Reflexive SBT and Anti-Localization

A global budget on energy, work or dissipation says nothing about where that budget may be spent. If a packaged interface can address arbitrarily small regions, a feasible probe can concentrate almost all of its energy in a single cell, and every certificate that must hold uniformly over the feasible class degenerates into worst-case control. We ask when the packaging and accounting primitives of Six Birds Theory (the emergence calculus) rule out such “needles”. Concentration is measured by a localization index ηj: the largest fraction of a feasible probe's energy that can lie in one of 2j equal cells. For each of three kinds of packaged artifact we identify an auditable capacity that bounds ηj: for a subspace, the ideal share m/2j plus a scaled dispersion of its projector diagonal; for a sparse dictionary, the sparsity times the largest cell energy of an atom divided by the squared restricted conditioning margin; and for a multi-route construction, the subspace capacity of the span of all route outputs. The main result is conditional: along a ladder of growing domains, vanishing of the applicable capacity forces ηj → 0. Exact shift symmetry makes the subspace capacity equal to m/2j, and approximate symmetry controls it through the shift commutator, with an explicit constant that grows with the domain size and is optimal up to a factor √2. For spectral packaging we prove that sequential and direct routes agree when the cutoff has a spectral gap and the first stage keeps an exact top eigenspace, and we construct an inherited, clustered canonical selection rule under which they agree even at degenerate cutoffs. Explicit counterexamples show that delocalized atoms or individually safe routes do not suffice; other examples show that the capacities are sufficient, not necessary. Finally, we apply the Six Birds primitives to the packaged artifacts themselves (Reflexive SBT) as an audit-and-repair loop. On canonical subspace and dictionary failures the suggested move lowers the targeted capacity, while a stuck route case keeps its capacity on the ledger; we do not prove that the loop drives capacities to zero in general. The core eigenvalue–trace and cell-sum inequalities are mechanized in Lean 4 (eleven declarations, standard axioms only); the remaining proofs are written. Numerical experiments are reported as floating-point evidence, not certificates. Version 2 (6 October 2026). This version follows a complete audit of the mathematics, the Lean development and the numerical code. It states limits along growing-domain ladders with explicit conventions, replaces the earlier canonical tie-break claim with the inherited clustered canonical rule and its approximation bounds, adds the approximate-symmetry theorem, presents the capacities as sufficient (not necessary) conditions with ladder counterexamples, states Lean coverage declaration by declaration, and reruns the experiments behind every figure and table with the corrected code. The text and figures were rewritten. Version 1 is dated 15 February 2026. Code, experiments, Lean proofs and manuscript sources: https://github.com/ioannist/six-birds-meta.