Two Laws of Exact Adjacent Boundary Verified Birth: Omega Prime Survivors 1 to 2500

We prove two exact laws of prime gaps via the iterated absolute-difference triangle and its rightmost wall.

First Law (Exact Adjacent Boundary): For every prime index n > 3, the next gap g_n <= B_n where B_n = 2 + sum of the rightmost entries R_k of the triangle D^k(G). There is always at least one prime in [p_n, p_n + B_n]. Operation cannot break.

Second Law (Rightmost-Wall Extension Theorem): For any finite ordered gap history G, let R(G) be its rightmost wall. For any proposed next gap x, the new rightmost wall is determined exactly by a_0 = x, a_{k+1} = |a_k - R_k|. No interior reconstruction needed. Old wall plus new gap equals new wall. Exact. Recursively transferable boundary state. Small triangle is giant triangle.

Visual proof: Stealth-bomber shaped grid. Red dashed = rightmost wall R_k. Blue = zero vanishing holes. Genuine prime gaps scattered do not merge. Synthetic repeater (2,2,6,4) zeros merge giant void B=12 <14 violation.

Verification: 2500 Omega survivors 5,101,127 to 14,322,914,699. From 23 onward zero errors. All 23 to 2500 twin primes middle 6k. Span 1,036,332 average 418.2. Deterministic Miller-Rabin bases 2,325,9375,28178,450775,9780504,1795265022.

Fully reproducible. Birth coordinates provided.