supportProject
plain-language theorem explainer
Pointwise cutoff that zeros a 15-class coefficient vector wherever the seed-hinge combinatorial incidence vanishes. Anyone proving that the flat-Hessian assembly form depends on coefficients only through supported edge classes cites this map. The body is a one-line incidence guard, not a derived identity.
Claim. Given a real coefficient assignment $c$ on the fifteen edge classes, the support projection is the map $d \mapsto c(d)$ when the seed-hinge incidence of class $d$ is positive, and $d \mapsto 0$ otherwise.
background
This module is the next kernel-checked increment after the 15-class Regge edge stencil: Freudenthal/Kuhn triangulation of the 4-cube, seed-hinge orbit, and a MODEL flat-Hessian assembly skeleton. The fifteen classes are imported, never redefined. The seed hinge is the triangle with vertex masks $0,1,3$; exactly two of the twenty-four monotone 4-simplices contain it.
Combinatorial incidence counts, for each class $d$, how many of those two seed-containing simplices carry $d$ as a local edge. Three classes are combinatorial decoys (incidence zero); the three hinge-boundary classes each have multiplicity two. The incidence function is the gate used here.
Upstream deficit notions (dihedral $2\pi-\sum\theta$, Schläfli hinge deficit, ledger cell deficit) motivate why off-support slots should not contribute, but this definition only uses the incidence count, not those deficit formulas.
proof idea
Definition, not a proof. For each class index $d\in\mathrm{Fin},15$, evaluate the seed-hinge incidence multiplicity; if it is zero, emit $0$, else emit the input coefficient $c(d)$. No lemmas are applied.
why it matters
Feeds the theorem that seed-orbit assembly is invariant under replacing $c$ by its support projection: the assembly contracts open per-hinge area weights against open per-hinge deficit kernels and is forced to vanish off the incidence support. That theorem is the formal statement that the MODEL class form depends on $c$ only through supported classes.
In the QG campaign this is deliverable-B scaffolding on combinatorial support, not completion of the flat Hessian of the 4D Regge action, not $S_{\mathrm{RS}}\to\mathrm{EH}_{4d}$, and not a flip of gap-action recovery. It keeps decoy classes from polluting the assembly before the open dihedral/Cayley–Menger kernels are supplied.
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