Entropy-Geometric Branch Selection in the Everettian Branch Measure: A C=1 Framework

The Everettian interpretation of quantum mechanics provides a unitary account of branching quantum histories but leaves open questions concerning the relative significance of branches and the emergence of observer measures. This paper develops an entropy-geometric extension of the Everettian Branch Measure (EBM) framework based on the microscopic C=1 theory of coherence dynamics. A saddle-point expansion of the entropy-weighted partition functional yields branch amplitudes carrying an entropy-dependent factor. The resulting branch measure is |A_i|² = |N_i|² exp(−2ΔS_i/k_B), where N_i is the fluctuation determinant and ΔS_i is the branch entropy relative to a homogeneous reference. The framework introduces the dimensionless control parameter Ξ = |ΔS|/k_B. The canonical C=1 soliton yields ΔS_soliton = −5.39 k_B, Ξ_soliton = 5.39. The Born rule, Observer Measure Principle, and Past Hypothesis remain explicit postulates of the framework. Paper 1 of 3 in the EBM+C=1 series. Companion papers: Paper 2 (cosmological and inflationary consequences) and Paper 3 (black-hole regime analysis).