rawCosineSupport
plain-language theorem explainer
The finite set of geometry-derived buckets that carry the raw cosine stencil: the image of all 216 tetrahedron/slot triples under the midpoint-displacement bucket key. Gravity analysts cite it as the production support for Regge TT Bloch folds and continuum moment identities. The body is a one-line Finset image of the universal triple set.
Claim. Define the raw cosine support as the finite set of buckets obtained by applying the geometry-derived bucket key (left slot, right slot, doubled midpoint phase displacement) to every triple in $(\mathrm{Fin}\,6)^3$. Equivalently, it is the image of all $216$ tetrahedron/slot triples under that key map.
background
This module is the C-DAG1 finite-cell assembly stage for Regge TT gravity. The cosine evaluator is built from a bucket's integer phase key, independently of any quadratic moment evaluator. For commensurate non-aliased modes the normalized canonical finite second variation equals the raw bucket-fiber Bloch fold, via cell cosine sums and explicit integer-turn phase wrapping.
A bucket is a triple (left slot, right slot, phase vector) with slots in $\mathrm{Fin},6$. The intended external convention only identifies $(f,g,u)$ with $(g,f,-u)$; this structure does not yet quotient fibers. The bucket key of a raw stencil triple $(t,f,g)$ is the slot pair $(f,g)$ together with the doubled midpoint displacement $2(\mathrm{mid}_g-\mathrm{mid}_f)$ in each coordinate.
The raw cosine support is exactly the set of all such keys as $(t,f,g)$ runs over the $6^3=216$ triples. Downstream algebraic closers treat this set as the production support for continuum and TT moment folds.
proof idea
One-line definition: take the universal Finset on $\mathrm{Fin},6\times\mathrm{Fin},6\times\mathrm{Fin},6$ and push it forward under the local bucket-key map. No lemmas are applied; the support is literally that image.
why it matters
This set is the production cosine support for the entire Regge TT Bloch pipeline. The algebraic closer proves it equals the Gate B bridge moment support, so continuum moment folds on this set match bridge moment folds and, under symmetry, equal $\tfrac12 x^T\mathrm{adj}(E)x$ (the C8 closed form). On unit-normalized real TT data the same fold yields the continuum coefficient $-1/4$ (P1.1b headline).
Inside the assembly module it is the support argument of the canonical finite equality: under a non-aliasing hypothesis the reduced finite second variation equals the raw bucket cosine Bloch fold over this set. It therefore anchors both the finite-cell identity and the continuum TT coefficient without importing spike or continuum-certificate modules.
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