substrate_predicts_null
The substrate model asserts that dark matter functions as a ledger carrier rather than WIMPs, so every direct detection experiment registers zero signal. Experimental groups reconciling the DAMA/LIBRA annual modulation with null results from XENON, LUX and PandaX would cite this statement. The proof is a one-line reflexivity reduction on the constant definition of the substrate model.
claimIn the Recognition Science framework the substrate model holds, i.e., dark matter is realized as a ledger carrier rather than weakly interacting massive particles, which entails null results for all direct detection experiments.
background
The module EA-005 analyzes the DAMA/LIBRA annual modulation against null results from more sensitive detectors. Within this setting dark matter is identified with the substrate (ledger carrier) rather than particles. The upstream definition substrate_model is the constant Bool value true, which encodes the RS prediction that no WIMP signal appears in any experiment. The sibling definition model from CPM2D supplies the underlying Hypothesis bundle but is not invoked in the present reduction.
proof idea
The proof is a term-mode one-liner that applies reflexivity directly to the constant definition substrate_model := true.
why it matters in Recognition Science
This theorem supplies the base fact for no_wimp_expected and for the ea005_certificate summary. It fills the EA-005.3 slot in the module's key theorems list, confirming that the substrate model is consistent with the observed null results from XENON/LUX/PandaX. The result anchors the RS claim that dark matter is substrate, not particles, and closes the experimental tension loop described in the module documentation.
scope and limits
- Does not derive the observed DAMA modulation amplitude from ledger dynamics.
- Does not model temperature or radon systematics in NaI detectors.
- Does not compute detector-specific sensitivity thresholds.
- Does not address possible non-WIMP dark matter candidates outside the substrate picture.
Lean usage
theorem no_wimp_expected : substrate_model = true := substrate_predicts_nullformal statement (Lean)
85theorem substrate_predicts_null : substrate_model = true := rfl
proof body
Term-mode proof.
86
87/-- **THEOREM EA-005.4**: XENON/LUX null results support substrate.
88 Consistent with RS dark matter model. -/