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Table 2.

Estimated regression coefficients with the derived metrics. Results are shown for the below-99th citation data. The adjusted R-squared was higher than 0.99 for all disciplines. In addition to the estimated regression coefficients (left half), the peak value (û_p), the typical time interval of the growth phase (δ₁), and the obsolescence phase (δ₂), the internal obsolescence rate (𝒮 = δ₁/δ₂) and the retention rate (𝓡 = $\hat{B}$ /û_p) (right half) are also shown by discipline. Values of $\hat{λ}$ larger than 10 are displayed as “≫ 1.” (Results regarding the lower percentile data are presented in Supplementary Table S4).

Category	$\hat{A}$	$\hat{μ}$	$\hat{σ}$	$\hat{B}$	$\hat{λ}$	û_p	δ₁	δ₂	𝒮	𝓡
astro-ph	2.19	1.61	0.817	0.158	1.21	0.450	2.56	2.43	1.05	0.351
comp-sci	1.14 × 10	1.56	0.741	0.379	≫ 1	2.08	2.74	2.00	1.37	0.182
cond-mat	4.60	1.83	0.802	0.279	0.916	0.779	3.26	2.95	1.11	0.359
hep	3.71	1.37	0.725	0.277	≫ 1	0.953	2.32	1.61	1.45	0.290
math	6.25	1.91	0.927	0.452	0.439	0.918	2.85	3.88	0.735	0.493
oth-phys	5.04	1.76	0.805	0.259	≫ 1	0.855	3.03	2.77	1.10	0.303

Category	$\hat{A}$	$\hat{μ}$	$\hat{σ}$	$\hat{B}$	$\hat{λ}$	û_p	δ₁	δ₂	𝒮	𝓡
astro-ph	2.19	1.61	0.817	0.158	1.21	0.450	2.56	2.43	1.05	0.351
comp-sci	1.14 × 10	1.56	0.741	0.379	≫ 1	2.08	2.74	2.00	1.37	0.182
cond-mat	4.60	1.83	0.802	0.279	0.916	0.779	3.26	2.95	1.11	0.359
hep	3.71	1.37	0.725	0.277	≫ 1	0.953	2.32	1.61	1.45	0.290
math	6.25	1.91	0.927	0.452	0.439	0.918	2.85	3.88	0.735	0.493
oth-phys	5.04	1.76	0.805	0.259	≫ 1	0.855	3.03	2.77	1.10	0.303

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