Collision Counting in a Rounded Hyperbolic Code Sequence

We study the rounded hyperbolic code sequence a_m = RNTE(2N²/m), where RNTE denotes round to nearest, ties to even. For adjacent decrements Δ_m = a_m − aₘ₊₁, we prove that Δ_m belongs to {0,1,2}, collisions are isolated, and the number of zero decrements equals the number of two-code skips. A critical-index boundary reduction yields the exact formula C_N = nint(N(3 − 2√2)) for every positive integer N, with limiting collision density 3 − 2√2. For N = 2^(p−1), the sequence encodes correctly rounded reciprocals of all p-bit inputs in the binary binade [1,2), at equal target precision. This bilingual release contains the complete English and Hungarian papers, together with a reproducibility source package including exact-arithmetic verification code, generated data, bibliography, documentation, and SHA-256 integrity records. The mathematical proof is independent of numerical enumeration. The accompanying verifier reproduces the published table and checks the result over the documented test ranges. AI research collaborator: Noa AI. Licensing:- Articles and PDFs: CC BY 4.0- Verification code: MIT License- Generated data: CC0 1.0