Complete Proof of Conjecture 10(2): Symmetry Bounds for Prime Transition Probabilities Modulo 6

RIGOROUS FINITE-SCALE LOWER BOUND FOR SAME-RESIDUE PRIME PAIRS MODULO 6 MAIN THEOREM (unconditional): For all N ≥ 10³,P_same(N) ≥ 0.00582 / log(log N) - 0.91 / log N KEY CONTRIBUTIONS: • Explicit Rosser-Iwaniec sieve bounds G_6m(N) ≥ 0.1 S(6m) N/(log N)²• Analytic proof: ∑f(m) ≥ 0.08 M/log M (M≥6)• Computational verification: 50,847,533 prime gaps up to 10^9• Empirical: 44.51% vs L-O-S asymptotic 34.64% (1416σ deviation) • Heuristic model: C_theor=0.0985 ≈ C_emp=0.1017 (1.3% match) DATA & CODE: Simple Python code for verification included 100% reproducible for more detaile/raw data/colaboration etc contact me. mail: fastgyuri@gmail.com Zenodo related: Prime gap conjecture [doi:10.5281/zenodo.18235682] Keywords :prime gaps, modulo 6, lower bounds, Rosser sieve, Hardy-Littlewood, Lemke Oliver Soundararajan, finite-scale analysis, number theory