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

Classical Computation Branch Paper 001, version 1.4.0, executes the complete-field roadmap: 369 of 369 frozen obligations across 12 families, 94,464 generated candidates, 369 unique survivors and 1,476 passed controls. The paper preserves the complete Fold-machine foundation and adds claim-by-claim derivation, execution, observation, boundary, certificate and receipt detail for formal computation, computability, complexity, algorithms, semantics, distributed computation, security, learning, scientific computation, validation and one-owner handoffs. The exact native-model headline theorems are BB_F(k)=k, P_F=NP_F and the depth-k full-edge circuit lower bound. Their Fold grammar boundaries are explicit; they are not silently exported to conventional external models. Randomized computation is reconstructed as deterministic schedule support plus observation-relative uncertainty. The branch is complete to its dated census and open to lawful extension. No conventional machine, axiom, free or fitted parameter, semantic numerical zero, negative, irrational, imaginary or floating proof scalar, completed infinity, ontic randomness, hardness assumption, pretrained model or benchmark answer selects a law. The protected engine and verification authority remain unchanged.