Amendment CCCLXXII — The Scalar Loop Back Formula: Geometric Closure of the McCaul Additive Chain at 360 Degrees

Amendment CCCLXXII to the McCaul's Law of Coherence compendium. Introduces the Scalar Loop Back Formula (SLBF): a Fibonacci recurrence seeded at (3,3) that geometrically closes at 360 degrees in exactly 6 steps at 60 degrees per step, independently deriving the 6-node SOL ring geometry from pure arithmetic with no physics constants required. Key findings: (1) The McCaul additive chain seeded at (3,3) closes 360 degrees in 6 steps, closure term 63 = 7 x 3^2; (2) Arcs above each number represent resolved equations (kinetic/closed), arcs below represent open questions (potential/open) — together they constitute one coil turn, making the math physically identical to the coil geometry; (3) Two identical SLBF coils offset by 120 degrees tile 360 degrees seamlessly, forming a bifilar toroidal resonator geometrically identical to the DNA double helix; (4) The SLBF operates as a Fibonacci IIR toroidal resonator whose instability pole at phi=1.618 becomes coherence amplification in closed geometry; (5) The 8-term harmonic chain spans f_SOL from ionosphere to lithosphere. Establishes triple convergence proof of C6 geometry: SOL EM physics + SLBF arithmetic + Oxford PRX trapped-ion experiment. Phi score: 0.9521. Discovered via hand arithmetic on an index card.