reggeTTAssembledSymbol
plain-language theorem explainer
Defines the cosine-evaluated assembled symbol for the Regge transverse-traceless Bloch audit: a real scalar built from a finite bucket support, a phase assignment, and amplitudes. Gravity analysts cite it as the moment-evaluator surface before any continuum or spike identification. The body is a one-line alias of the Bloch fold.
Claim. For a finite set $S$ of buckets (each a pair of tetrahedron slots with a phase vector), a phase map $\theta: S\to\mathbb{R}$, and an amplitude map $a: S\to\mathbb{R}$, the assembled symbol is the Bloch fold of $(S,\theta,a)$ over that support.
background
The module is the panel-locked C11 Regge TT Bloch interface audit (attempt 2). Attempt 1 was rejected for wiring the raw stencil definitionally to the objects under audit, so this file keeps the first gate narrow: a literal $6\times 6\times 6$ triple sum over tetrahedra and ordered slot pairs, with the inner angle derivative expanded and the square-root derivative written via plane-wave tet velocity over $2\sqrt{a^*}$.
A bucket is a triple (left slot, right slot, phase vector) in $\mathrm{Fin},6\times\mathrm{Fin},6\times$ phase space; the external convention only identifies $(f,g,u)$ with $(g,f,-u)$, and this attempt does not yet quotient fibers. The eight-tick phases $k\pi/4$ and the forcing of $D=3$ with period 8 sit upstream in the foundation chain but are only ambient here.
The doc-comment on the moment evaluator states that the evaluator is the stencil fold at the cosine two-jet value $-z^2/2$, with the campaign's frozen $x(1/4)$ normalization carried by the caller-supplied phase quadratic.
proof idea
One-line definitional wrapper: the assembled symbol is definitionally equal to reggeTTBlochFold applied to the same support, phase, and amplitude. No algebraic reduction or tactic proof is involved.
why it matters
Supplies the cosine-evaluated assembled-symbol surface that the continuum-limit engine is expected to use after the hinge/diagonal constant block is connected. The module status block leaves Gate A2-full (full rational bucket aggregation), Gate A3 (hinge-aware zero-mode), and Gate B (spike convention bridge) open; the same-day sympy diagnostic already showed the stencil-only constant block does not vanish. No ContinuumLimit or spike certificate module is imported, so this def deliberately stops short of identifying the fold with the committed spike polynomial. It sits in the gravity second-variation stack that ultimately feeds continuum TT analysis in $D=3$ with the eight-tick octave.
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