Abstract
<jats:p>This work constitutes Level L3 of the TAGC programme. Level L2 established the canonical minimal geometry R of the 64-node assembly and its canonical enrichment, a pseudometric of signature (1,15). L3 is governed by the Structural Sufficiency Principle (EM-L3-01): no new geometric structure may be introduced unless the inherited information is shown to determine it uniquely; where sufficiency fails, the valid result of the level is the proof of that insufficiency together with the minimal additional principle required. Impossibility theorems thereby become first-class results. Phase 0 closes the invariant inventory of the geometry through its intersection numbers, eigenmatrix, and a parameter-rigidity theorem that separates the object within its category. Among the forced structures: the full automorphism group is determined as the wreath product S4 wr S16, closing an open inclusion of L2; the meta-group partition is intrinsic, yielding a canonical two-scale fibration; and a unique flat transport is forced, every curvature-like invariant of which vanishes identically. Among the impossibility results: neither a genuine metric distance nor a distinguished trajectory class is forced. The compatible invariant metrics form an irreducibly two-parameter family, and in both cases the single missing datum is the same, an ordered scale on the two relational classes. Finally, the canonical relational representation of L2 is shown to be faithful precisely at the coarse sixteen-class scale by dimensional necessity, while the fine scale is recovered canonically by the forced fibration, completing the two-scale programme deferred by L2. No physical interpretation is introduced.</jats:p>