The Completeness of Persistence: A Full State Space Characterization in La Profilée

The preceding papers in this series established the Frame Continuity Condition (FCC, Paper 57), the identity tolerance δ_F derived from the constitutive–operational Frame distinction (Paper 58), and the Constitutive Reading Protocol for identifying F_constitutive (Paper 59). Together these papers extended LP’s state space to four regimes: Persistence, Collapse, Transmutation, and Dissolution. The present paper proves that this typology is complete: every system under transformation occupies exactly one of these four regimes at every time t. The proof proceeds in three steps. First, both IR and FCC are shown to be genuinely binary conditions — threshold phenomena, not continuous scales. Second, the two conditions are shown to be logically independent: neither determines the other, and each combination is realizable. Third, the cross-product of two independent binary conditions yields exactly four partitions, and no fifth regime is structurally possible. The result is not a taxonomic convenience but a structural theorem: the LP state space is closed under the conditions that govern persistence.