isolate_tensor_contribution
plain-language theorem explainer
The declaration defines the isolated tensor contribution to the gravitational wave action expansion as the unconditionally true proposition on any scale factor and tensor perturbation. Researchers expanding the Einstein-Hilbert action around an FRW background in RS cosmology would cite it when separating tensor modes from scalar and vector contributions. It is established directly by a one-line assignment of the constant True with no further reduction.
Claim. For any positive scale factor function $a(t)$ and any transverse-traceless tensor field $h_{TT}(t,i,j)$, the isolated tensor contribution to the action is the proposition that holds unconditionally.
background
The module imports the FRW metric setup and tensor decomposition to expand the action for gravitational waves. ScaleFactor is the structure consisting of a map $a : ℝ → ℝ$ together with the axiom that $a(t) > 0$ for every time $t$. TensorPerturbation is the structure carrying a field $h_{TT}$ that obeys the transverse condition (vanishing sum over one spatial index) and the traceless condition (vanishing trace). The separate scale definition supplies the phi-powered rung values used elsewhere in the cosmology layer.
proof idea
The definition is a direct one-line wrapper that assigns the constant proposition True to the pair of inputs; no lemmas are applied and no tactics are required.
why it matters
The definition supplies a placeholder that isolates tensor contributions inside the quadratic action expansion around the FRW background, preparing the ground for later verification of the full action form in the same module. It fits the Recognition Science separation of tensor modes within the D=3 spatial setting and the eight-tick octave structure, though the declaration currently has no recorded downstream uses.
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