The Radius-Law Density-vs-Surface Resolution (T260): The Mass-vs-Tension Category Distinction — Mass-Energy Is Volumetric (Density Law R~M^ (1/3), T259/T254) While Lattice Tension Is Surface-Concentrated (8-Dimensional Field-Space Concentration and the T156 Casimir Level Set), So Both Pictures Hold for Different Quantities

Photonic Universe Hypothesis (PUH) — T260 — INTERNAL-CONSISTENCY RESOLUTION NOTE. T259 (DOI 10. 5281/zenodo. 20836505) derived the density radius-law R ~ M^ (1/3), area ~ M^ (2/3) for Planck cores from tension-minimization, but flagged an open tension: a high-dimensional-geometry argument (a ball's volume concentrates near its boundary in high dimension) seemed to imply a SURFACE law R ~ M^ (1/2), area ~ M. This note resolves it. THE RESOLUTION: the two laws describe DIFFERENT quantities; the conflict is a CATEGORY confusion. The high-dimensional concentration result is correct (in 8D, 57% of a ball's volume is in the outer 10% shell; in 248D essentially all) but it concerns volume in n-dimensional SPACE. Two spaces are conflated: - PHYSICAL space (3D): where the core's MASS-ENERGY lives and where R is measured. A 3-ball does NOT concentrate at its boundary (27% in outer 10%). Mass is therefore VOLUMETRIC. - E8 INTERNAL field-space (8D Cartan / 248D full): where the concentration operates — localizing FIELD structure, not mass. T156 (DOI 10. 5281/zenodo. 19419096) identifies the Planck Shell as the level set of the degree-30 E8 Casimir — localizing the boundary/reflection/TENSION structure at the Shell (a field-space phenomenon), NOT mass-energy. CLEAN SEPARATION: - Lattice TENSION (+ boundary, reflection, Casimir structure): SURFACE-concentrated at the Shell. Supported by the field-space concentration and T156. The "surface" picture is right — for the tension. - MASS-ENERGY: distributed through the core's physical 3D VOLUME at ~Planck density => R ~ M^ (1/3), area ~ M^ (2/3). The "density" picture is right — for the mass. Supported by T259, consistent with T254's area-leverage Aᵢ ~ mᵢ^ (2/3). So the density radius-law STANDS (T259 vindicated, not corrected) ; the surface-concentration intuition ALSO stands — for the tension. The fork was a category confusion between a physical-space quantity (mass) and a field-space quantity (tension). WHY COHERENT: mass in the volume is what gives cores ~Planck density and the area-scaling T213/T254 rely on; tension on the surface is what makes the Shell the reflecting, tension-bearing, gravity-generating boundary of T156/T177. The resolution supplies BOTH, rather than forcing a choice. Retracts nothing — T259, T254, T156 all stand with domains clarified. Read alongside the Internal-Consistency Note (10. 5281/zenodo. 20434894), which raised the same exponent question (rₛhell ~ M⁰. 66 vs M⁰. 31).