The Spectral Gap of the 120-Pole Fibonacci Sphere as a Candidate Mechanism for the QCD Mass Gap

The center Z₃ of SU(3) forces center-vortex flux to branch trivalently; a trivalent graph on S²carries exactly 12 pentagonal defects; arranged icosahedrally they admit I_h-vertex-transitivetrivalent polyhedra with V ∈ {20, 60, 60, 120}, of which V = 120 is the unique free orbit.Placing 120 points on the sphere by the golden-angle lattice and coupling them with w(r) = K₀exp(−r/d_c) at the hemisphere chord d_c gives a graph Laplacian whose first nonzero eigenvalueis λ₁ = 2.266475 at the ledger binding K₀_fb(D_ang) (2.299420 at the historical K₀* = 0.169 of theMarch paper; exactly proportional to K₀). With the proposed form Δ(R) = λ₁ħc/R this yields 306–511 MeV across R = 0.875–1.46 fm (311–519 MeV at the historical binding), a flux-tube width ξ =R/λ₁ = 0.454 fm at R = 1.03 fm (0.448 fm) against the lattice value 0.45 fm, and a vacuum energydensity 219 MeV/fm³ (228 MeV/fm³) against the scale (200 MeV)⁴/(ħc)³ = 208 MeV/fm³, with nofitted parameter. The confinement radius R_conf = 0.471 fm of the March paper is shown toequal √(ħc/σ_lattice) identically and is withdrawn as a framework prediction. The hemispherespectral identity λ₁/(Tr L/N) → 2(3e − 8)/(e − 2) with its exact −2/N correction and the packingremainder Ψ_F is included, and its two previously unsynced correction factors are defined by astated computation (0.99656 × 0.99865 = 0.995214). The dimensional-transmutation exponentC = d_c + b_fib is compared with a target C_target derived here for the first time in print fromthe lattice string tension; the match is binding-dependent: +0.05 % at the March pair (retiredD, historical K₀), +2.24 % at the ledger canon pair, −0.007 % at the spectral-identity pair, andthe March 0.05 % headline is withdrawn. An agent-based simulation with no imposed latticereproduces λ₁ within 1.3 % at N = 120, the best match over N = 60–160; re-run here underthe ledger binding with the original seeds, N = 120 stays the best match at every K₀ object(+1.34 %, +0.92 %, +1.29 %). We state the chain as a candidate mechanism for the mass-gaphalf of the Yang–Mills problem, independent of and complementary to any rigorous existenceconstruction, and we registered in advance (commit 0619d2d7, OpenTimestamps receipt) whatsuch a construction must look like for the mechanism to apply.