Symbol in context

$i$

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

Meanings in context

Article-grounded definition

Symbol i

the cell at row.

Read equation 3 in How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works →

Article-grounded definition

Symbol i

assigned a latent strength $\theta_i$ , and the estimated probability that system A ’s output is preferred over system B ’s in a given comparison is.

Read equation 1 in Frontier AI Model Comparisons: A First-Principles Introduction →

Article-grounded definition

Symbol i

the pair.

Read equation 6 in How Llama's Architecture Actually Works, Generation by Generation →

Article-grounded definition

Symbol i

the fraction of those calls actually covered by a working.

Read equation 3 in Ten Failure Modes That Define Production Tool-Protocol Integrations →

Article-grounded definition

Symbol i

close to zero, because nothing in the base protocol gives a server a caller-supplied key to deduplicate against.

Read equation 5 in Ten Failure Modes That Define Production Tool-Protocol Integrations →

Article-grounded definition

Symbol i

the step.

Read equation 8 in The Economics and Physical Limits of Running AI Agents at Scale →

Article-grounded definition

Symbol i

a position index.

Read equation 11 in Measuring What a RAG System Retrieves, Not Just What It Answers →

Article-grounded definition

Symbol i

the if workers.

Read equation 13 in Ten Failure Modes in Agentic Coding, from Prompt Injection to False Completion →

Article-grounded definition

Symbol i

resolved.

Read equation 2 in How to Evaluate Codex Beyond SWE-bench and Vendor Scores →

Used in 145 equations

C_n = \sum_{i=1}^{n} c_i = n\,p_{\text{in}}(\tau+\delta) + p_{\text{in}}\,\sigma\,\frac{n(n-1)}{2} + n\,p_{\text{out}}\,\bar{o}

The Economics and Physical Limits of Running AI Agents at Scale · 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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i

The Economics and Physical Limits of Running AI Agents at Scale · Equation 27

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

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\mathbb{E}[C_n] \approx \sum_{i=1}^{n} \frac{c_i}{1-q_i}

The Economics and Physical Limits of Running AI Agents at Scale · Equation 29

This equation gives an approximation: it relates the quantities while allowing an approximation.

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\frac{q}{1-q}\sum_i c_i

The Economics and Physical Limits of Running AI Agents at Scale · Equation 31

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

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i

The Economics and Physical Limits of Running AI Agents at Scale · Equation 33

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

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i

The Economics and Physical Limits of Running AI Agents at Scale · Equation 34

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

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(i-1)\sigma

The Economics and Physical Limits of Running AI Agents at Scale · Equation 35

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

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i

The Economics and Physical Limits of Running AI Agents at Scale · Equation 36

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

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i

Comparing the Main Approaches to AI Agent Architecture · Equation 11

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

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i

Comparing the Main Approaches to AI Agent Architecture · Equation 13

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

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i

Comparing Frontier Model Pricing Without Comparing Apples to Oranges · Equation 1

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

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i

Comparing Frontier Model Pricing Without Comparing Apples to Oranges · Equation 5

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

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T_{\mathrm{start}} = T_{\mathrm{sys}} + T_{\mathrm{mem}} + T_{\mathrm{env}} + T_{\mathrm{tools}} + \sum_{i=1}^{k} M_i

How Claude Code's Memory Actually Persists Across Sessions · 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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i

How Claude Code's Memory Actually Persists Across Sessions · Equation 3

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

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\mathrm{Cost}_n = 1.25\,c\,T_p + (n-1)\,(0.1\,c\,T_p) + c\sum_{i=1}^{n} T_{v,i}

How Claude Code's Memory Actually Persists Across Sessions · Equation 9

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

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i

Ten Failure Modes That Define Production RAG · Equation 15

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

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\ell_i

Ten Failure Modes That Define Production RAG · Equation 18

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

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L_i \approx \lambda_i \, \tau_i \, \ell_i,

Ten Failure Modes That Define Production RAG · Equation 19

This equation gives an approximation: it relates the quantities while allowing an approximation.

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\ell_i

Ten Failure Modes That Define Production RAG · Equation 23

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

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\mathrm{DCG@}k = \sum_{i=1}^{k} \frac{2^{\,\mathrm{rel}_i}-1}{\log_2(i+1)}, \qquad \mathrm{nDCG@}k = \frac{\mathrm{DCG@}k}{\mathrm{IDCG@}k}

Measuring What a RAG System Retrieves, Not Just What It Answers · Equation 11

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

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\mathrm{rel}_i

Measuring What a RAG System Retrieves, Not Just What It Answers · Equation 12

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

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i

Measuring What a RAG System Retrieves, Not Just What It Answers · Equation 13

a position index.

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\mathrm{score}(D,Q) = \sum_{i=1}^{n} \mathrm{IDF}(q_i) \cdot \frac{f(q_i, D)\,(k_1+1)}{f(q_i, D) + k_1\left(1 - b + b\,\dfrac{|D|}{\mathrm{avgdl}}\right)}

What Actually Happens Between a Query and an Answer in RAG · 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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i

Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures · Equation 35

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

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L_{\text{total}} = L_{\text{enc}} + \sum_{i=1}^{k} \left( L_{\text{retrieve}}^{(i)} + L_{\text{LLM}}^{(i)} \right).

Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures · Equation 36

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

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i

Standardising the Record: How Writing Became Evidence · Equation 2

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

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F_n = \prod_{i=1}^{n} f_i,

Standardising the Record: How Writing Became Evidence · Equation 4

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

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Y_{\mathrm{pkg}} = Y_{\mathrm{assy}} \prod_{i=1}^{N} Y_i .

When the Substrate Became the Product · Equation 14

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

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P_{\mathrm{bypass}} = \prod_{i=1}^{n} p_i,

The Attack Surface That Reads · Equation 3

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

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\mathcal{L} = -\frac{1}{B} \sum_{i=1}^{B} \log \frac{\exp(\langle u_i, v_i \rangle / \tau)}{\sum_{j=1}^{B} \exp(\langle u_i, v_j \rangle / \tau)},

One Model, Many Modalities: What Multimodal Systems Actually Share · Equation 6

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

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iii

Meanings in context

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Used in 145 equations

$i$