The integration axiom that closes the Grand Problem. Individual record-breaks pay per leaf; this axiom pays when the full registry — one ground-truth source for every (shape × field) tuple's current best decomposition — exists as a reproducible, content-addressed, machine-checkable artifact.

**Deliverables.** 1. A registry file (JSON or TOML) keyed by (m, n, p, field) → {mults, citation_doi, decomposition_ipfs_cid, verifier_image_cid}. 2. A verifier Docker image, content-addressed, that accepts a submission for any registered (shape × field) and runs the appropriate tensor-sum check. 3. Reproduction proof: the Omenion reproduction harness re-runs the registry's verifier against every registered decomposition and confirms all pass.

**Verification.** Omenion's staged harness fetches the registry, pulls the verifier image by CID, and runs it against every registered decomposition. Axiom passes when all leaves pass and the registry format validates against a declared schema.