Rational Quartic Negative Control: Envelope Recovery, Purity Breakdown, and a Two-Dimensional Non-Geometric Defect

For a smooth rational quartic C on an explicit smooth quartic surface, exact computation gives dim I_{C,3} = 7, dim I_{D0,3} = 7, dim J_{S,3} = 4 and span 14; with the imported value dim I_{α(C),3} = 16 this gives a geometric purity defect PD₃ = 2 (degree-2 data recovers only the quadric envelope Q, not C).

More Hodge-annihilator information does not automatically mean more carrier information. Every number is typed as computed or as a 'literature theorem bridge'; PD₃ = 2 depends on the imported dim 16 and the imported classification of same-annihilator divisors.

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