gamma_gap_analysis
plain-language theorem explainer
The gamma_gap_analysis theorem records that the barrier analysis for deriving the Euler-Mascheroni constant holds in the current formalization. Researchers investigating the ledger-zeta link for prime distribution in Recognition Science would cite this as the status marker for C-011. The proof is a direct term-mode application of trivial that confirms the proposition without further steps.
Claim. The gap analysis for the Euler-Mascheroni constant holds, with the correspondence between gap-45 structure and zeta zeros remaining open.
background
The module formalizes the Euler-Mascheroni constant γ ≈ 0.5772 in the Recognition Science framework under registry item C-011. It records that bounds are proved while first-principles derivation remains blocked on ledger-zeta development, with a noted dependency on the Riemann hypothesis. The upstream Constants structure bundles CPM constants Knet, Cproj, Ceng, Cdisp together with the nonnegativity condition on Knet.
proof idea
The proof is a term-mode one-line wrapper that applies the trivial tactic to establish the proposition directly.
why it matters
This declaration marks the current status of C-011, noting that gap-45 is forced by D=3 while the Mertens theorem connection to zeta zeros stays open. It positions the constant within the broader RS constants registry pending ledger-zeta closure. No parent theorems are recorded in the used-by edges.
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