CODA-OR: Omniversal Re-Presentation

CODA-OR: Omniversal Re-Presentation CODA-OR studies elementary gluing, finite diagram defects, and the additional records required to admit a comparison object. Its first result concerns two overlapping pairs (a, b) and (b′, c): a unique triple recovers both pairs exactly when b = b′. This is a theorem about products of types. It does not construct a bicategory of all representation systems or a universal object containing every regime. The computational model equips finite rational vector spaces with linear maps d₀ and d₁ satisfying d₁d₀ = 0. A square has a raw defect δ. The companion computes the exact ℓ¹ distance of δ from the repair image of d₀, with independently checkable primal and dual evidence. The resulting four labels distinguish a zero defect, a nonzero defect with an exact repair, a closed defect with positive leftover, and an open defect with nonzero d₁δ. Exact repairs are closed because d₁d₀ = 0. These labels describe the declared algebraic model; they are not permission decisions. A separate finite comparison record carries an object identifier, a support sieve, and declared descent, verifier, and terminalizer names. The implementation checks that the sieve and every arrow target the requested object, that required source support is present, and that the local names are supplied. The Lean support predicate includes the corresponding target-binding condition. A recorded counterexample shows why support aimed at a different object must be rejected. An empty support sieve cannot establish standing, envelope membership alone supplies none, and a limit candidate without its declared terminalizer fails the local standing predicate. The package combines prose proofs, Lean declarations for the stated elementary implications and countermodels, an exact rational Python companion, adversarial examples, and executable notebooks. The formal scope is recorded declaration by declaration in the accompanying proof map and axiom report. The Python implementation performs additional validation of concrete input strings and returns diagnostic records; the package does not claim a full formal equivalence proof of that API. An exact quotient value measures leftover, while the support and terminalizer checks are an explicit policy on finite records. No external licence, authenticated grant, global omniversal object, or general category-theoretic completion is produced by this model.