From Distinction to Information: An Exact, Parameter-Free and Machine-Closed Derivation of Information Science from Smithian Fold Theory

From Distinction to Information is the standalone paper for the completed Information Science branch of the third clean-room reconstruction of Smithian Fold Theory (SFT). From the separately admitted Foundation and Mathematics receipts it derives, in dependency order, symbols and distinguishability; encoding and decoding; exact information quantity; entropy and uncertainty; compression and redundancy; finite channels and capacity; noise and error; exact finite coding; mutual and conditional information; conservation, loss and transformation; classical and probabilistic information correspondence; and quantum-information support correspondence. The branch does not import a conventional bit, logarithmic information measure, stochastic cause, fitted distribution, unregistered metric, complex amplitude, pretrained model or application output as a premise. Information is retained as complete generated alternative support and exact retained/closed distinction ledgers. Entropy preserves every observation class, exact positive support part and unresolved pair. Probability describes observation-relative uncertainty over deterministic support. Channel capacity is the complete family of greatest structurally distinguishable input selections, and exact correction follows from disjoint registered error-image supports. The twelve complete claim grammars execute 11,776 generated candidates. Every candidate is decided, each grammar has exactly one all-preserving survivor, and every claim passes minimality, named-shape uniqueness, a depth-independent base/successor certificate, four adverse-control classes, cryptographic sealing and implementation-distinct recomputation. The 42-page paper documents every derivation in full: dependencies, theorem, complete candidate axes, rejection reasons, unique survivor, operational laws, witnesses, induction certificate, meaning, correspondence boundary, limitations and exact source, validator, seal and receipt identities. The accompanying evidence/source release contains the Markdown paper, archival PDF, frozen inventory, all twelve claim packages, 11,776 candidate records and decisions, controls, certificates, executable law modules, independent validators, engine receipts, tests, publication evidence map and checksum ledger. The one-command cross-platform verifier passes the full test suite with 100 percent executable-line coverage of the core admission engine and independently reruns all 34 admitted derivations through Information Science. The quantum result is deliberately bounded to finite information-support correspondence: one Fold distinction, complete Fold-word basis support, pair-cell joint support and exact observation records. Phase, interference, entanglement, gates, measurement dynamics, quantum correction and fault tolerance remain obligations of the later Quantum Computation branch. The next dependency branch is Formal Computation.