The Structural Theorem of Capitalism: Full Structural Characterization, Public Replacement, and Joint Settlement

This paper proves a structural theorem covering all forms of capitalism: the complete exclusion of capital relations has the absence of asymmetry in permissions as its minimal support; every actual capital relation can be reconstructed from its own evidence of production, dependence, and control, and can enter a common social contract for termination and continuation. Coverage comes from universal proofs over laws, constructor types, execution sequences, and actual histories. For any production sequence, public replay preserves the full successor state, actual physical quantities, provision for every member's living and maintenance needs, and task services, while eliminating capital control. From any point in an actual run, a disposition procedure produces either a witness of complete abolition or a specific obstruction within a finite number of steps determined by the current internal workload. Success jointly preserves members' independent execution, productive capacity, executable futures, and full-account non-loss for every person and good, together with a strict gain; failure retains the precise responsibility and an entry for continuation. Debt not represented at the financial entry appears as a specific matrix discrepancy. Mechanisms fixed before unknown events support paid local information, real risk settlement, and continuing innovation beyond the quoted menu; throughout any actual continuation, cumulative receipts for one contribution origin across all account positions cannot exceed its issued quantity. Complete responsibilities are carried through coalitions, open mechanisms, and institutional changes, without requiring the existing ledger to be finite. For settlement costs, a financial tail with sufficient resources has an actual optimum, while another complete settlement domain supplies a strictly cheaper complete settlement for every completing candidate. By distinguishing the grounds of basic participation, repayment for contributions, and continuing control, the paper connects these results to theories of production relations, property rights, innovation, and common governance. It shows how production can continue while domination ceases to acquire permanent standing from the necessity of its functions.