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Enforce floating arithmetic prerequisites for polynomial certificates

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Emily Boudreaux
2026-09-17 09:35:59 -04:00
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experiments/POLYNOMIAL_ENTHALPY_ADMISSIBILITY_2026-09-17.md
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@@ -19,3 +19,5 @@ Tests cover nodal-positive/interior-negative cubics, a positive polynomial with
`PreparedStellarEnthalpyStrategy<State>` resolves the enthalpy block from the compiled form type and captures the initial physical enthalpy as its anchor. Every full-state check denormalizes the state; pointwise positivity is not invariant under a general diagonal Riesz normalization. The strategy minimizes the full normalized linear-residual norm over the sufficient one-dimensional repair interval, verifies the actual normalized root candidate after rounding, and rejects a non-descent result. Unrelated blocks of the normalized correction are retained bit for bit. It does not prepare an operator or change an accepted state. A valid unaltered full candidate costs one Jacobian action for its true merit slope; an altered direction costs three actions (family model plus the actual rounded chosen direction). The anchor's certificate is cached only when coefficients agree exactly on every rank.
A standalone extraction of the scalar/tensor certification engine was compiled with the system C++20 compiler and exercised before module integration. It certified a strictly positive quadratic with negative coarse coefficients and a three-dimensional zero-face bubble; it proved a negative pocket of depth 1e-10; it returned unresolved for an exact tangential zero. Production module compilation and MPI execution remain part of the integration campaign.
Arithmetic requirements are enforced at compilation: `__FAST_MATH__` and a positive `__FINITE_MATH_ONLY__` are rejected, and static assertions require IEC 559 binary64 with subnormal support. Runtime floating-point modes must retain gradual underflow; the application must not enable flush-to-zero after construction. The existing Release build was inspected: `-O3 -g -DNDEBUG -std=c++23 -flto=thin -arch arm64`; no unsafe floating-point flags were present in the generated build commands.