Independent audit: Bernstein V6 strongly monotone grand theorem

Audit target

Review draft PR #119 and the theorem package on branch:

research/bernstein-v6-grand-inner-cone

Primary files:

• math/bernstein_obstacle/GRAND_THEOREM_V6.md
• math/bernstein_obstacle/EXPLICIT_OPERATOR_COROLLARIES_V6.md
• math/bernstein_obstacle/audit_packets/PANEL_E_MONOTONE_OPERATOR_GRAND_THEOREM.md
• math/bernstein_obstacle/lean/MONOTONE_OPERATOR_FORMALIZATION_SPEC.md

Principal proposed extension

Under the corrected regular-interface, mesh, regularity, and bounded-multiplier hypotheses, the Bernstein obstacle rate

||u-u_n^B||_{H1} <= C (h_n^r + h_{Gamma,n}^{3/2})

is claimed for hemicontinuous, strongly monotone, Lipschitz operators, without symmetry, linearity, or an energy functional.

Required checks

1. Verify every sign in the nonlinear inner-cone Falk inequality.
2. Verify that strong recovery plus inner inclusion gives the stated Mosco theorem.
3. Verify the translated nonzero-obstacle majorant theorem.
4. Verify the same-cone perturbation estimate.
5. Check the explicit convection-diffusion and tanh reaction examples.
6. Determine whether the corrected free-boundary recovery and multiplier assumptions really transfer unchanged to the nonlinear/nonsymmetric operator class.
7. Search for the closest prior theorem combining Bernstein coefficient inner cones, exact pointwise feasibility, Mosco recovery, and a 3/2 interface rate for strongly monotone VIs.
8. Identify any missing existence, regularity, boundary, or complementarity hypothesis.

Acceptable verdicts

• PASS
• PASS AFTER STATED CORRECTION
• FAIL, with an exact counterexample or invalid step

A narrower corrected theorem is a successful audit outcome.

Trust boundary

This is an internal theorem derivation. It is not independently confirmed and the new operator theorem is not yet Lean-verified. There is no cash bounty attached to this issue.

Read draft PR #119 and the four files under math/bernstein_obstacle/, starting with GRAND_THEOREM_V6.md and the audit packet. Check each required inequality, recovery, perturbation, and example claim against the stated hypotheses, then search for prior theorems. Done means a PASS, PASS AFTER STATED CORRECTION, or FAIL verdict with exact corrections or a counterexample.