Operation Self-Reference, LogSumExp Uniqueness, and a κ(L)=C/L Scaling Law Connecting Casimir Forces to Dark Energy

We propose operation self-reference as a primitive concept in physics. From this primitive we rigorously derive: (1) natural numbers, (2) translation covariance as a theorem, (3) LogSumExp as the unique smooth parallel-merge operation, (4) quantum linearity from right-distributivity. Beyond these theorems, we present conjectural extensions: a correspondence between warped translation and AdS geometry (heuristic), and a κ(L)=C/L scaling law connecting Casimir forces (C>7.9 at μm) to dark energy (C≈8.6 at Gpc) across 33 orders of magnitude in L. A consistency relation H₀≈(c/C)√(Λ/3) reproduces the observed Hubble constant. All results are tagged with confidence levels. Theorems (★★★), conditional derivations (★★), conjectures (★), and hypotheses (H) are explicitly distinguished. Open gaps (rank-1 to rank-2 Noether current, Standard Model gauge group, fermion masses) are honestly acknowledged. This is a theoretical framework, not a completed physical theory.