Reflexive SBT and Anti-Localization

In plain words

Six Birds leans on accounting: budgets that bound total energy, work or dissipation. A budget like that can still allow a needle, a probe that piles almost everything into one tiny region. Needles force worst case bounds and undo the point of coarse packaging. This paper asks when packaging plus accounting rules them out. Its move, called Reflexive SBT, is to apply the six birds to the products of the analysis itself: the packaged subspaces, the dictionaries of allowed states, and the ladder of routes as resolution gets finer.

A localization number measures how much allowed energy can sit in one cell at a given scale. The paper bounds it by three auditable capacities. One measures how unevenly a subspace's projector sits on the diagonal. One measures how badly small groups of dictionary atoms are conditioned, since nearly cancelling atoms can build a needle. One charges multiple routes by the size of their union. The main theorem is conditional: if these capacities vanish along a ladder of refinements, localization goes to zero.

Controlled experiments back each failure mode. Shift invariant channels follow the predicted bound, while diagonal disorder pushes localization quickly toward its maximum. Needles appear exactly when small support conditioning collapses, and are absent in random baselines. Route mismatch in spectral packaging spikes only at degenerate cutoffs and disappears under a canonical tie break. A closure loop shows targeted moves lowering the capacities in these cases.

What it shows

• A localization metric for packaged feasibility, computed by an eigenvalue method.
• Three capacity terms, each matched to a failure mode with an explicit counterexample.
• A conditional theorem: vanishing capacity implies anti localization along a ladder.
• A route stability result for spectral packaging with a canonical tie break.

What it does not claim

It does not prove that Reflexive SBT drives the capacities to zero in general. The step from capacity to anti localization is proved; the loop's reductions are shown only on controlled examples.

Cite

Tsiokos, I. (2026). Reflexive SBT and Anti-Localization. Zenodo. https://doi.org/10.5281/zenodo.23184180