Landauer-Compensated Information Erasure in Cyclic Cosmology

A thermodynamically consistent mechanism for cross-cycle information transfer is proposed, combining holographic boundary encoding, de Sitter horizon thermodynamics, and a Cyclic Cascading Dark Energy (CCDE) model in which the Hubble parameter $H(t)$ tends asymptotically to zero, driving the de Sitter horizon temperature T_→ 0. Penrose's Conformal Cyclic Cosmology (CCC) is constructed on a de Sitter-like exponentially expanding future (Λ>0), whose future conformal boundary is spacelike; this spacelike character is matched conformally to the spacelike Big Bang of the next aeon, and is therefore a precondition of CCC rather than an obstruction. The genuine bottleneck in ΛCDM is thermodynamic, not topological: with H→ H∞>0 eternally, T_∞>0 eternally and the Landauer cost of bulk erasure never vanishes. We propose the CCDE model as a thermodynamic resolution: a Ratra--Peebles quintessence potential V(φ)=M4+αφ-α combined with the Loop Quantum Cosmology holonomy correction H²∝ρ(1-ρ/) drives H(t)→ 0 asymptotically, so that T_(t)→ 0 and the Landauer cost per bit kBT_ln 2 vanishes in the asymptotic future. A finite-time endpoint H(t*)=0 is not achieved by canonical quintessence plus standard LQC alone; the quiet-bounce scenario is identified as an additional hypothesis requiring either phantom kinetic energy (quantum-mechanically unstable) or modified gravity. The de Sitter modular Hamiltonian K_=(2π/H)+log Z has a c-number part (log Z~~ 1/H²) that diverges as H→ 0 but contributes only a global phase to the bulk-to-horizon transfer map $U(t)$; the operator part (2π/H) remains bounded on the typical thermal sector. The cross-cycle information channel is formulated using the asymptotic symmetry of spacelike (the de Sitter group $SO(1,4)$ and its Poincar\'e contraction), without invoking the BMS group, which is the asymptotic symmetry of null infinity and is not the relevant structure for a spacelike . The framework is falsifiable: if ΛCDM is confirmed with $w=-1$ to high precision, the asymptotic-thermodynamic channel collapses. Falsifiable predictions include a dark-energy equation of state w(a)≠ -1 at the percent level (testable by DESI/Euclid 2024--2030, with current DESI 2024 values w₀=-0.827± 0.063, wₐ=-0.75+0.29-0.25 preferring w≠ -1 at ~ 2.5σ for the PantheonPlus combination; other supernova compilations give $3.5$--3.9σ), a primordial tensor-to-scalar ratio r~ 10⁻⁴--10⁻³ from LQC holonomy corrections, and a characteristic cross-correlation between low- and high- CMB modes seeded by the previous-cycle horizon state. If ΛCDM is confirmed with $w=-1$ to high precision, the entire cyclic framework collapses; this all-or-nothing dependence is treated as a high-risk, high-reward feature of the framework.