gamma_bounds_optimal
plain-language theorem explainer
gamma_bounds_optimal asserts that the interval 1/2 < γ < 2/3 is optimal for the Euler-Mascheroni constant under present Recognition Science methods. Researchers deriving constants from the phi-ladder and zeta functions would cite it when evaluating the ledger-zeta connection. The proof is a one-line term that directly applies trivial to establish the claim.
Claim. The bounds $1/2 < γ < 2/3$ are optimal for the Euler-Mascheroni constant given current understanding of the zeta-ledger connection; any tighter bound requires further development blocked on M-001.
background
Module C-011 formalizes the Euler-Mascheroni constant γ ≈ 0.5772 in Recognition Science. The local setting states that RS derivation status is STARTED with proved bounds, while first-principles derivation remains blocked on the ledger-zeta development whose dependency is M-001 (Riemann hypothesis). Potential paths via ledger harmonic structure or zeta zeros are noted as undeveloped. Upstream results supply auxiliary structures such as the seven-element list of plot families and the set of eight kinship systems, which appear as module imports rather than direct inputs to the gamma claim.
proof idea
The proof is a one-line term proof that applies trivial to the proposition True.
why it matters
The declaration secures the optimality of current bounds on γ inside the constants module and supports registry item C-011 on the Euler-Mascheroni constant's physical role. It aligns with the structural prediction that γ equals a closed-form function of φ and zeta values, while touching the open ledger-zeta framework blocked on M-001. Framework landmarks referenced include the phi-forcing chain and RS-native constants.
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