Symbol in context

$R$

This entry links every published equation using this exact notation. Its meaning may change between equations.

Meanings in context

Article-grounded definition

Symbol R

the reference.

Read equation 1 in Cognitive Bias Was the Label; Attention Sink Is the Suspect →

Article-grounded definition

Symbol R

the writing.

Read equation 1 in AI for Science and Medicine: A First-Principles Introduction →

Article-grounded definition

Symbol R

the mean radius.

Read equation 7 in How Planetary Science and Exploration Actually Work →

Article-grounded definition

Symbol R

the sum of each individual stat’s remainder modulo four.

Read equation 6 in The EV Formula Is an Exact Production Function Trainers Solved by Accident →

Article-grounded definition

Symbol R

the response: the amount the population’s mean should shift in the next generation, if the difference between survivors and non-survivors was genetic rather than purely environmental.

Read equation 1 in Darwin's Finches: The Beak the Grants Measured for Forty Years →

Article-grounded definition

Symbol R

the gas constant.

Read equation 7 in Einstein's Random Walk and the Mathematics of Genetic Drift →

Article-grounded definition

Symbol R

the no standard agent benchmark publishes.

Read equation 15 in The Hardest Unsolved Problems in AI Agent Evaluation and Reliability →

Article-grounded definition

Symbol R

the bitrate.

Read equation 12 in How Multimodal Models Actually Handle Video, Audio, and Space →

Article-grounded definition

Symbol R

the event that the retriever’s top- k results contain sufficient evidence to answer the query, and let “correct” mean the generated answer is judged faithful and relevant.

Read equation 17 in Measuring What a RAG System Retrieves, Not Just What It Answers →

Article-grounded definition

Symbol R

the ratio.

Read equation 1 in The Logistics Tail: Sustainment as the Binding Constraint on Organised Force →

Article-grounded definition

Symbol R

a half-pitch.

Read equation 1 in Patterning at the Limit: What Actually Happens When a Chip Is Manufactured →

Article-grounded definition

Symbol R

System reliability under task distribution D.

Read equation 8 in Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex →

Article-grounded definition

Symbol R

task reward.

Read equation 22 in Reliable AI Agents Are Control Systems, Not Chatbots →

Article-grounded definition

Symbol R

reliability at the required horizon.

Read equation 21 in Humanity Has Always Been a Human–Technology System →

Used in 76 equations

\delta R = 1\times10^{-11}

The Valley of Stability Is a Fitness Landscape · Equation 1

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Equation guide → · This term → · Article →

R = \frac{aM}{g\,c_T}\cdot\frac{L}{D}\cdot\ln\!\left(\frac{W_1}{W_2}\right)

Flight at the Energy Floor: Transport Selection to 2100 · Equation 1

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Equation guide → · This term → · Article →

D = \frac{RT}{N}\cdot\frac{1}{6\pi k P},

Einstein's Random Walk and the Mathematics of Genetic Drift · Equation 7

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Equation guide → · This term → · Article →

R

Einstein's Random Walk and the Mathematics of Genetic Drift · Equation 8

the gas constant.

Equation guide → · This term → · Article →

LR = 1 - 2^{-b}

The Metabolism of Civilization: Energy to 2100 · Equation 7

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Equation guide → · This term → · Article →

R = 1 - \sum_{i=1}^{n} w_i \cdot \mathbb{1}[\text{trial } i \text{ failed}],

The Hardest Unsolved Problems in AI Agent Evaluation and Reliability · Equation 15

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Equation guide → · This term → · Article →

R

The Hardest Unsolved Problems in AI Agent Evaluation and Reliability · Equation 18

the no standard agent benchmark publishes.

Equation guide → · This term → · Article →

F_1 = \frac{2PR}{P + R},

From Origins to Frontier: A History of Frontier AI Model Comparisons · Equation 1

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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R

From Origins to Frontier: A History of Frontier AI Model Comparisons · Equation 3

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Equation guide → · This term → · Article →

R = \sum_{i} \Pr(\text{failure mode } i) \cdot B_i

Why Average Success Rate Hides the Failures That Matter Most · Equation 12

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Equation guide → · This term → · Article →

R(t)

Multimodal AI in 2035: Scenarios and Falsifiers · Equation 2

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Equation guide → · This term → · Article →

C(t) = \mathbb{1}\!\left[U(t) \ge u^{*}\right] \cdot \mathbb{1}\!\left[R(t) \ge r^{*}\right]

Multimodal AI in 2035: Scenarios and Falsifiers · Equation 3

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

Equation guide → · This term → · Article →

R(t)

Multimodal AI in 2035: Scenarios and Falsifiers · Equation 7

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Equation guide → · This term → · Article →

R = \frac{f_s}{h} \cdot n_q \cdot \log_2 K \text{ bits per second.}

How Multimodal Models Actually Handle Video, Audio, and Space · Equation 12

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Equation guide → · This term → · Article →

R(t) = \mathbb{1}\!\left[A(t) \ge a^{*}\right] \cdot \mathbb{1}\!\left[S(t) \ge s^{*}\right]

Mechanistic Interpretability in 2035: Scenarios and Falsifiers · Equation 4

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

Equation guide → · This term → · Article →

R(t)

Mechanistic Interpretability in 2035: Scenarios and Falsifiers · Equation 5

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Equation guide → · This term → · Article →

R(t)

Mechanistic Interpretability in 2035: Scenarios and Falsifiers · Equation 11

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Equation guide → · This term → · Article →

R(t)

Mechanistic Interpretability in 2035: Scenarios and Falsifiers · Equation 14

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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R(m)

Anthropic in 2035: Four Scenarios, Their Signals, and What Would Falsify Them · Equation 1

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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\text{Safeguard}(m) = \begin{cases} \text{ASL-2}, & R(m) < \tau_3 \\ \text{ASL-3}, & \tau_3 \le R(m) < \tau_4 \\ \text{ASL-4}, & R(m) \ge \tau_4 \end{cases}

Anthropic in 2035: Four Scenarios, Their Signals, and What Would Falsify Them · Equation 3

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

Equation guide → · This term → · Article →

R

Measuring What a RAG System Retrieves, Not Just What It Answers · Equation 17

the event that the retriever’s top- k results contain sufficient evidence to answer the query, and let “correct” mean the generated answer is judged faithful and relevant.

Equation guide → · This term → · Article →

P(\text{correct}) \;=\; \underbrace{P(R)\,P(\text{correct} \mid R)}_{\text{grounded in retrieved evidence}} \;+\; \underbrace{P(\lnot R)\,P(\text{correct} \mid \lnot R)}_{\text{correct without sufficient retrieved evidence}}

Measuring What a RAG System Retrieves, Not Just What It Answers · Equation 19

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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P(\text{correct} \mid \lnot R)

Measuring What a RAG System Retrieves, Not Just What It Answers · Equation 20

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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P(\text{correct} \mid R)

Measuring What a RAG System Retrieves, Not Just What It Answers · Equation 21

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Equation guide → · This term → · Article →

R

Measuring What a RAG System Retrieves, Not Just What It Answers · Equation 22

the event that the retriever’s top- k results contain sufficient evidence to answer the query, and let “correct” mean the generated answer is judged faithful and relevant.

Equation guide → · This term → · Article →