Independent working preprint and reproducibility package presenting two exact finite constructions developed within the Necessary Temporal Structure (NTS) research framework: an explicit 79-element unlabeled poset whose order complex has H1 = Z/3, and a restricted finite stratified history model (SLD_vol) with exact finite kernels, associative volume-balanced gluing, a strongly positive decoherence functional, I3 = 0, nonzero second-order interference, and a color-preserving tensor completion. The release does not claim a derivation of the Standard Model, a Lorentzian continuum limit, or experimental validation. Code, exact matrices/certificates, independent implementations, adversarial tests and integrity hashes are included.