(1) In plain English, spacetime_emergence_cert packages the claim that 4D Lorentzian spacetime (metric signature (1,3), light-cone causality, proper time, and arrow of time) is forced by the J-cost functional together with the T0–T8 chain; spacetime is not an input but a derived structure.
(2) It matters in Recognition Science because it replaces the usual postulate of background spacetime with a theorem of cost minimization, making the entire Lorentzian geometry (including c = 1) a consequence of the single Law of Logic.
(3) The formal statement is read as a structure SpacetimeEmergenceCert whose fields bundle proved lemmas such as dimension count, diagonal metric η with one negative entry, interval = spatial − temporal, and the unique (1,3) signature; the surrounding theorems supply the explicit equalities and inequalities.
(4) Visible dependencies in the supplied source are the imports of DimensionForcing, PhiForcing, and the J-cost definitions; certificates referenced include spacetime_dim_eq_four, lorentzian_signature, lightlike_iff_speed_c, arrow_of_time, and signature_unique. The RealityFromDistinction module exposes the nonempty witness spacetime_emergence_cert_nonempty.
(5) The declaration does not prove the upstream J-cost uniqueness or the full T0–T8 forcing chain; those reside in separate modules.