Symbol in context

$V$

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

Meanings in context

Article-grounded definition

Symbol V

the remaining fringe visibility.

Read equation 3 in How Fast Can a Horizon Learn Which Path You Took? →

Article-grounded definition

Symbol V

production volume in metric tons per year — a real economy-of-scale effect, but one that only partially offsets the bioreactor ceiling above it.

Read equation 1 in The Domestication of Everything: Biotech's Loop, Closed →

Article-grounded definition

Symbol V

the current associative strength between a stimulus and an outcome.

Read equation 1 in Prepared Fears: How Evolution Biased What the Mind Learns to Dread →

Article-grounded definition

Symbol V

the field-wide growth rate of.

Read equation 2 in AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them →

Article-grounded definition

Symbol V

either a deterministic function or an invocation of some policy $\pi_v$ .

Read equation 15 in Comparing the Main Approaches to AI Agent Architecture →

Article-grounded definition

Symbol V

the executable verification.

Read equation 1 in Engineering Reliable Codex Workflows with Instructions, Tests, Sandboxes, and Human Gates →

Used in 59 equations

V(n) \propto n(n-1)

Tool Protocols and the Model Context Protocol in 2035 — Scenarios, Signals, and Falsifiable Predictions · Equation 2

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

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V(\phi) = -\mu^2\,\phi^\dagger\phi + \lambda\,(\phi^\dagger\phi)^2, \qquad \mu^2 > 0,\ \lambda > 0.

The Vacuum Has a History: Symmetry Breaking as Speciation · Equation 2

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

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\frac{\Gamma}{V} = A\,e^{-S_E},

The Vacuum Has a History: Symmetry Breaking as Speciation · 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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\mathcal{L}_{\text{seq}} = -\sum_{t=1}^{T} \log p_\theta\!\left(z_t \mid z_{<t}\right), \qquad z_t \in \{0, 1, \dots, V-1\}

Adapters, Native Pretraining, and Unified Tokens: The Main Multimodal Architectures, Compared · Equation 9

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

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V(t)

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them · Equation 2

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

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G(t) = C(t) - V(t), \qquad \frac{\mathrm{d}G}{\mathrm{d}t} = \frac{\mathrm{d}C}{\mathrm{d}t} - \frac{\mathrm{d}V}{\mathrm{d}t}.

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them · 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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\mathrm{d}V/\mathrm{d}t

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them · Equation 4

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

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V

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them · Equation 5

the field-wide growth rate of.

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V

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them · Equation 6

the field-wide growth rate of.

Equation guide → · This term → · Article →

V(t)

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them · Equation 7

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

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V(t)

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them · Equation 8

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

Equation guide → · This term → · Article →

V(t)

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them · Equation 9

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

Equation guide → · This term → · Article →

V(t)

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them · Equation 10

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

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G = (V, E), \qquad v \to v' \text{ fires iff } \gamma(v, v') = 1,

Comparing the Main Approaches to AI Agent Architecture · Equation 15

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

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v \in V

Comparing the Main Approaches to AI Agent Architecture · Equation 16

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

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V

Why Materials Fail: Fracture, Flaws and the Inspection Interval · Equation 25

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

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P_s = \exp\left[-V\left(\frac{\sigma}{\sigma_0}\right)^{m}\right],

Why Materials Fail: Fracture, Flaws and the Inspection Interval · Equation 27

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

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\forall V.\ \operatorname{packing}(V) \implies \exists c.\ \forall r.\ 1 \le r \implies \operatorname{card}\!\left(V \cap B(0,r)\right) \le \frac{\pi r^{3}}{\sqrt{18}} + c\,r^{2}

What a Proof Assistant Changes · Equation 1

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

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\mathrm{Attention}(Q, K, V) = \mathrm{softmax}\!\left(\frac{QK^{\top}}{\sqrt{d_k}}\right)V.

From n-Grams to Reasoning Models: A Technical History of the Language Model · 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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V(s_T,g)

Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex · Equation 5

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

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R=\mathbb{E}_{g\sim D}\mathbb{E}_{\tau\sim P(\tau\mid g)} \left[V(s_T,g)\right].

Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex · Equation 8

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

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V

Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex · Equation 25

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

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V=1

Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex · Equation 26

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

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V=0

Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex · Equation 27

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

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\mathcal E = (D,M,H,B,P,X,V,\tau),

OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence · Equation 45

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

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V

OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence · Equation 52

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

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A(\Delta)=I(\Delta)\land P(\Delta)\land V(\Delta)\land H(\Delta),

Engineering Reliable Codex Workflows with Instructions, Tests, Sandboxes, and Human Gates · 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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V

Engineering Reliable Codex Workflows with Instructions, Tests, Sandboxes, and Human Gates · Equation 5

the executable verification.

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m^*(x)=\arg\max_m \left[p_m(x)V(x)-C_m(x)-H_m(x)-R_m(x)\right],

The Economics of Codex: Tokens, Sandboxes, Review Time, and Software Throughput · Equation 13

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

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VVV

Meanings in context

Symbol V

Symbol V

Symbol V

Symbol V

Symbol V

Symbol V

Used in 59 equations

$V$