The Arrow of Proximity, Minimal Architectural Resolution of an Inherited Geometric Order-Indeterminacy — The L4 Level of the TAGC Programme

This work constitutes the L4 level of the TAGC programme. Level L3 proved that the canonical minimal geometry of the 64-node assembly does not force a genuine metric distance: the compatible invariant metrics form a two-parameter family, and, decisively, the proximity order (whether intra-group or inter-group pairs are the closer) is undetermined, since two canonical inherited constructions select opposite orders. This proved insufficiency is the genuine obstruction that licenses the present level. L4 is governed by the principle EM-L4-01 (Minimal Exogenous Resolution): when an inherited category is insufficient to force a structure, that structure may be forced by importing the least automorphism-invariant datum from an adjacent closed level, and no more; the unresolved freedom is then characterised explicitly. We import a single bit, the sign contrast of the two relational couplings of the inherited effective operator (fixed ratio minus 20, hence opposite signs, with the intra coupling positive), a datum independent of the free spectral magnitude. This contrast reduces the L3 ambiguity to one binary architectural choice; once fixed, the proximity order is uniquely determined and magnitude-independent: the intra class is proximal. Neither the contrast nor the choice suffices in isolation. The imported datum fixes no distance ratio, leaving an explicitly characterised one-parameter scale modulus. The order-dependent half of L3's trajectory impossibility is thereby discharged, while geodesic lengths remain modulus-dependent. No physical interpretation is introduced, and no magnitude of the effective operator is imported.