Certified Residue Ledgers: Separating Exact Closure, Numerical Tolerance, and Statistical Evidence

This technical note specifies a Certified Residue Ledger (CRL): an evidence contract separating exact modular closure, certified numerical enclosure, operational tolerance and statistical evidence. It gives branch-preservation and verdict-soundness arguments, including negative increments and boundary crossings, and a restricted eventual-decisiveness theorem for rational-affine pi inputs. An appendix develops model-relative finite-state reduction, ranked minimality certificates and minimum supplementary records for recovery. The PDF and source ZIP include CRL-NUM-001, a bounded standard-library Python generator and recomputation checker, JSON schemas, examples, test results and a SHA-256 manifest. The release replay reproduced 111 expected outcomes: 89 ACCEPT, 19 REJECT and 3 UNDETERMINED. Certificate validity and tolerance verdicts remain separate. These selected tests are not comparative benchmarks, independent replication or formal software verification. General CRL implementation, the finite-state appendix implementation, statistical validation, comparative benchmarks and novelty assessment remain pending. No performance superiority, new physical mechanism or operational authority is claimed. Charles McClure is the human author. Codex assisted with exposition, internal skeptical review, code and local checks. A local Qwen model supplied one bounded advisory theorem check; its proposed counterexample was rejected with a recorded assessment. AI tools are not authors. This technical note has not been externally peer reviewed. Version 1.0; manuscript revision 003, November 1, 2026. All rights reserved for the manuscript and original companion materials; referenced third-party works retain their own rights.