Definition. Materialized harness state [ftip-00C8]
✍️source

    Let \(\mathcal V_{\rm fold}\) be a space of fold versions. For each \(v\in \mathcal V_{\rm fold}\), fix a deterministic map

    \[ F_v:\mathcal H_{\rm pers}\times \mathcal E_{\rm har} \longrightarrow \mathcal H_{\rm pers}. \]

    Given an initial persistent state \(h_0\), event stream \(L_n=(e_0,\ldots ,e_{n-1})\), and version sequence \(\boldsymbol v=(v_0,\ldots ,v_{n-1})\), its materialized harness state is obtained recursively by

    \[ h_{i+1}=F_{v_i}(h_i,e_i),\qquad 0\leq i<n. \]

    The materialization record is the tuple \((h_0,L_n,\boldsymbol v,(F_v)_v)\). Omitting a version or the initial state defines a family of possible materializations, not one replayable state.