Landauer-Compensated Information Erasure in Cyclic Cosmology

A thermodynamically bookkept mechanism for cross-cycle information transfer is formulated from three independently specified ingredients: a holographic encoding isometry from bulk degrees of freedom onto the cosmological horizon, the Gibbons-Hawking thermodynamics of that horizon, and a Cyclic Cascading Dark Energy (CCDE) sector in which a Ratra-Peebles quintessence potential $V(\phi)=M^{4+\alpha}\phi^{-\alpha}$ drives $H(t)\to 0$ as $t\to\infty$. The encoding isometry is unitary on its domain and therefore incurs no Landauer cost. Any residual irreversible bulk erasure into the horizon bath still obeys $E_{\text{erase}} \ge N_{\text{bit}} k_{\text{B}} T_{\text{dS}} \ln 2$. In $\Lambda$CDM one has $H\to H_\infty > 0$, so the instantaneous cost per bit remains strictly positive, while the horizon capacity $S_{\text{dS}}^\infty \sim 10^{122}$ and the Smarr energy $c^5/(2G_{\text{N}}H_\infty)$ are amply larger than any conventional bulk accounting. Vanishing of the instantaneous cost for arbitrary finite $N_{\text{bit}}$ is therefore not forced by the second law in $\Lambda$CDM; it is a structural requirement of the present program and is realized if and only if $T_{\text{dS}}(t)\to 0$, i.e. if and only if $H(t)\to 0$. That limit is not available to a true cosmological constant. Canonical quintessence cannot produce a finite-time endpoint $H(t_*)=0$. The holonomy correction of loop quantum cosmology is retained only in the high-density regime, where it replaces the would-be singularity of a previous contraction by a bounce; at $\rho/\rho_{\text{crit}}\sim 10^{-123}$ the correction is parametrically absent and does not cascade the late-time dynamics. The de Sitter modular Hamiltonian generates the Tomita-Takesaki flow of the static-patch state and does not intertwine the bulk and horizon Hilbert spaces; the transfer map is an independent encoding isometry. On the Ratra-Peebles tail the conformal time to the infinite future converges, so the unphysical compactification admits a spacelike future boundary. The relevant cross-cycle data are conformal field data on that boundary, not the two Casimir invariants of $\mathrm{SO}(1,4)$ and not Bondi-Metzner-Sachs charges (the latter belong to null infinity). The tracker equation of state is $w_\phi = (\alpha w_{\text{B}}-2)/(\alpha+2)$; for $\alpha=2$ in a matter background this is $w_\phi = -1/2$, already excluded by Planck 2018, so observational viability requires the field to have left the tracker into potential domination with a super-Planckian excursion. The construction is falsified if $w=-1$ is confirmed at a level that forbids a rolling sector capable of driving $H\to 0$.