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Equation 5 · Part 1 · The Safeguards Behind a Claude Refusal, and What They're Actually Trading Off

Symbol p_esc

pescp_{\text{esc}}
pescp_{\text{esc}}

What this part means

the because.

Its job in the formula

pep_esc is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

Because pescp_{\text{esc}} is small on ordinary traffic, the average cost collapses toward cprobec_{\text{probe}} even though cexchangec_{\text{exchange}} did not get any cheaper — which is the documented reason Anthropic reports the overhead falling from 23.7% to roughly 1% between generations, alongside a drop in the harmless-traffic refusal rate to 0.05% and, across more than 1,700 cumulative red-teaming hours against the new system, one high-risk vulnerability found, which Anthropic describes as a detection rate of 0.005 per thousand queries — the lowest of any defense it reports having evaluated [ 1 ] .

The passage around this formula

Because pescp_{\text{esc}} is small on ordinary traffic, the average cost collapses toward cprobec_{\text{probe}} even though cexchangec_{\text{exchange}} did not get any cheaper — which is the documented reason Anthropic reports the overhead falling from 23.7% to roughly 1% between generations, alongside a drop in the…

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Sources cited in the surrounding passage

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