OUCH v3.7-Lite: Admissibility Bounds for a Second-Order Growth-Response Coefficient

This technical note presents OUCH v3.7-Lite, a public-scope admissibility audit of the second-order growth-response coefficient b₀ used in the reconstructed OUCH growth-sector response. The note examines whether the inherited reconstructed value b₀ = −0.356337 is mathematically admissible under conservative response conditions for the effective operator F_irr(χ) = 1 + αχ(1 + b₀χ). The audit checks positivity, monotonic damping, response monotonicity, and the saturating-response interpretation over bounded χ domains. The result is conservative: b₀ = −0.356337 is admissible and compatible with a saturating second-order response, but it is not derived from first principles in this note. The coefficient remains phenomenological under the public-scope model level. This release is not a production-code calibration, not a survey likelihood analysis, and not an observational forecast.