The Polynomial Certificate of Transputation: MDL Unification, Quantum Measurement, and the SRRG Fixed Point

The quantum measurement problem - why a superposition produces a single definite outcome, and why with probability |cₖ|² - remains unresolved across standard interpretations of quantum mechanics, which either postulate collapse, multiply unobservable branches, or explain apparent classicality without resolving outcomes. This paper provides a formal derivation of the measurement mechanism from first principles within the GTE (Generative Triple Evolution) framework. The GTE polynomial p (L, C, R) = C+R-CR-LCR over 7, the unique Minimum Description Length (MDL) -minimal encoding of the Standard Model generation structure, carries a complete formal certificate of the quantum measurement mechanism. Its Perfect Self-Containment (PSC) projection is, the discrete adjudicator that defines the measurement orbit GEN₁ GEN₂ GEN₃ VAC - the only PSC-consistent trajectory in the cellular automaton dynamics - and this projection is characterized in three parts: agrees with p on the binary sector \0, 1\³ (Rule 110), overrides p on the ten SM-orbit neighborhoods to enforce generation-orbit consistency, and projects to zero on all remaining 325 neighborhoods. The polynomial's real diagonal encodes the Self-Referential Renormalization Group (SRRG) adjudication fixed point phi = (5-1) /2 0. 618 (machine-certified, ). A Three-Level MDL Unification Theorem () shows that (X) = ₓ X K (x PSC) operates at three nested, non-circular domains: theory selection (p from rule space), field dynamics (via the PMDL variational principle), and quantum event adjudication (Born rule via transputation). The polynomial p is the connecting object: it is the output of Level 1, enters the PMDL action at Level 2, and its PSC-projection defines the orbit used at Level 3. A two-sided computability classification (; hardness core) locates transputation exactly: record-truth on the diagonal fragment is ⁰₁-complete, the adjudicator is limit-computable with boundedly many mind changes under a named premise bundle, and hence T (diag) = 0' exactly - the Gold-Putnam trial-and-error stratum, with no computable convergence modulus. Quantum measurement is trial-and-error computation at the halting degree, and no stronger: physics requires exactly one Turing jump. The same degree-0' structure reappears at the field level: the irreducible residual of the PMDL action is a left-c. e. \ real of degree exactly 0', so the cosmological constant inherits the transputation classification. Differential Self-Adjudicative Computation (DSAC) is positioned as the continuum member of the D adjudicator class, bridging the discrete projection and the transputation selector D: its relaxation-to-coherence dynamics is the physical realization of the computable stage sequence whose limit is the adjudication outcome.