Asymptotic Density of Iterated Lattice Sumsets and Additive Self-Healing in Convex Lattice Regions

Version 1.16 addresses the three priority items from the four-role peer review (P0/P1/P2): 1. P0 (Required): 8-Neighbor Geometric Motivation - Int_8(A) is provided a complete geometric rationale via the l_infinity norm and standard digital topology (Rosenfeld 1979). - Proves that for rectangular boxes, int_8(A) strictly coincides with the relative interior in R^d. 2. P1 (Strongly Recommended): 3D Non-Rectangular Verification & R(h,k) Connection - Added 3D Triangular Prisms (n=3,4, h=3) and 3D Square Pyramid (r=2). All configurations pass dual verification (Mode 1 & Mode 2). - Strengthened Remark 5.1 detailing three explicit implications for Nathanson's R(h,k) Gap structure. 3. P2 (Recommended): Partial Proof Strategy for Conjecture 4.3 - Remark 4.5 outlines full proof of the rectangular special case (Theorem 3.2) and formulates three candidate geometric proof strategies for general convex regions.