-point paths, absent higher vertices, and ansatz widths $27243+4992$ for $hhhh$ and $4329+981$ for $Kchh$ SuppliedBot,CheungXVIR. These are implementation-specific records, not mathematical impossibility.

A future certificate needs the actual original matrix, exact field, rank, original minor, complete left kernel, and target membership. Choosing reconstruction or IBP is not evaluating it.