next_steps
plain-language theorem explainer
The next steps string enumerates six development priorities for Recognition Geometry, from writing a foundational paper through connecting to quantum patterns. Framework researchers planning extensions would reference this list to sequence follow-on work. The definition is a direct string literal formed by concatenation of the enumerated items.
Claim. The string constant listing the natural next steps for Recognition Geometry equals the concatenation of the six items: write the paper Recognition Geometry I, build concrete examples, fully instantiate from the RS ledger, prove spacetime is 4D from recognizer structure, develop recognition geometry of time evolution, and connect to quantum recognition patterns.
background
Recognition Geometry integrates components under axioms RG0-RG7: nonempty configuration space, locality via neighborhood refinement, nontrivial recognizers, indistinguishability equivalence, finite resolution events, local connectedness of preimages, composition of recognizers, and existence of comparative recognizers. Configurations are primitive; events arise from recognizers; space is the quotient C_R = C/~. The module supplies the complete integration and summary, linking RS ledger states to configuration space and measurements to recognizers.
proof idea
The definition constructs the string by direct concatenation of the six enumerated text lines.
why it matters
This declaration supplies the explicit roadmap after the integration of axioms RG0-RG7 and results such as the well-defined quotient structure, symmetry group, no-injection theorem, and chart structure. It flags open directions including dimension theory (spacetime 4D from recognizer structure) and the quantum bridge, directly following the module's summary of the Recognition Science foundation.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.