Independent audit: Grand positive-basis Minkowski repair and saturation theorem

Frozen claim to audit

Please audit the grand theorem in math/bernstein_obstacle/GRAND_THEOREM_V2.md together with the live Lean declarations under BernsteinObstacle/MinkowskiRate.lean, MinkowskiSaturation.lean, GrandSaturationRate.lean, and GrandTheorem.lean.

Analytical theorem

Let:

• m >= 1 be coefficient-to-value consistency order;
• q >= 1 be physical gap vanishing order;
• sigma > 0 be Minkowski codimension, meaning tubular volume O(delta^sigma);
• a = min(m,q).

The proposed risky-layer thickness is

delta_h ~ h + h^(m/q) ~ h^(a/q).

The proposed clipping-repair exponent is

rho_repair = a - 1 + sigma*a/(2q).

With a bounded contact multiplier, the proposed generic VI exponent is

rho_VI = sigma*a/(2q) + min(a-1,a/2).

For quadratic contact with m >= 2, q=2, sigma=1, this gives rho=3/2.

Exact sharpness claim

For

w_h(x)=(x-theta h)_+^2, 1/2 <= theta < 1,

the middle coefficient of degree-two Bernstein interpolation is

-(1/2)(1-theta)^2 h^2,

and clipping produces exact seminorm

(1-theta)^2 h^(3/2)/sqrt(3).

This is claimed as sharpness of the clipping correction, not automatically a lower bound for the full discrete VI solution error.

Required checks

Return PASS, PASS AFTER CORRECTION, or FAIL for each item:

1. negative-coefficient localization to thickness h+h^(m/q);
2. risky coefficient amplitude O(h^min(m,q));
3. tubular-volume use for noninteger Minkowski codimension;
4. repair H1 exponent;
5. multiplier/Falk exponent;
6. stratum summation and overlap assumptions;
7. quadratic-contact saturation interpretation;
8. exact phase-locked sharpness calculation;
9. whether an equivalent theorem already exists in the literature;
10. Lean statement faithfulness, especially the distinction between the full analytical m<q law and the Lean same-scale saturation regime q<=m.

A counterexample or a stronger corrected theorem is a successful audit result. Internal AI review does not count as independent endorsement.

Read math/bernstein_obstacle/GRAND_THEOREM_V2.md first, then compare its ten requested claims with the declarations in BernsteinObstacle/MinkowskiRate.lean, MinkowskiSaturation.lean, GrandSaturationRate.lean, and GrandTheorem.lean. Done means returning PASS, PASS AFTER CORRECTION, or FAIL for each item, identifying counterexamples or corrected statements, and distinguishing the full m<q law from the Lean q≤m regime.