cert_inhabited
plain-language theorem explainer
The theorem establishes that the gravitational coupling score card certificate structure is inhabited by exhibiting an explicit term that satisfies the native bracket interval and exceeds the codata value for the RS-native alpha_G prediction. Researchers auditing the Recognition Science mass ladder and phase 0 rows would cite this to confirm a valid certificate exists for the dimensionless gravitational coupling. The proof is a direct term construction that instantiates the structure with the precomputed certificate.
Claim. There exists a certificate $c$ such that $4.5times10^9 < alpha_G^{rm RS} < 4.85times10^9$ and $alpha_G^{rm codata} < alpha_G^{rm RS}$, where $alpha_G^{rm RS}$ denotes the RS-native prediction $G m_e^2/(hbar c)$ in coherence-mass units.
background
In the Recognition Science framework the dimensionless gravitational coupling is defined as $alpha_G^{rm RS} := G m_e^2/(hbar c)$ using the in-framework constants $G$, $hbar$, $c$ and the structural electron mass. The module treats this as phase 0 row P0-AG of the physical derivation plan; the raw RS-native value is $O(10^9)$ while the SI CODATA target is $O(10^{-45})$, with the gap flagged as a hypothesis bridge requiring an explicit dimensional map. The certificate structure AlphaGScoreCardCert is the record type whose fields are the native bracket predicate on the predicted row value together with the strict inequality against the codata datum.
proof idea
The proof is a one-line term that constructs an element of Nonempty AlphaGScoreCardCert by applying the structure constructor to the pre-defined cert term.
why it matters
This declaration confirms the existence of a valid certificate for the alpha_G score card, closing the Lean status for the phase 0 row P0-AG in the masses module. It supports downstream checks on the phi-ladder mass formula and the alpha band by guaranteeing that the predicted interval (4.5e9, 4.85e9) is populated. The module doc notes the open dimensional bridge question to SI units; the declaration itself is a terminal existence check with no further dependents.
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