v8 - Mother Residue (RM): A Unified Non-Canonical Scalar Field Framework for Dark Matter and Dark Energy

Description (v8): This version (v8) presents the consolidated formulation of the Mother Residue (RM) framework as a non-canonical scalar field model aimed at providing a unified dynamical interpretation of the dark sector. The RM field is described by a Lagrangian of the formℒ_RM = A(φ) X^n − V(φ),where the kinetic and potential structure naturally generate two effective dynamical regimes: a matter-like clustering regime (w ≈ 0, c_s² ≪ 1), a dark-energy-like acceleration regime (w ≈ −1 or mildly w < −1). At the background level, the model reproduces the standard ΛCDM expansion history within observational bounds while embedding ΛCDM as a limiting case.At the linear perturbation level, the low effective sound speed ensures clustering behavior compatible with large-scale structure formation. This version includes: full Lagrangian formulation, background cosmology, linear growth analysis, effective parameter-level comparison with observational constraints (H₀, Ω_m, Ω_b, n_s, σ₈), discussion of large-scale phenomenological implications. The analysis is performed at the background and linear-growth level.A full Boltzmann-code implementation and joint likelihood analysis are left to future work. This release supersedes previous versions and represents a stabilized theoretical formulation of the RM framework suitable for archival and citation purposes.