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 Λₑff = (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) = sum₍=₀^3 A₃₍ (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) 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).