rsbridge_status
plain-language theorem explainer
rsbridge_status defines a fixed string that reports successful instantiation of Recognition Geometry axioms by Recognition Science structures. A researcher tracing the emergence of physical space from ledger states would cite it to confirm the structural correspondence. The definition is a direct concatenation of status lines, one per bridge component, with no computation or case analysis.
Claim. The bridge status is the string listing successful mappings: ledger states form a configuration space, the R̂ operator supplies locality, measurements act as recognizers, the 8-tick cycle enforces finite resolution, and the J-cost function supplies a metric obeying non-negativity, self-distance zero, symmetry, and the triangle inequality.
background
The module establishes the concrete link between Recognition Science and the abstract Recognition Geometry framework. RS supplies ledger states as the underlying set, the R̂ operator for local neighborhoods, and the 8-tick cycle for finite resolution. Recognition Geometry then derives physical space as the quotient of ledger states under recognition equivalence and extracts a metric from comparative recognition cost.
proof idea
The declaration is a plain definition that builds the status string by concatenating eleven fixed lines, each naming one bridge component and its RG axiom. No tactics or lemmas are applied; the body is a single string literal terminated by the phrase “RS BRIDGE COMPLETE”.
why it matters
The definition closes the summary section of the RS-to-RG bridge, directly supporting the master claim that Recognition Science instantiates all listed RG axioms (RG0 through RG7). It records that physical space emerges as a recognition quotient and that the metric arises from the J-cost comparative recognizer. The entry sits at the end of the module and is the only human-readable checkpoint for the entire correspondence.
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