Emergent Structures as Factorization of an Anonymous Complex Wave Multiset: Working Hypotheses and a Numerical Verification Program for Simplices, Localization, Condensates, and Dynamics

We formulate a working hypothesis asking whether structures such as space, time, particles, vertices, edges, and complete networks can be uniquely read out from a multiset of anonymous complex waves alone, without being assumed as foundational. The base state is defined as a complex wave multiset identified under permutations. Emergent structures - simplices, harmonic series, localization, condensates, and persistent objects - are defined as unique factorizations of anonymous subsets that simultaneously satisfy zero-square closure, finite recurrence, integer ratios, common phase, low rank, and complex Gram consistency. The complete network is not an input but a reconstruction certificate that becomes known only after a unique simplex reconstruction. Dynamics is defined not as trajectories of named constituents but as preservation of factorization type with a changing common phase center. We propose ground-truth embedding experiments with complete provenance erasure, blind controls without planted structure, permutation-invariance tests, perturbation tests, and persistence tests, thereby fixing a falsifiable problem setting that verifies emergent structures without breaking anonymity.