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

i,j \in \{L,R\}

How Much of Gravitationally Induced Entanglement Is in the Eye of the Frame · Equation 2

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

Equation guide → · This term → · Article →

\mathcal{L}_{\text{eff}} = \mathcal{L}_{\text{SM}} + \sum_i \frac{c_i}{\Lambda^{2}}\,\mathcal{O}_i

How Particle Physics Beyond the Standard Model Actually Works · 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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V_m[t+1] = V_m[t] + \sum_i w_i s_i[t] - \frac{V_m[t]}{\tau}

How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works · Equation 2

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

Equation guide → · This term → · Article →

I_j = \sum_i V_i\, G_{ij}

How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works · Equation 3

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

Equation guide → · This term → · Article →

T(\mathbf b)=\exp(-i\mathbf b\cdot\mathbf P/\hbar)

The Clock That Comes Back Wrong by Exactly Its Mass · 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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G(\mathbf v)=\exp(-i\mathbf v\cdot\mathbf K/\hbar)

The Clock That Comes Back Wrong by Exactly Its Mass · Equation 22

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

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[K_i,P_j]=i\hbar\,m\,\delta_{ij}\,\mathbb 1,

The Clock That Comes Back Wrong by Exactly Its Mass · Equation 27

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

Equation guide → · This term → · Article →

X=-i\mathbf b\cdot\mathbf P/\hbar

The Clock That Comes Back Wrong by Exactly Its Mass · Equation 31

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

Equation guide → · This term → · Article →

Y=-i\mathbf v\cdot\mathbf K/\hbar

The Clock That Comes Back Wrong by Exactly Its Mass · Equation 32

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

Equation guide → · This term → · Article →

[X,Y]=\frac{im}{\hbar}\,\mathbf b\cdot\mathbf v\,\mathbb 1.

The Clock That Comes Back Wrong by Exactly Its Mass · Equation 33

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

Equation guide → · This term → · Article →

T(\mathbf b)\,G(\mathbf v)\,T(-\mathbf b)\,G(-\mathbf v)=e^{[X,Y]}=\exp\!\left(\frac{im}{\hbar}\,\mathbf b\cdot\mathbf v\right)\mathbb 1.

The Clock That Comes Back Wrong by Exactly Its Mass · Equation 38

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

Equation guide → · This term → · Article →

[K_i,P_j]=\frac{i\hbar}{c^2}\,\delta_{ij}\,H,

The Clock That Comes Back Wrong by Exactly Its Mass · Equation 51

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

Equation guide → · This term → · Article →

\mathrm{CAI}(\pi) = \frac{1}{N}\sum_{i=1}^{N} \mathbb{1}\left[\text{trial } i \text{ converges on the recolored true target, not the red decoy, within the paper's own 2-meter success radius}\right] .

Every Test Changed the Scene and Kept the Chair Red · Equation 6

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

Equation guide → · This term → · Article →

1/|i-j|^{\alpha}

Every Crystal Has Its Own Speed of Light · Equation 14

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

Equation guide → · This term → · Article →

M(q) = \frac{d\varphi}{dq}, \qquad v(t) = M\big(q(t)\big)\, i(t)

From Origins to Frontier: A History of Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute · 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 →

i

The Bend an Elevator Cannot Fake · Equation 12

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

Equation guide → · This term → · Article →

e = (i,j)

The Bend an Elevator Cannot Fake · Equation 19

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

Equation guide → · This term → · Article →

i

The Bend an Elevator Cannot Fake · Equation 21

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

Equation guide → · This term → · Article →

\Gamma^0_{0i} = \partial_i \ln U = \phi_{,i}

The Bend an Elevator Cannot Fake · Equation 80

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

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H_{\mathrm{int}}^{(n)} =\hbar\Omega\, \frac{\mathbf J\cdot\boldsymbol\sigma^{(n)}}{2j}, \qquad U_n=\exp\!\left(-i\kappa \frac{\mathbf J\cdot\boldsymbol\sigma^{(n)}}{2j}\right),

A Reference Frame Becomes Classical by Publishing Its Orientation · Equation 80

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

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\{(\mathbf{s}_i, P_i)\}

How Materials Discovery and Degradation Actually Work · Equation 5

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

Equation guide → · This term → · Article →

\mathbf{s}_i

How Materials Discovery and Degradation Actually Work · Equation 7

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

Equation guide → · This term → · Article →

B = \frac{1}{N}\sum_{i=1}^{N} (p_i - o_i)^2

Futures Methods and Technological Scenarios in Practice: An Advanced Technical Guide · 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

Futures Methods and Technological Scenarios in Practice: An Advanced Technical Guide · Equation 3

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

Equation guide → · This term → · Article →

R_{wp} = \sqrt{\frac{\sum_i w_i \left(y_i^{\mathrm{obs}} - y_i^{\mathrm{calc}}\right)^2}{\sum_i w_i \left(y_i^{\mathrm{obs}}\right)^2}},

Materials Discovery and Degradation in Practice: An Advanced Technical Guide · Equation 5

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

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E(i,j)

The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It · Equation 3

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

Equation guide → · This term → · Article →

i

The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It · Equation 4

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

Equation guide → · This term → · Article →

U(i,j) = \log_2\!\big(E(i,j)/E(j,i)\big)

The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It · 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 →

U(i,j) = -U(j,i)

The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It · Equation 8

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

Equation guide → · This term → · Article →

U(i,j)=2

The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It · Equation 9

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

Equation guide → · This term → · Article →

iii

Meanings in context

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Used in 145 equations

$i$