General Theory of Meta and Universal Representation

This preprint introduces the General Theory of Meta and Universal Representation (GTMUR), also denoted (Ω_χ), as the certified representation-transport layer in the broader Omega-stack framework. GTMUR studies how authority-bearing artifacts may be compared, translated, refined, quotiented, forgotten, approximated, lifted, or reinterpreted without silently creating, destroying, or mutating certified authority. The central object of the theory is the bicategory Reg_χ, whose objects are representation regimes, whose 1‑morphisms are certified typed representation morphisms, and whose 2‑morphisms are certified comparisons between such transports. The core certificate is χ_F : D_B F ⇒ F̅ D_A. which expresses compatibility between representation change and finite descent. This certificate is necessary for authority transport, but it is not sufficient by itself: the target regime must still verify and terminalize the transported artifact. The core thesis is that representation change cannot preserve authority unless it is typed, descent‑compatible, loss‑ledgered where needed, and terminalized in the target regime. The paper develops regime records, certified morphisms, finite‑core actions, descent‑square certificates, certificate pasting, relative bicategory construction, loss‑ledger discipline, no‑creation for lossy morphisms, terminal non‑bypass, descent compiler soundness, transport obstruction classes, and 2‑cell soundness. Several results are proved as conditional theorems relative to declared coherence data, semantic definitions, functoriality assumptions, and certificate‑completeness hypotheses. The paper deliberately separates the clean representation‑transport doctrine from later applications. Companion notes quarantine possible instantiations involving LLM/QM finite operator packets, path‑action repair histories, agentic IDE design, political and economic audit grammars, adversarial governance, and recursive ledger/audit substrates. These are not required for the main GTMUR preprint and are presented only as boundary notes for future work. This release is intended as a v1.0 preprint and first public archival version of GTMUR. Search factorization remains explicitly labeled as a principle pending formal search‑space definitions.