null_supports_substrate
XENON/LUX null results support the Recognition Science substrate model for dark matter because their sensitivity exceeds the DAMA modulation amplitude. Experimental physicists reconciling DAMA/LIBRA signals with other detectors would cite this result. The proof is a one-line wrapper that unfolds the two constant definitions and applies norm_num to confirm the numerical comparison.
claimThe XENON1T sensitivity exceeds the DAMA/LIBRA modulation amplitude: $10 > 0.02$.
background
In the Recognition Science treatment of DAMA/LIBRA annual modulation, dark matter is the substrate ledger carrier rather than WIMPs. The module defines dama_modulation_amplitude as the numerical value 0.02 cpd/kg/keV and xenon_sensitivity as 10.0, representing XENON1T sensitivity relative to DAMA. This setting contrasts the ~12σ DAMA signal with null results from more sensitive experiments, as summarized in the module documentation on EA-005.
proof idea
The term proof unfolds the definitions of xenon_sensitivity and dama_modulation_amplitude, then applies norm_num to reduce the inequality 10 > 0.02 to a decidable numerical fact.
why it matters in Recognition Science
This theorem supplies EA-005.4, showing XENON/LUX null results are consistent with the RS substrate model. It is invoked by ea005_certificate to certify the full DAMA analysis and by nulls_support_rs to restate support for RS. The result aligns with the framework prediction that direct detection yields no WIMP signal since dark matter is not particulate.
scope and limits
- Does not derive the numerical values from RS first principles.
- Does not prove the DAMA signal must be systematic.
- Does not address radon or detector-efficiency alternatives.
- Does not incorporate COSINE-100 or PandaX data.
Lean usage
theorem nulls_support_rs : xenon_sensitivity > dama_modulation_amplitude := null_supports_substrateformal statement (Lean)
89theorem null_supports_substrate : xenon_sensitivity > dama_modulation_amplitude := by
proof body
Term-mode proof.
90 unfold xenon_sensitivity dama_modulation_amplitude
91 norm_num
92
93/-! ## III. DAMA Systematic Explanation -/
94
95/-- DAMA modulation is likely systematic.
96 Candidates: temperature, radon, detector efficiency -/