fieldTheoryStub
plain-language theorem explainer
This definition supplies a placeholder instance of the FieldTheoryFacts structure in the relativity fixtures module. It lets proofs continue by assuming trace-free stress-energy and a conservation law for fields without deriving them from the Recognition Science equation. Researchers extending the framework to general relativity would cite it during scaffolding phases. The body uses parameter introduction followed by direct simplification on the structure.
Claim. Let FieldTheoryFacts denote the structure requiring that the stress-energy tensor is trace-free for a field configuration, metric, volume form and parameter, together with a conservation identity for the field with given mass-squared term. The stub supplies an instance of this structure by direct simplification.
background
The module supplies stub instances for hypothesis classes that replace sorries while keeping them outside production namespaces. FieldTheoryFacts encodes two core properties: the trace of the stress-energy tensor vanishes, and the associated current is conserved under the metric and volume form. These stubs maintain a clear trust boundary between assumed facts and results derived from the J-cost or Recognition Composition Law.
proof idea
The definition opens the trace-free property by introducing the field, metric, volume, parameter and point, then applies simplification against the FieldTheoryFacts structure. The conservation theorem is handled identically by introducing the field, metric, volume, parameter, mass-squared term, hypothesis and indices before simplification. An instance declaration registers the stub as the default implementation.
why it matters
The stub supports incremental construction of relativity results inside the Recognition Science framework by providing temporary stand-ins for field-theory axioms. It belongs to the set of fixtures that isolate open derivations from the forcing chain (T0-T8) and the phi-ladder. As scaffolding it marks the remaining task of obtaining these properties directly from the functional equation rather than by assumption.
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