Stratified Universality

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1 \begin{table}[htbp]
2 \centering
3 \small
4 \caption{The publication theorem spine.  Section numbers are resolved by the final build; the logical order, rather than the numbering, is authoritative.}
5 \label{tab:block14-theorem-suite}
6 \begin{tabularx}{\textwidth}{@{}L{0.16\textwidth}L{0.22\textwidth}YL{0.14\textwidth}@{}}
7 \toprule
8 Stage & Principal result & Exact role in the proof & Location \\
9 \midrule
10 Resolved source & Additive-Karoubi envelope & Literal finite packet objects and profile-indexed realization source & \cref{thm:additive-karoubi-envelope} \\
11 Typed atlas & Bridge passports and obstruction separation & Reversible overlaps are separated from directional loss & \cref{sec:strata-bridges-obstructions} \\
12 Finite assembly & Profiled atlas assembly & Bilimit, theorem transport, groupoid core, and global directional functors & \cref{thm:atlas-assembly} \\
13 Native normalization & Certified stratum atlases & Complete local coordinates on declared semantic slices & Part II \\
14 Higher coherence & Normalizer-induced coherence & Unique semantic normalizers force all certified overlap cycles to commute & \cref{thm:block13-normalizer-coherence} \\
15 Invariant descent & Certified invariant-descent theorem & Coherent local invariants descend through effective object and morphism gluing & \cref{thm:block13-certified-invariant-descent} \\
16 Global completeness & Tagged componentwise invariant & The descended invariant reflects isomorphism on the five-component union & \cref{thm:block13-global-completeness,thm:block14-main} \\
17 Lane transport & Finite profiled Universal Lane Transport Theorem & Exact block transport, refinement, selection, residuals, conditional fold loss, and certified descent & \cref{thm:block15-universal-lane-transport,thm:block15-lane-descent} \\
18 Twisted transport & Holonomy-Twisted Universal Lane Transport Theorem & Matrix-local-system synthesis, base-fiber invariant normal form, orbit coarsening, and orbital path algebra & \cref{thm:block16-holonomy-twisted-lane-transport,cor:block16-base-fiber-invariant-normal-form,thm:block16-orbit-descent,thm:block16-permutation-orbital-calculus} \\
19 Task semantics & Relative semantic quotient theorem & Behavioral cores, task quotients, semantic diamonds, and exact task loss & \cref{thm:block17-main-semantic,thm:block17-semantic-diamond,thm:block17-task-change} \\
20 Carrier and observer change & Factorization and base-change theorems & Joint semantic completion, exact bridge loss, relation modules, and carrier-indexed aggregation & \cref{thm:block18-carrier-factorization,thm:block18-bridge-loss-exact,thm:block18-observer-base-change,thm:block18-carrier-indexed-observer} \\
21 Admissibility and lifting & Class-relative defect and enhancement gates & Completion/gap/escape, geometry-class separation, and typed enrichment lifting & \cref{thm:block19-admissibility-monotonicity,thm:block19-convex-quadratic-separation,prop:block19-forgetful-lifting} \\
22 \bottomrule
23 \end{tabularx}
24 \end{table}

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