Tension Field Distribution

The Tension Field Distribution, T(θ,φ), is the field of tension over the spherical boundary of a null well, the pattern in which the parent universe's information is stored on that surface. In the book's holographic account of null wells, information falling in is not destroyed but projected from the collapsing interior onto the boundary, where information density scales with area rather than volume. The tension field is the carrier: its variation across the boundary, by polar angle θ and azimuthal angle φ, encodes what the parent universe held, and it writes the boundary's information density ρ_I(θ,φ), in Zinf bits per area, whose integral over the sphere, I◫ = ∮ ρ_I(θ,φ) · R² dΩ, is the surface's total information. The Encoding Density ρℹ = N▣/(4πr∅²) sets how densely bits sit on that surface, and the Projection Operation Π[I_3D] = ∫_V ρℹ · δ(r − r∅) d³r reduces volume information to the boundary shell at the null well radius, conserving total information through gravitational collapse. The book writes the Surface Information Integral as I◫ = ∮_∂null ρ_I(θ,φ) · R² dΩ, where I◫ is the total surface information content, tagged [1ᵇ], ∂null the null well boundary surface, ρ_I(θ,φ) the information density on the boundary [1ᵇ·𝕃⁻²], which the Tension Field Distribution writes, R the boundary radius [𝕃], θ and φ the polar and azimuthal angles [∅], and dΩ the solid angle element [∅]. The Tension Field Distribution connects to Surface Information Integral, Holographic Information Mapping, Encoding Density, Null Well Boundary, Boundary Encoding and Null Well Radius.