Andrew Fribush

fig. 2.14.3: the decaying terminal hazard and its tail integral beside the integrand and sum printed in equation (194)

fig. 2.14.3 · the decaying terminal hazard and its tail integral beside the integrand and sum printed in equation (194).
TAIL ADDS +0.2045; THE PRINTED (194) GIVES −0.2045ONE LINE IS THE HAZARD s YEARS AFTER T (delta_T = 0.0005, g_delta = −0.00244);SHADED IS ITS TAIL INTEGRAL; ACCENT IS THE DRAFT’S.00.00040.00080.0012TT + 500T + 1,000T + 1,500YEARS AFTER THAZARD PER YEARTAIL AS DEFINED,delta_T e^(g_delta s)DECAYS; TAIL +0.2045PRINTED (194)INTEGRATES e^(−s g_delta),WHICH GROWSTHEN (194) ADDSdelta_T / g_delta= -0.2045

g_delta is the signed growth rate of the hazard on the asymptotic path, negative here, so the terminal hazard delta_T e^(g_delta s) decays and its integral from T to infinity is −delta_T / g_delta. 97.4% of that area lies inside the 1,500 years drawn. Parameters from Appendix B.1 as used in checks.py.

source: Existential Risk and Growth derivation audit, checks.py lines 58-62 and results.json (eq194); audit.md lines 55-67 · tailIntegral.data.ts

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Andrew Fribush, software and computer engineer in Austin. I build consequential systems where software meets institutions: finance, healthcare, commerce, government data, and the mechanisms that govern AI agents. Taking new engagements: hello@andrewfribush.com.