Theoretical Framework and Observational Pipeline for Ramanujan-Bose Interval Cosmology

This paper proposes Ramanujan–Bose Interval Cosmology (RBIC), a cosmological framework in which dark energy emerges dynamically from a curvature-coupled quantum interval field. The central theoretical object is the Ramanujan–Bose constant B_RB(z), derived from the statistical competition between Ramanujan partition asymptotics and Boltzmann suppression via modular S-duality. Unlike phenomenological dark energy models, the coupling strength is not a free parameter — it is determined entirely by microphysical condensate statistics. The framework predicts a falsifiable deviation in the effective dark energy equation of state: w_eff(z = 0.5) ≈ −0.97 ± 0.03, accessible at DESI Year-3 precision. Two gravitational-wave signatures are derived: a definite condensate oscillation frequency accessible to SKA/PTA, and a speculative LISA-band signal pending future computation. A complete observational pipeline is developed covering Pantheon+ supernovae, BAO, CMB shift parameter, and fσ8 growth data, with a mock MCMC demonstration of parameter estimation. The paper additionally introduces the Observer-Frame Temporal Decoupling (OFTD) hypothesis as a speculative extension — proposing a geometric reinterpretation of Heisenberg uncertainty and wavefunction collapse via proper-time separation between macroscopic observers and quantum objects. This is the second paper in a connected theoretical programme. The first paper, "Interval in Cosmos" (Zenodo: 10.5281/zenodo.18951782), established the foundational geometric framework. The present work is submitted to the Journal of Astrophysics and Astronomy (Indian Academy of Sciences).