Status: Theorem-level E47 construction plus an exact, falsifiable fine-structure closure candidate.

Executive result

The two plates establish results at two distinct logical levels:

$$ \boxed{\text{a closed finite-dimensional theorem for }E_{47}} \qquad+\qquad \boxed{\text{an exact symbolic candidate for }\alpha^{-1}} $$

The first result is mathematically established. The second is arithmetically exact and extremely close to the stated experimental reference, while the

Linked child pages

• Canonical Corrected Formalism — Exact E47 Facts, Numerical Benchmarks, and Evidence Boundaries — authoritative theorem, correction, and evidence-boundary source.
• Babylonian Mathematics — Sexagesimal Computation, Square Roots, and the Newton–Heron Lineage — exact scalar-recursion theorem, historical lineage, and target-design boundary.
• Alpha from Omega Electromagnetic Closure — exact conditional arithmetic and the open physical-derivation problem.
• Visual Companion — E47 Canonical Theorem Plate — concise visual statement of the established finite-dimensional result.
• Python and Numerical Validation — executable reconstruction, residuals, and machine-verification record.
• Open Questions Observatory — Solutions, Partial Closures, and Validation Queue — uniqueness audit, falsification criteria, and unresolved obligations.

47-scalar ledger audit · Batch 9

The reviewed synthesis plate contains a strong exact core and a larger family of declared extensions.

Exact or directly derivable scalars: carrier dimension, Casimir values and multiplicities, sector dimensions, filter eigenvalues, $K^2$ eigenvalues, protected/transient dimensions, $\Omega_c=47/125$, projector identities, leakage complementarity, kernel energy, spectral gap, continuous attenuation, stable Euler bound, and the corrected Babylonian fixed-point recursion.

Deterministic recomputation: the closure polynomial

$$ 7750000z^3-15500000z^2+14947211z-3840793 $$

factors over the reals with unique real root $z=47/125$. The displayed generator

$$ \Phi(Q)=\frac12Q^3-\frac53Q^2+\frac1{24}Q $$

gives