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theorem proved wrapper high

empiricallyCovered

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The theorem asserts that every Option A combination identifier is assigned a complete falsifier protocol consisting of dataset class, predicted observable, and failure mode. Researchers validating Recognition Science predictions against data would cite it to confirm that no implemented C1-C9 theorem lacks an empirical test protocol. The proof is a direct one-line wrapper that applies the universal construction lemma protocolFalsifiable_all.

claimEvery combination identifier $c$ admits a falsifiable protocol: for all $c$, there exist a dataset class, predicted observable, and failure mode such that the protocol record matches $c$.

background

The Option A Empirical Protocol module converts the falsifier registry into a Lean proposition guaranteeing total coverage: no implemented theorem combination is left without a dataset class, predicted observable, and failure mode. EmpiricallyCovered is the proposition that for every CombinationID $c$, ProtocolFalsifiable $c$ holds, where ProtocolFalsifiable packages the three matching fields. This rests on the upstream theorem protocolFalsifiable_all, which states that for any $c$ the protocol record is constructed by direct application of datasetClass $c$, predictedObservable $c$, and failureMode $c$.

proof idea

The proof is a one-line wrapper that applies the lemma protocolFalsifiable_all to discharge the universal quantifier over CombinationID.

why it matters in Recognition Science

This supplies the all_covered field inside empiricalProtocolCert, closing the module requirement that every implemented Option A theorem carries a falsifier protocol. It supports the empirical testability of the Recognition Science forcing chain and phi-ladder mass formulas by ensuring no coverage gaps remain in the C1-C9 set. The result touches the framework's demand for concrete failure modes without addressing the numerical content of the datasets themselves.

scope and limits

formal statement (Lean)

 105theorem empiricallyCovered : EmpiricallyCovered :=

proof body

One-line wrapper that applies protocolFalsifiable_all.

 106  protocolFalsifiable_all
 107

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (2)

Lean names referenced from this declaration's body.