The Interior Observer Cosmological Framework — Paper 16: The Gauge Projection Degree: Completing the Dark Energy Derivation via Transfer Homogeneity, Composite Uniqueness, and Geometric Slot Locality

Paper 16 of the Interior Observer (IO) Cosmological Framework resolves the last open seam in the dark energy derivation chain: why the gauge projection factor enters as √(1+γ²) (degree 1) rather than (1+γ²) (degree 2). Paper 9 labeled this the "phenomenological one-leg ansatz." This paper provides conditional closure through seven new theorems (transfer homogeneity, form-degree response, carrier representation, slice-family collapse, axiom elimination, two-fiber transfer degree, and a no-universal-1-form selector), a composite uniqueness theorem combining marginal trapping locality with bipartite transfer structure, and a universal transport no-go derived from framework self-consistency (GTTP violated at 20.15σ). Under the explicit premise package P1–P6, √(1+γ²) is the numerically unique correction factor for a local boundary-to-bulk transfer observable. The result is DERIVED/THEOREM conditional on the premise package — the same epistemic structure as Paper 15's Rosetta Boundary Observable Theorem. Twenty-seven failed derivation approaches are documented. Supplement S1 contains the self-consistent transport no-go computation. v1.2 - Paper 19 correction annotations. Abstract updated with two founding premises. Core results entirely unaffected: composite uniqueness theorem, P1-P6, degree-1/degree-2 transfer machinery, marginal trapping locality, 27 dead approaches. P6 universal transport no-go (GTTP at 20.15σ) revalidated unchanged on Paper 19 background. Paper 19 uses Paper 16 as link 5 of 6 in the RT chain deriving the IO Friedmann equation. Appendix entries for background-dependent quantities (projection map, N_eff = Δ, Ω_k) superseded.