OUCH v3.5: Operator for Universal Cosmological Hysteresis as an Irreversible Damping Model for Late-Time Structure Growth

OUCH v3.5 presents the Operator for Universal Cosmological Hysteresis as a controlled and falsifiable model of irreversible damping in late‑time structure growth. The framework is motivated by the thermodynamic irreversibility of halo formation—collapse, virialization, merging, shock heating, tidal disruption, and phase‑space mixing—which generate entropy and path dependence in the cosmic growth history. A raw entropy reservoir Eraw(a) is not a physically admissible growth coupling because it is cumulative and unbounded. OUCH v3.5 therefore introduces a bounded irreversible fraction χ(a)=SirrSrev+Sirr, and constructs from it an irreversible friction operator Firr(a)=1+α χ(a) [1+b0 χ(a)]. The audited numerical implementation shows that OUCH does not modify the Poisson‑sector gravitational source term. Instead, it multiplies the friction term in the linear growth equation, producing a smooth monotonic suppression of late‑time structure growth. Using a Planck‑normalized baseline S8,ΛCDM≃0.83, the integrated scan yields representative values S8,pred=0.810 (α=0.09),0.786 (α=0.20),0.768 (α=0.29). We adopt a conservative fiducial value αfid=0.20 and identify α≃0.13–0.30 as the principal phenomenologically viable interval. In the UOG interpretation, α=β T0λ, so the microphysical closure condition is βT0/λ∼0.1–0.3. Values much smaller leave the S8 tension unchanged; values much larger over‑damp structure formation. OUCH v3.5 is a growth‑sector damping audit, not a full likelihood analysis nor a derivation of the dark‑energy equation of state. The benchmark parameters controlling Eraw(a) are treated as mass‑function‑motivated calibration inputs, with their detailed Press–Schechter/Sheth–Tormen derivation reserved for a technical appendix. A unified UOG cosmology requires that background‑sector and growth‑sector projections of irreversibility share a consistent transition history; this consistency condition is the next step beyond the present audit.