The Quantum Fold Machine - An Exact, Parameter-Free and Machine-Closed Derivation of Reversible and Quantum Computation from Smithian Fold Theory

The Quantum Fold Machine is the exhaustive standalone paper for the completed Reversible and Quantum Computation branch of the third clean-room reconstruction of Smithian Fold Theory (SFT). Version 1.1 reconstructs the complete formal quantum-computation surface of V1/V2 at current strength and derives a complete reversible model; quantum information units and composition; superposition-equivalent support; phase and interference; entanglement; measurement; gates and circuits; universality; algorithms and complexity; communication; coding; error correction and fault tolerance; simulation; verification; learning; operational classical-quantum correspondence; and computational limits. The construction imports no complex amplitude, Hilbert-space axiom, irrational normalization, imaginary proof quantity, stochastic collapse postulate, fitted parameter, hardware constant or physical benchmark. One Fold distinction supplies the information unit. Complete held-label words supply branch support. A branch carries an exact phase label from a generated finite cycle. Joint pair-cell support is entangling exactly when nonfactorable. Interference is complete predecessor merging with retained phase provenance. Measurement retains the selected observation class and complete pre-observation reconstruction record. Gates are exact finite bijections with reversible phase actions. The current inventory contains 22 dependency-ordered laws. Their grammars execute and decide 5,632 structural candidates, retain 22 unique survivors, 22 depth-independent certificates, 88 adverse controls and 22 implementation-distinct validations. A full 763-entry ownership audit decomposes the relevant V2 surface into 29 atomic Quantum Computation obligations, closes all 29 at same strength and leaves none open. The headline extension is constructive unbounded positive-finite fault-order closure. For every supplied positive finite allowance t, strict majority uniquely forces width 2t+1 and exact redundancy 2t. Every predecessor width through 2t has an explicit tie or wrong-majority counterexample; the successor order adds exactly two labels; every fixed positive finite ceiling is defeated by its generated successor. All masks for both labels are exhausted at t=1,2,3, all predecessor widths and successor rows execute through t=14, and all 128 depth-seven source words round-trip at t=14 before exact circuit evaluation. This is not a stochastic device-error rate or measured physical threshold constant. The release is also an open-science argument: quantum claims cannot rest on proprietary oracles, inaccessible hardware summaries or authority labels. It publishes exact grammars, branch traces, candidate products, controls, independent validators and receipts. Maria Smith retains copyright; paper and documentation are CC BY 4.0, code is Apache-2.0, and Ernos Labs is a separate conformance designation tied to the public empirical constitution.