canonicalPeriodicDeficitDerivativePackage

This module does not freely assert the physical Dirichlet equality. It packages the exact obligations needed to instantiate PhysicalSixTetCubicDirichletModel on a periodic Freudenthal torus scaffold.

The underlying complex is the canonical encoded periodic Freudenthal torus: a 3D triangulation $K$ with incidence consistency, built from the endpoint-incidence data of the periodic lattice. Edge-slot bookkeeping records how edges partition into incidence slots on that encoded torus. The local-angle length-chain rule package supplies the flat chain-rule identities relating dihedral angles to edge lengths; the local dihedral derivative package is the first-variation data for those angles.

A deficit-angle directional-derivative package is the structured object that lets one differentiate hinge deficits along vertex potentials. Upstream, conformal Schläfli cancellation is obtained from a length-chain package plus incidence bookkeeping on the dihedral derivatives; that cancellation is the bridge from combinatorial bookkeeping to a well-defined deficit package.

Definitional assembly, not a tactic proof. Bind the canonical encoded periodic Freudenthal torus $P$, its local-angle length-chain package $L$, and its local dihedral derivative package $A$. Pass the edge-slot bookkeeping of $P$ into conformal Schläfli incidence bookkeeping (on $A$), feed that with $L$ into conformal Schläfli cancellation from the length chain, and finally apply the constructor that builds a deficit package from conformal Schläfli cancellation. The result is a fully determined DeficitAngleDirectionalDerivativePackage on $P.K$.

In the canonical Track 1.B branch the deficit package is no longer an arbitrary hypothesis: it is fixed by the periodic Freudenthal geometry and the flat local-angle chain rule. Downstream, the specialized deficit-derivative evaluation theorem reads derivatives off this package. The main consumers are the local-correspondence endpoints that identify mixed hinge-deficit data with the concrete edge-stencil Dirichlet energy: the strong form (eventual vanishing of weighted deficit derivatives), the weaker stationary-Schläfli forms (with cell-tet or length-chain targets), and the mixed-hinge edge-stencil target built from a local-angle hypothesis. Those endpoints are the remaining obligations toward the physical six-tet cubic Dirichlet model on the periodic lattice, linking discrete Regge first variation to continuum Dirichlet energy in the RS gravity track.