simple-case-gatelisted

# Simple-case gate Use this whenever proposing or evaluating a mathematical or physical mechanism, proof architecture, ansatz, recursion, or claim intended to hold across a family. ## Non-negotiable rule Identify the simplest admissible nondegenerate case and make the exact proposal work there before increasing order, weight, depth, rank, spin, loop number, or the number of free parameters. A genuine failure in that case forbids trying harder cases in the hope that added complexity will repair a proposal that was claimed to work in every case. ## Gate 1. State the proposal and its domain precisely. If a simple case is excluded, derive the exclusion from the proposal rather than adding it after seeing a failure. 2. Choose the lowest-complexity case inside that domain. Verify that it is nondegenerate and that the test is sensitive to the proposed mechanism. 3. Test the complete proposal, with the same definitions, normalization, and conventions intended for the general case. Preserve the first exact residual or counterexample. 4. If it fails, stop escalation. Diagnose whether the cause is an implementation error, convention mismatch, degeneracy, false auxiliary assumption, or failure of the idea. 5. Either modify the proposal for a principled reason that explains the residual and retest the modified proposal on the same simple case, or abandon/narrow the claim. 6. Proceed to harder cases only after the simple gate passes. A modified proposal is a new prop