Paper C: Surface Energetics and Thermodynamic Structure of the Holosphere Lattice

Paper C develops a surface thermodynamic reporting layer for the Holosphere lattice under clearly stated regime conditions. The construction applies only when boundary defect growth is surface-dominated (area-leading rather than volumetric), drift residuals remain bounded so that their variance is well defined, and curvature-regulated smoothing signatures support a nonnegative irreversible channel. Within that gated regime, boundary vacancies carry calibrated strain energy, surface entropy is area-extensive under a fixed topological charge constraint, and a coherence temperature is defined from bounded drift variance using inherited calibration anchors. The resulting surface first law separates reversible curvature response from irreversible curvature-regulated redistribution. A turnkey drive sweep over multiple drive amplitudes (control and constrained evolution) provides artifact-level diagnostics including boundary radius, thickness, eccentricity, global exceedance fraction, and curvature story strips. Across the tested range, curvature-organized smoothing persists and global exceedance remains small at a fixed anchor, supporting the existence and sign of the irreversible channel without invoking volumetric transition. Paper C therefore establishes a contract-gated, artifact-auditable surface thermodynamic description whose validity is explicitly regime-limited and whose constants are inherited rather than tuned.