Structural–Spectral Computing (SSC): A Topology-Aware Representation-First Computing Paradigm for Complex, Dynamic Systems

Structural–Spectral Computing (SSC) is a representation-first computing paradigm for

complex systems whose relational organization evolves over time. SSC transforms system states

into harmonic coordinates induced by time-varying structural operators and performs inference,

optimization, prediction, and control in an adaptive reduced spectral space. This version extends

graph-based SSC with a topology-aware representational layer. The extension permits graphs,

simplicial complexes, hypergraphs, and filtered relational objects to serve as structural substrates;

it further incorporates persistent topological summaries and higher-order Hodge operators as

diagnostics of multiscale organization. The resulting framework separates two complementary

roles: structural spectra provide computational coordinates, while topology supplies observables

for validating representation choice, tracking persistent organization across scale, and detecting

higher-order reconfiguration. SSC therefore does not identify topology with spectral analysis,

nor does it treat topological summaries as standalone predictors. Instead, it treats both as

components of a unified computational pipeline: represent the system at an appropriate structural

level, transform it into adaptive harmonic coordinates, monitor spectral and topological change,

and compute in the smallest representation that preserves the task-relevant organization. The

framework is substrate-independent: it is classically implementable with established tools, and

quantum or hybrid backends are optional accelerators whose value remains an open empirical

question.