Minimal Sequential Representation of the P2_n Sector: Context–Memory Tradeoff and Two-State Classical Realization — RCD Program, Technical Note REP-0 (v0.1)

Technical Note REP-0 of the RCD program (continues BMR-1, DOI 10.5281/zenodo.23717139, and the Adjudication Record "Relational Memory under Causal Erasure", DOI 10.5281/zenodo.23717352). Question: how much internal memory does a covariant sequential rule need to generate and transport the erasure-closed sector P2_n = {chain, p1, p2}, which the scalar Rideout–Sorkin (RS) family cannot support (BMR-1, Theorem 3)? Result (theorem, all N ≥ 4): over the local RS alphabet Σ_RS (letter = (|past|, #maximals)) the minimal clocked linear representation has dimension d_clk = 2, with an explicit witness D2_N for the lower bound and an explicit two-state automaton for the upper bound; over the full covariant alphabet Σ_cov (letter = isomorphism class of the past) d_clk = 1 (context–memory tradeoff: the information RS discards when it replaces the shape of the past by two numbers reappears as one internal bit). The two-dimensional representation is classical — real nonnegative matrices and one hidden bit — and a commuting realization exists with one negative weight; P2_n demands neither noncommuting nor complex amplitudes. The stationary (clockless) dimension d_stat remains open after an inconclusive numerical search. Exhaustive mechanical control of all lemmas over all natural histories at N = 4..7; all scripts with a SHA-256 manifest. English and Spanish versions; the Spanish text prevails.