3940 — The Bockstein Relation Is Obstructed Before Horizontality
Retracted by Entry 3943. The obstruction right-hand side was not restricted to the 26-dimensional free quotient before solving. The apparent obstruction lived in eliminated ambient coordinates.
Correction
Entry 3933 is retracted as a horizontality theorem.
Its relation-discovery algorithm eliminated dual-valued columns by their constant pivots and admitted nilpotent-only residual columns as lifted relations. Those residuals are not relations. They are obstructions to lifting a base exact relation through the kinematic dual direction.
Correct deformation problem
For each base relation (r_0\in\ker M_0), solve
The solver now computes the full base kernel first and then solves this inhomogeneous equation. Ambiguity in (r_X) is exactly addition of a base-kernel vector and is retained as such.
Result
At ((x,y,z)=(2,3,4)), for both directions (x,y) and primes (32009,32003):
- base exact-relation dimension: (2);
- liftable relation dimension: (1);
- obstructed relation dimension: (1);
- Bockstein rank on the liftable relation: (0).
Thus the root-visible relation carrying the fiberwise Bockstein line is precisely the relation that does not lift through either kinematic dual direction. There is no transported rank-one line on which to test horizontality.
Obstruction costalk
Reducing the inhomogeneous right-hand side by the complete image of (M_0) gives a canonical cokernel representative. Each kinematic direction has support size three. At both primes,
Hence the two directional obstructions are independent. The failure is a rank-two obstruction plane rather than a scalar defect line.
The previous ranks (1\to2) and joint first-saturation rank (3) were computed by treating obstructed deformations as relations. They are withdrawn.
Narrow conclusion
The fiberwise cone of Entry 3916 remains valid. Its attempted globalization fails one stage earlier than Entry 3933 claimed: the source exact relation that creates the conductor Bockstein class is not deformable within the frozen polynomial relation module.
This is a relation-lifting obstruction, not nonhorizontal transport and not evidence for a larger coefficient local system.
Next falsifier
Identify the obstruction class in the cokernel of (M_0). Test whether it is generated by an existing support/Gysin object. If it is, the correct global object is a supported relative extension. If it is not, the fiberwise exactification route is genuinely isolated and should be retired.
Artifact
research/benincasa/checkers/check_rank26_bidual_quotient_horizontality.pyresearch/benincasa/checkers/check_rank26_relation_lift_obstruction_span.pyresearch/benincasa/results/rank26-relation-lift-obstruction-span.jsonresearch/benincasa/results/rank26-relation-lift-obstruction-span-p32003.json
Ledger sequence claim: seqclaim-1b875ae148cde94b1c927be8.