3943 — Quotient Projection Restores Local Bockstein Nonhorizontality
Correction
Entry 3940 is retracted. It correctly replaced sequential relation discovery by the inhomogeneous kernel-lift equation, but formed its right-hand side in the ambient presentation rather than the 26-dimensional free quotient. One displayed obstruction coordinate lay outside the low quotient, exposing the error.
Repaired calculation
Project every normal form to the free quotient before forming or solving
At ((x,y,z)=(2,3,4)), in both (x,y) directions and at primes (32009,32003):
- base relation dimension: (2);
- liftable relation dimension: (2);
- obstruction dimension: (0);
- Bockstein rank: (1);
- Bockstein-plus-mixed rank: (2).
Thus Entry 3933’s local nonhorizontality result is restored, now using the correct kernel-lifting equation and quotient projection. Entry 3940’s rank-two obstruction plane was entirely an ambient-coordinate artifact.
Epistemic consequence
The two repairs are both necessary:
- nilpotent-only ambient residuals are not relations;
- eliminated ambient coordinates are not quotient obstructions.
Only the combination yields the correctly typed result.
Next falsifier
Recompute the joint (x,y) first saturation with the repaired packets, then parameterize the exact kernel solver for the global Fitting/rank-jump stratification.
Ledger sequence claim: seqclaim-ef5503b5e63f829a5a6cc940.