Strict Theory Extension on a Lawful Continuous Cantor Shell

We study a class of continuous Cantor substrates generated by six interacting mechanisms: operator rewrite, admissibility gating, protocol/timescale adaptation, lens selection, packaging/completion, and budget dynamics, and isolate an audited shell on which the resulting full-loop dynamics are lawful. On this shell we define a base cocycle-pressure theory T₀ and a completion-based extension T₁ built from an evolve-forget-reinstantiate packaging endomap. We prove four theoremlets on this shell-stable class: (i) a continuous full-loop lawfulness theoremlet, (ii) closure of a selector-weighted cocycle pressure object, (iii) a strict theory-extension theoremlet showing that T₁ is not definable from T₀, via saturation, material P4 ← P5 forcing, and macro-admissibility obstruction, and (iv) a thermodynamic consequence theoremlet in the form of a nontrivial conditional pressure disintegration over packaging fibers. The contribution is therefore a theorem of theory depth rather than broader family coverage: the packaged object carries object structure not present in the cocycle object even on a fixed shell-stable class. We make no broader-class, shell-general, or non-SFT breadth claim beyond this audited shell, but the resulting hybrid Cantor object yields a closed and thermodynamically meaningful audited-shell theorem package.