neutron_lifetime_implies_decay_allowed
plain-language theorem explainer
The declaration shows that the RS ledger placeholder for neutron lifetime forces the beta-decay Q-value to be positive. Nuclear modelers using the Recognition framework for weak decays would cite it to confirm structural consistency with the 0.782 MeV energy release. The proof is a one-line term extraction of the first conjunct from the ledger conjunction.
Claim. If the ledger condition on neutron lifetime holds (i.e., both the free-neutron beta-decay Q-value and mean lifetime are positive), then the beta-decay Q-value satisfies $Q > 0$.
background
The module addresses P-015 on what determines neutron lifetime in Recognition Science, where the experimental bottle/beam discrepancy is noted as unresolved. Neutron lifetime is fixed by weak-decay phase space with $Q^5$ scaling, matrix-element structure, and rung-determined mass inputs from the phi-ladder, but full numerical derivation remains blocked. The key upstream definition neutronDecayQ supplies the free-neutron beta-decay Q-value as the constant 0.782 MeV, while neutron_lifetime_from_ledger encodes the conjunction that both this Q-value and the free neutron mean lifetime are positive. The imported lifetime definition supplies noncomputable values as powers of phi.
proof idea
The proof is a term-mode one-liner that projects the first conjunct from the hypothesis h of type neutron_lifetime_from_ledger, directly yielding neutronDecayQ > 0.
why it matters
This anchors consistency of the neutron-lifetime placeholder by guaranteeing positive energy release for beta decay, supporting the P-015 registry item where Q^5 scaling and phi-ladder mass inputs are central. It aligns with the broader Recognition framework landmarks of the phi-ladder and eight-tick octave, though the full lifetime derivation stays open. No downstream theorems are recorded yet.
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