The sixteenth grouping of this series closed with one residue named three times: Paper 54's (b5) — "a boundary definition that stands without a declared fixed background" — Paper 55's (t5), and Paper 56's closure ledger all point at the same place, "the dressed region algebra (46's (p1) with its beyond-weak-field row (p4) ), " returned to the backlog "with owners unassigned. " This paper opens the seventeenth grouping — the Shared-Frontier Program (57 region → 58 composition → 59 curved standing) — defines its charter (pre-committed verdict domains; a mandatory class-exhaustion kill; a strict-recovery obligation; annotation-only upgrades; a backlog ownership table with no silent orphans), and takes the region seat. The question audited: do the corpus's region-anchored objects — D0's tubes and record regions, Paper 54's window triple, Paper 56's patch — require a Global Localizer, an assignment of supports declared independently of the record data? The paper constructs a dressed region package on Paper 46's three anchor classes: a coherent anchor displacement field (an injective embedding with an explicit interpolation construction and proved bounds, so region operations survive transport automatically), a poset of dressed regions, and a support assignment into the fixed ambient net with net-like axioms at their honest strengths — isotony proved; spacelike compatibility margin-conditioned; covariance and naturality as common-core/envelope sandwich statements consuming net isotony only, the genuine automorphism displayed exactly where it exists, and the paper stating plainly that no canonical algebra isomorphism exists for nonuniform relational support motion on a fixed net — the residual collar is priced and left unread by every declared consumer. Three results ride on the package. The unification lemma with certificate fidelity: the window and the patch are images of one anchor-carried region object; Paper 42's (a1) chain-membership boundary is exactly preserved under admissible re-anchorings (Paper 54's Proposition 1, lifted) ; no frozen 54-verdict or 56-cell flips — proved on fence-typed and tube-invariant data alone, no algebra comparison consumed. The membership criteria: Paper 46's open (p2) closes at criterion grade via an exact transport identity (the Wasserstein-1 distance of translated mollifiers equals the displacement) — the world-tube class unconditionally; the anchor-record class by an exact a-priori criterion plus a best-possibility lemma (unconditional closure is impossible; 46's own witness is the counterexample) ; the matter-field class by a sufficient criterion only — and (p3) 's tiers become a classification theorem on the lifted family. The strict-recovery lemma: Paper 46's source package, the window, the patch, and every frozen corner number return unchanged (nu = 2. 28x10³ / 5. 32x10⁴ s^-1; Q-dotₑxp = 9. 1x10^-21 / 2. 1x10^-19 W; the twelve cells). Anchor-carried is not background-free, and the thesis is scored at exactly that strength: what the package removes is the independent region declaration — supports become functions of anchor data, given the ambient weak-field background and the certified cell assignment; removing the background scaffold itself is (r5), scored open and built elsewhere. FrontierStatus (region) = scoped at model grade: (r1) - (r4) closed on the declared anchor classes ( (r3) at criterion grade), (r5) open. Nothing is adopted, calibrated, or scored; no band moves; the substantive preferred-localization face is declined, not refuted.
Tomoyuki Uchida (Sun,) studied this question.