Executable scalar-completion gate for TEST 010. Run ./verify.sh.
The test first checks the exact background equations. Conditional four-dimensional radion formulas are retained as diagnostics but cannot override a failed five-dimensional gate.
- Test: TEST 010 / GP-1S.
- Question: Can a minimal canonical Goldberger–Wise-type scalar complete and stabilize the exact flat GP-1 bulk while preserving a healthy observable response?
- Result:
GP1S-D— a nonconstant stabilizing scalar is incompatible with the exact flat five-dimensional background. A conditional healthy conformal radion also cancels from the leading lensing sum and cannot supply the declared halo signal. - Assumptions: Canonical bulk scalar, exact static flat background, declared boundary variation, and no backreacted warped replacement.
- Recovery contents: background and boundary derivations, conditional radion diagnostics, validity gates, verification suite, citations, machine-readable result, failure register, and Arbiter packet.
- Limitations: This is a scoped rejection of the minimal flat completion, not a rejection of independently derived warped or otherwise stabilized models.