Cyclotomic Dark Energy: The Cosmological Constant from Fermion Phase-Closure

This paper provides a smoking-gun validation of the Golden Mandala framework and Information-Pressure Theory (IPT) by proving that the same cyclotomic polynomials which determine sub-percent fermion mass corrections also determine the cosmological constant, with zero additional inputs. Nine dressed fermion channels in the mandala are each assigned a cyclotomic polynomial Φₙ(π) by their closure-loop structure on S². The cyclotomic-Young correspondence, originally derived to explain whether each particle's mass receives a curvature tax or coherence bonus, assigns each channel a sign: alternating polynomial coefficients yield destructive interference (pay), all-positive coefficients yield constructive interference (collect). These polynomials, signs, and channels are independently fixed by the fermion mass derivation. Weighting each polynomial by the channel's mandala-derived spin degrees of freedom (χNc = 6 for color-carrying orbits, χ = 2 for witness-dominant) and summing with the forced signs gives a total signed boundary loading of Σ_Φ = −695.64. Six pay channels overwhelm three collect channels: the boundary expends more free energy maintaining its fermion records than it receives in coherence bonuses. Dividing by the geometric capacity of the encoding space (χs)³ = 1000 and subtracting the broken-weak-monopole collar defect — a rigid topological ratio Nc³/(χ⁴s²·8π) = 27/(3200π), measuring how much of the broken W±/Z connection modes fail to project onto the uniform boundary sector — gives the prediction: Ω_Λ = |Σ_Φ|/(χs)³ − 27/(3200π) = 0.6930 DESI 2024 + CMB: Ω_Λ = 0.693 ± 0.005. Agreement: 0.01σ. No thermodynamics. No degree-of-freedom counting of 76 continuous fields. No free parameters. The bosons do not appear explicitly because they are the edges the fermions traverse: each power of π in the cyclotomic polynomial represents one edge-crossing on the mandala. Counting fermion phase-windings and counting bosonic degrees of freedom are two measurements of the same boundary stress. This result unifies the particle mass spectrum and the vacuum energy as two projections of the same geometric object: the cyclotomic phase structure of fermion closure loops on S². The mass formula uses δ_f = W²/(s·Φₙ(π) + C) — the polynomial modulated by witnessing cost and capacity. The cosmological sum uses DOF × Φₙ(π) — the raw polynomial weighted by boundary occupation. One is the per-channel encoding cost. The other is the total boundary loading. Both are read from the same mandala. KEYWORDS cosmological constant; dark energy; cyclotomic polynomials; Information-Pressure Theory; golden mandala; fermion mass dressing; boundary encoding; phase-closure; Standard Model; zero free parameters; DESI; causal diamond; vacuum energy; unification