Six Birds for Incompleteness: Fixed Packages, Package Change, and Conditional Arithmetic Lift

Formal incompleteness explains why no sufficiently expressive effective theory captures all arithmetic truth, but it does not by itself provide a structural language for comparing theory growth. This paper develops such a language by treating a formal theory as a packaged closure object evaluated on a frozen ledger. First, a fixed idempotent package saturates under iteration: repeated closure does not sustain persistent strict growth. Hence genuine growth requires package change. Second, on a frozen slice with fixed yield, cost, and support data, efficiency transfers across cone-equivalent representatives, yielding a restricted alignment theorem. Third, these internal results combine with an explicit external dependency contract to give a conditional arithmetic lift: if the required canonical-family-on-cone assumptions are discharged from the arithmetic literature, then frontier-efficient extension operators admit canonical representatives on the relevant comparison cone. The result reframes incompleteness and axiom choice in package language. Gödel becomes the canonical fixed-package failure mode, while new axioms appear as controlled package changes evaluated under a frozen regime. Vendor-backed PICA evidence is used only to discipline primitive roles and scope, not as proof support.