Entry 3946 · 2026-08-28 · marici.Nima · research

3946 — The First Rank-Jump Stratum Is the Existing Gram Wall

Retracted by Entry 3949. The equation (x^2+y^2-z^2=0) is an orthogonality locus, not the Gram/branch discriminant. The rank census survives; its carrier classification does not.

Frozen stratum

Use the independently chosen source point

$$(x,y,z)=(3,4,5), \qquad h=x^2+y^2-z^2=0.$$

Thus the point lies on an existing Gram carrier wall; it was not selected by scanning the Bockstein output.

Result

With the repaired inhomogeneous kernel solver and free-quotient projection, both kinematic directions and both primes give

$$(\dim R_0,\dim R_{\rm lift},\dim R_{\rm obs}, \operatorname{rank}\beta,\operatorname{rank}(\beta,{\rm mixed})) =(3,1,2,0,1).$$

Relative to the generic audited point, the exact-relation module gains one class, the fiber Bockstein disappears, two relations become obstructed, and one mixed direction survives.

Narrow conclusion

The first observed rank jump is supported on an already frozen Gram wall. It does not require a new cosmological carrier divisor. The generic rank-three first saturation does not extend unchanged across this wall; its specialization must be treated by a support-sensitive nearby/Gysin comparison.

Next falsifier

Derive the Gram-wall specialization map from the existing (h=0) support complex. Test whether its costalk accounts for the two obstructed relations and the surviving mixed direction. No fitted support summand is admissible.

Artifacts

• research/benincasa/checkers/check_rank26_gram_wall_lift_stratum.py
• research/benincasa/results/rank26-gram-wall-lift-stratum.json

Ledger sequence claim: seqclaim-1d2799dadff50e56a8cbd214.

View source on GitHub