systematic_dominant
plain-language theorem explainer
Systematic effects dominate explanations for ANITA upgoing events because the assigned probability 0.70 exceeds the sum of rare standard-model configurations (0.25) and beyond-standard-model or geometric effects (0.05). Experimental physicists reviewing anomalous EeV cosmic-ray detections would cite this result when deciding whether new physics is required. The proof is a one-line wrapper that unfolds the three probability definitions and reduces the numerical comparison via norm_num.
Claim. $P_mathrm{systematic} > P_mathrm{rare SM} + P_mathrm{BSM}$ with the concrete assignments $P_mathrm{systematic}=0.70$, $P_mathrm{rare SM}=0.25$, $P_mathrm{BSM}=0.05$.
background
The ANITAUpgoing module assigns three noncomputable real-valued probabilities for the possible origins of the four detected upgoing EeV events: systematic effects (instrumental or atmospheric) at 0.70, rare standard-model shower configurations at 0.25, and BSM or RS curvature-defect contributions at 0.05. These sit inside the EA-004 analysis that also invokes Earth opacity at these energies and the small sample size N~4. Upstream results supply the probability definitions themselves together with the Born-rule probability map from QuantumLedger and the collision-free ledger axioms from OptionAEmpiricalProgram.
proof idea
The term proof unfolds p_systematic, p_rare_sm and p_bsm, then applies norm_num to discharge the concrete numerical inequality 0.70 > 0.25 + 0.05.
why it matters
This theorem supplies the decisive comparison inside the ea004_certificate string that concludes the ANITA events are most likely systematic and do not warrant new physics. It implements the RS verdict that BSM probability remains low (~5 percent) and that geometric-defect explanations stay speculative. The result closes the probability-ranking step of the experimental chain that begins from the attenuation and statistical-limitation lemmas.
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