A Model-Composition Syntax for Observer-Explicit Self-Referential Time-Series Systems: The Observer--Reflector Complex (ORC)

This record provides the preprint of “A Model-Composition Syntax for Observer-Explicit Self-Referential Time-Series Systems: The Observer--Reflector Complex (ORC). ” The manuscript proposes the Observer--Reflector Complex (ORC) as a model-composition syntax and conceptual-structure schema for observer-explicit self-referential time-series systems. ORC types and connects a source series S, an observer-side local frame O, a target-side local frame T, continuous and finite label layers, a synchronization operator, and a partial return map from synchronization events to source-series events. The model is motivated by the problem of representing a financial-market chart not merely as a price sequence, but as a price--discrete time domain representation space in which observation-related role labels can be treated as typed conceptual roles with computational bearers. The observer-related vocabulary is used as an interpretive layer, while the formal core consists of typed source-series transformations, derived local frames, finite-state labeling, synchronization sets, and partial return maps. In the BTCUSD implementation, the target-side frame is realized by a harmonic-mean closure and its chord. The observer-side frame is realized by returning momentum-oscillator-derived evaluation motion to the price axis through price-range mapping, velocity extraction, RSI evaluation, and source-conditioned reverse-engineered RSI. The resulting local-frame geometries are summarized by min--max--current triangles, mapped through continuous and finite labeling layers, and compared by diagonal finite-state alignment. Synchronized snapshots and horizontal levels are stored as market-memory records and compared with later filtered local extrema. Ten representative level--extremum correspondences show relative errors of 0. 0931%--2. 3802%, with a median of 0. 6797%. The contribution is a conceptual-structure schema, working ontology, and executable symbolic-numeric instantiation for describing how local-frame synchronization derived from one series can partially return to that same series as structured events. Supplementary materials and data are available on Zenodo at DOI: 10. 5281/zenodo. 20061576. This manuscript is a separate conceptual-structure and symbolic-numeric modeling version of ORC, substantially reframed from the earlier comprehensive ORC preprint at DOI: 10. 5281/zenodo. 19882581. The earlier supplementary/data record is available at DOI: 10. 5281/zenodo. 19880153. The finite labeling layer also relates to the LSMT₁ preprint at DOI: 10. 5281/zenodo. 15315456.