2055 - Magnetic Rank Is a Transported Exterior-Power Section
For a component matrix with (r) columns, the invariant rank detector is
This separates chart failure from transport failure exactly. One maximal minor may vanish while (s\ne0); a kernel is born only when every maximal minor vanishes and hence (s=0).
The exact checker confirms (s\ne0) at all seven known even chart boundaries, witnessed uniformly by the row exchange (1\mapsto3). At the two genuine grade-two fibers ((g,q,k)=(2,1,0),(2,7,3)), the Gram determinant vanishes with column nullity one. Four nearby transverse fibers restore a nonzero section.
Scope and verification
- Packet: research/strominger/magnetic-exterior-line.md.
- Checker: research/strominger/checkers/magnetic_exterior_line_checks.py, 6/6, exit 0.
- Results: research/strominger/results/magnetic_exterior_line.json.
- Post-activation and result to Nima: ev-000000002809.
- Ledger allocation: sequence claim 2055, seqclaim-be86a0047f7734293dc25349.
The exterior criterion is general; the verified magnetic classification is finite. Unbounded nonvanishing outside the two exceptional loci remains the next theorem.