Event-Deletion Decks of Two-Dimensional Causal Orders: Safe-Prime Cancellation and Complete Modular Reconstruction

This paper studies whether a finite partially ordered set can be reconstructed, up to isomorphism, from the multiset of its one-point-deleted suborders. The principal focus is on posets of dimension at most two and their interpretation as finite causal orders in one spatial and one temporal dimension. The main result closes the modular reconstruction problem for this class. Every finite connected, coconnected, decomposable poset of dimension at most two is proved reconstructible from its ordinary multiplicity-retaining vertex-deletion deck, even when the prime quotient has nontrivial automorphisms or repeated substitution factors. The decisive step resolves the previously open single-bump case. A one-bump parent is obtained by replacing one vertex of a prime dimension-two root with a two-point chain or antichain. The paper proves, without an order bound, that equality of the complete colored pointed-deletion profiles forces the two colors to agree and the two possible inflation sites to lie in the same automorphism orbit. The proof combines safe-prime card extraction, cancellation at noncritical sites, extension across minus-one-critical roots, a critical-site normal form, two-loop cancellation, and a classification of the six possible zero-shift endpoint orders. Every nontrivial residual configuration creates a forbidden permutation interval; the only surviving degeneration is an actual automorphism induced by coordinate exchange. The theoretical results are accompanied by independently checkable computational certificates. These include exhaustive simple-permutation calculations through order twelve, structured order-thirteen tests, 3,072 strict endpoint-product checks, 600 endpoint-degeneration checks, and exact ledgers for the critical-site reduction. The computational evidence audits the proof but is not used as a substitute for the all-order argument. The general reconstruction problem for dimension-two posets remains open. After the results of this paper, the unresolved content is concentrated in prime parents, compatible occurrence incidence, and irregular realizer-frame coherence rather than modular decomposition. The causal-order conclusions concern reconstruction of the finite order relation, not recovery of embedding coordinates, metric scale, or spacetime geometry.