Microscopic Origin of QIMG Thermalisation: From the Thermalisation Lagrangian Lₜₕ to Channel Rates Γᵢ(T)

Quantum-Informational Metric Genesis Cosmology (QIMG Cosmology) was introduced as a post-FRW extension of the Cyclic Black Hole Information Reintegration Theory (CBHIRT). In this framework, CBHIRT supplies the pre-geometric informational initial conditions inherited from Page-time black-hole correlations, while QIMG describes how this inherited structure may be represented after FRW activation as an effective metric geometry and an informational stress-energy tensor, \[ Tⁱⁿᶠᵒμν[I]. \] A subsequent thermalisation module proposed that this effective QIMG stress-energy representation may enter a controlled realisation regime and become physically expressed as radiation, matter, entropy, temperature, and hot primordial plasma. However, that module remained primarily phenomenological: it introduced a thermalisation map, a residual sector, a physically realised sector, and channel rates, but did not yet derive these structures from an underlying microscopic or action-level formulation. The present work develops the next layer of the CBHIRT--QIMG programme by proposing an effective microscopic origin for QIMG thermalisation. Its central aim is to construct a covariant thermalisation action \[ Sₜₕ = ∫ d^4x √-g\, Lₜₕ, \] from which the transfer current \[ Jᵗʰν \] and the temperature-dependent channel rates \[ Γ_i(T) \] may be systematically motivated. The object undergoing thermalisation is not raw information itself, but the residual QIMG stress-energy representation \[ Tʳᵉˢμν = (1-Θₜₕ) Tⁱⁿᶠᵒμν, \] which acts as a pre-thermal effective reservoir after FRW activation. The physically realised sector is described by \[ Tᵖʰʸˢμν = Tʳᵃᵈμν + Tᵐᵃᵗᵗᵉʳμν + Tᵖˡᵃˢᵐᵃμν, \] where the plasma tensor represents collective interaction and coupling effects rather than a double counting of radiation and matter. The paper formulates a thermalisation Lagrangian density containing residual-sector operators, channel operators, coupling scales, and covariant response functions. The transfer current is derived from the variation of the effective action and interpreted as the covariant flow of stress-energy representation from the residual QIMG sector into physical radiation, matter, and plasma channels. The corresponding channel rates are expressed schematically as \[ Γ_i(T) = {Λₜₕ⁸} {λ_i^2 κₜₕ^2} \, εᵣₑₛ\, Tμνᵣₑₛ Tαβᵣₑₛ ρi,μναβ(T) , \] where \(ρi,μναβ(T)\) denotes the finite-temperature spectral response of the physical channel \(i\), and the brackets indicate coarse-grained thermal averaging. This construction does not claim a direct conversion of information into energy. Instead, it provides an action-based mechanism by which an already established QIMG stress-energy representation may become physically realised through covariant thermalisation channels. In this sense, the present work supplies the microscopic completion of the previous thermalisation module and connects the CBHIRT--QIMG informational-geometric hierarchy to the Hot Big Bang radiation--matter plasma phase.