An infrared-effective cosmographic deformation of ΛCDM from the closed-form β0=β1 subclass of Hassan-Rosen bigravity: spectral (1+z)^6 signature and DESI 2024 constraints

We present an infrared-effective cosmographic deformation of ΛCDM derived from the closed-form β0=β1 subclass of exchange-symmetric Hassan-Rosen bigravity (companion paper II). The subclass reduces to a single dynamical parameter ε0 ≡ ξ0−1 once Λ_eff = (m²/2)(5β1+3β2) is fixed by H0. In the linearised matching regime ε ≈ ε0(1+z)³ valid for |ε| ≪ 1, the Hubble parameter admits the exact polynomial spectral decomposition 3 H²(z) = sumₙ₌₀³ A₃ₙ (1+z)³ⁿ with A3 ∝ ε0, A6 ∝ ε0², A9 ∝ ε0³. The (1+z)^6 amplitude A6, absent from ΛCDM and CPL parametrisations, is the distinctive observational signature of the subclass. A four-amplitude χ² fit against DESI 2024 BAO (7 redshift bins) and Pantheon+ SNe Ia (1580 SNe at z>0.01, calibrators excluded) gives the 95% CL upper bound Ω6 ≡ A6 / (3 H0²) < 6 × 10^-5, equivalent to |ε0| < 0.009 (linear regime, β2 > β1 > 0). The bound is dominated by the DESI Lyα-QSO bin at z=2.33; a conservative fallback excluding the Lyα bin yields Ω6 < 7.5 × 10^-4 (|ε0| < 0.032). The headline bound is robust across the physical coupling-ratio range β2/β1 in [1, 10] and confirmed by leave-one-out jackknife stability across the BAO bins. A complementary grid scan of the exact closed-form H(z) reveals a second viable region at ε0 ~ 0.25-0.30 where the spectral decomposition is incomplete and the model mimics ΛCDM at current data precision; the two regimes are complementary, not contradictory. Planck 2018 CMB is excluded from the joint χ² because the linearised expansion fails at z* = 1090. A Fisher forecast for Euclid spectroscopic BAO predicts a ~4.8x improvement in σ(Ω6) relative to DESI 2024. Information criteria favour ΛCDM (ΔAIC = -4, ΔBIC ≃ -15) at the cosmographic level; we present this work as a cosmographic deformation constraint, not as a complete cosmological model. The paper is mathematically validated by 9 PASS / 1 ATTN sympy verification (the residual ATTN being a CPL sign-convention clarification, not a bug). Companion to paper I (DOI 10.5281/zenodo.19988039), paper II, and the cosmic-voids paper (DOI 10.5281/zenodo.18753649).