Application of the most frequent value method for $$^{39}$$Ar half-life determination
Bibliographic record
Abstract
Abstract An evaluation method supported by robust statistical analysis was applied to historical measurements of $$^{39}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>39</mml:mn> </mml:msup> </mml:math> Ar half-life. The method, based on the most frequent value (MFV) approach combined with bootstrap analysis, provides a more robust way to estimate $$^{39}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>39</mml:mn> </mml:msup> </mml:math> Ar half-life, and results in $$T_{1/2}($$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> </mml:mrow> </mml:mrow> </mml:math> MFV $$) = 268.2^{+3.1}_{-2.9}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>268</mml:mn> <mml:mo>.</mml:mo> </mml:mrow> <mml:msubsup> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>2.9</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>3.1</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> years with uncertainty corresponding to the 68% confidence level. The uncertainty is a factor of 3 smaller than that of the most precise re-calculated $$^{39}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>39</mml:mn> </mml:msup> </mml:math> Ar half-life measurements by Stoenner et al. and a factor of 2.7 smaller than that of the adopted half-life value in nuclear data sheets. Recently, the specific activity of the beta decay of $$^{39}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>39</mml:mn> </mml:msup> </mml:math> Ar in atmospheric argon was measured in several underground facilities. Applying the MFV method to a specific activity of $$^{39}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>39</mml:mn> </mml:msup> </mml:math> Ar from underground measurements results in $$ SA_{{^{39}\text {Ar}}/\text {Ar}}(\text {MFV}) = 0.966^{+0.010}_{-0.018} \, \, \text {Bq/kg}_{\text {atmAr}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:msub> <mml:mi>A</mml:mi> <mml:mrow> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>39</mml:mn> </mml:msup> <mml:mtext>Ar</mml:mtext> </mml:mrow> <mml:mo>/</mml:mo> <mml:mtext>Ar</mml:mtext> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mtext>MFV</mml:mtext> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>966</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.018</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.010</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace/> <mml:mspace/> <mml:msub> <mml:mtext>Bq/kg</mml:mtext> <mml:mtext>atmAr</mml:mtext> </mml:msub> </mml:mrow> </mml:math> with uncertainty corresponding to the 68% confidence level. In this paper the method to determine the half-life of $$^{39}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>39</mml:mn> </mml:msup> </mml:math> Ar using the specific activity of $$^{39}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>39</mml:mn> </mml:msup> </mml:math> Ar in atmospheric argon is also discussed.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".