Goldbach Gap Characterization

Goldbach gap = parity barrier. CRT guarantees local conditions always satisfiable. Gap is exponential_quantification (K4) — no sieve lifts local to global.

Goldbach Gap Characterization

Summary

Goldbach gap = parity barrier. CRT guarantees local conditions always satisfiable. Gap is exponential_quantification (K4) — no sieve lifts local to global.

Statement

\label{prop:goldbach-gap}
CRT guarantees local conditions are always satisfiable.
The gap is the \emph{parity barrier}: no sieve or finite verification
can lift local solutions to a global proof.  The
\texttt{exponential\_quantification} forbidden move (K4 violation)
captures this gap precisely.

\textbf{Registry:} III.P44.\quad
\textbf{Scope:} established (meta-theorem about proof limitations).

Proof / Justification

No immediate manuscript proof block was extracted in this pilot run.

Source Context

• Registry source: book-03.jsonl line 265
• Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.tex lines 213-222

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookIII.Bridge.ConjectureGaps
• Name: goldbach_gap_parity

Dependencies

• Canonical: III.P43, III.D69

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.