After Turing: The Fold Machine - An Exact, Parameter-Free and Machine-Closed Derivation of Classical Computational Science from Smithian Fold Theory

After Turing: The Fold Machine is the exhaustive standalone paper for the completed Classical Computation branch of the third clean-room reconstruction of Smithian Fold Theory (SFT). Version 1.1 reconstructs the complete V1/V2 computation surface at current strength and derives, in dependency order, Formal Computation; Computability; Computational Complexity; Algorithms and mathematical data structures; Semantics and mathematical programming theory; Concurrent and Distributed Computation; Cryptography and Computational Security; Learning and Intelligence Theory; and Scientific Computation. The headline native-model results are exact. For every admitted positive finite description depth k, the native Fold Busy-Beaver function is BB_F(k)=k. Exact evaluation emits the same unique lawful trace checked by the proof system, giving P_F=NP_F in the admitted Fold grammar. Every admitted depth-k Fold circuit requires its k forced transition edges; all 16,384 subsets of the depth-14 edge carrier were exhausted and only the full support survived. The paper states the comparison boundaries explicitly: these theorems do not silently become claims about arbitrary external Turing-machine tables, conventional P versus NP, or imported circuit models. The branch imports no Turing machine, lambda calculus, conventional complexity class, probability cause, cryptographic hardness assumption, pretrained model, fitted parameter, floating proof value, application answer or earlier SFT executable answer as a derivational premise. Empty One is structural rather than numerical zero; complementary held labels replace negative proof quantities; and randomized algorithms execute complete registered deterministic schedule support rather than assume an uncaused stochastic transition. The frozen inventory contains 116 dependency-ordered laws. Their grammars execute and decide 29,696 generated structural candidates, retain 116 unique survivors, 116 depth-independent base/successor certificates, 464 adverse controls and 116 implementation-distinct validations. A separate 763-entry ownership audit decomposes the relevant V1/V2 material into 134 atomic Classical Computation obligations, closes 134 at same strength, leaves none open and preserves four explicit corrections or reconciliations. The manuscript documents every derivation's dependencies, theorem, grammar, eliminations, survivor, minimality, uniqueness, witnesses, induction, controls, correspondence boundary and exact evidence identities. The release is also an explicit open-science position. It publishes source, candidate products, decision vectors, controls, validators and receipts so scientific authority rests on inspectable and revocable evidence rather than paywalls, proprietary oracles, credentials, capital or consensus. 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.