information_preservation

This module (Gravity Track 3.C) derives the triangular Page curve from Schmidt-balanced ledger dynamics instead of postulating a piecewise-linear ansatz. Evaporation is parameterized by a transfer fraction $t\in[0,1]$: bulk capacity falls as $S_{BH}(1-t)$ while radiation capacity grows as $S_{BH},t$. The joint bulk$\otimes$radiation state stays pure under unitary evolution from a pure initial bulk, so Schmidt's theorem forces equal reduced entropies bounded by $\min(\log d_{\mathrm{bulk}},\log d_{\mathrm{rad}})$.

The unitarity Page curve is defined as that saturated bound: $S_{\mathrm{rad}}(t)=\min(\mathrm{bulkCapacity},\mathrm{radiationCapacity})$. The sibling endpoint lemma already records that at $t=1$ bulk capacity is zero and radiation capacity equals $S_{BH}$, hence the min collapses to zero whenever $S_{BH}\ge 0$. That vanishing is the content named here as information preservation.

One-line term wrapper that applies the sibling endpoint lemma pageCurveFromUnitarity_at_one. That lemma unfolds the min definition, rewrites with the capacity endpoint facts (bulk capacity vanishes at $t=1$; radiation capacity equals $S_{BH}$), and finishes by min_eq_left under the nonnegativity hypothesis on $S_{BH}$.

This is the unitarity signature of the dynamical Page curve: all entropy initially in the bulk has been transferred to radiation, and radiation entropy returns to the pure-state value zero because no bulk degrees of freedom remain to entangle with. It sits inside the structural package that replaces Session 101's kinematic triangular ansatz by a derived $\min$ of two linear capacities forced by Schmidt purification. No downstream consumers are wired yet; the declaration closes the $t=1$ endpoint of the same recipe that forces the Page-time peak at $t=1/2$. Within Recognition Science gravity it records that ledger-tick transfer plus purity already yields information-preserving evaporation without an extra postulate.