Symbol in context

$P$

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

Meanings in context

Article-grounded definition

Symbol P

the target property, $\mathbf{s}$ is a structural descriptor vector (lattice parameters, coordination, bonding topology).

Read equation 1 in How Materials Discovery and Degradation Actually Work →

Article-grounded definition

Symbol P

the power, in watts, that a system actually draws to sustain that bandwidth, attributable specifically to the memory-and-fabric subsystem rather than the whole machine.

Read equation 4 in An Optical Fabric Turns Off-Package Memory Into an Extension of the Die →

Article-grounded definition

Symbol P

the radius.

Read equation 5 in Einstein's Random Walk and the Mathematics of Genetic Drift →

Article-grounded definition

Symbol P

the population count.

Read equation 5 in Demography, Migration, and Urban Futures in Practice: An Advanced Technical Guide →

Article-grounded definition

Symbol P

price in dollars per kilogram.

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

Article-grounded definition

Symbol P

the cut into square patches of size.

Read equation 3 in How Multimodal Models Actually Handle Video, Audio, and Space →

Article-grounded definition

Symbol P

the plan.

Read equation 6 in Comparing the Main Approaches to AI Agent Architecture →

Article-grounded definition

Symbol P

inflated by memorisation rather than by any generalisable capability, and every end-to-end score computed against that reference set overstates what the retrieval component is doing.

Read equation 23 in Measuring What a RAG System Retrieves, Not Just What It Answers →

Article-grounded definition

Symbol P

driven down — at which point the prior matters less to the conclusion [ 3 ].

Read equation 2 in What a Biosignature Has to Rule Out →

Article-grounded definition

Symbol P

the policy.

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

Used in 78 equations

P(\text{at least one surviving copy}) = 1 - q^{N}.

The Hardest Unsolved Problems in Open-Weight AI · 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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P(\text{at least one surviving copy})

The Hardest Unsolved Problems in Open-Weight AI · Equation 7

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

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P

What Multimodal AI Actually Costs, Modality by Modality · Equation 3

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

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N_{\mathrm{tok}}(H,W) = \left\lceil \frac{H}{P} \right\rceil \times \left\lceil \frac{W}{P} \right\rceil

What Multimodal AI Actually Costs, Modality by Modality · 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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P

The Hardest Unsolved Problems in Multimodal AI · Equation 3

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

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N_{\mathrm{tok}} = \frac{H}{P} \cdot \frac{W}{P},

The Hardest Unsolved Problems in Multimodal AI · 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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P(y_A \succ y_B \mid x) = \sigma\big(r_\phi(x,y_A) - r_\phi(x,y_B)\big),

The Main Technical Approaches to AI Alignment, Compared · 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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P(Y \mid X) = \prod_{t=1}^{T} P(y_t \mid y_{<t}, X).

The Jagged Frontier Fallacy: Deconstructing Harvard's Canonical AI Productivity Study · 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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P(t)

Small and On-Device AI in 2035: Scenarios and Falsifiers · Equation 1

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

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D(t) = \mathbb{1}\!\left[P(t) \ge p^{*}\right] \cdot \mathbb{1}\!\left[L(t) \ge \ell^{*}\right]

Small and On-Device 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.

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P(t)

Small and On-Device AI 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 →

P(t)

Small and On-Device AI in 2035: Scenarios and Falsifiers · Equation 8

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

Equation guide → · This term → · Article →

P

How Multimodal Models Actually Handle Video, Audio, and Space · Equation 3

the cut into square patches of size.

Equation guide → · This term → · Article →

N_{\mathrm{tok}} = \frac{H}{P} \cdot \frac{W}{P}

How Multimodal Models Actually Handle Video, Audio, and Space · Equation 4

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

Equation guide → · This term → · Article →

N_{\mathrm{tok}} = \frac{H}{P} \cdot \frac{W}{P} \cdot \frac{T}{P_t}.

How Multimodal Models Actually Handle Video, Audio, and Space · Equation 7

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

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T(w, h) = \left\lceil \frac{w}{P} \right\rceil \times \left\lceil \frac{h}{P} \right\rceil,

Building a Multimodal AI Application That Actually Uses Its Inputs · Equation 10

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

Equation guide → · This term → · Article →

P

Building a Multimodal AI Application That Actually Uses Its Inputs · Equation 13

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

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P

Building a Multimodal AI Application That Actually Uses Its Inputs · Equation 14

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

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v_\ell = \frac{1}{|P|}\sum_{i \in P} h_\ell(x_i^{+}) \;-\; \frac{1}{|N|}\sum_{i \in N} h_\ell(x_i^{-}), \qquad h_\ell \leftarrow h_\ell + \alpha\, v_\ell,

Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared · Equation 25

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

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P

Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared · Equation 26

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

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P(\text{at least one success in } k \text{ tries}) = 1 - (1-p)^k.

Ten Failure Modes That Define Deployed AI Safety Systems · 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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P = \pi_{\text{plan}}(o_0,\ g), \qquad a_t = \pi_{\text{exec}}(P,\ o_t).

Comparing the Main Approaches to AI Agent Architecture · 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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P

Comparing the Main Approaches to AI Agent Architecture · Equation 7

the plan.

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\text{FPR}(\tau) = P(\text{block} \mid \text{benign}), \qquad \text{FNR}(\tau) = P(\text{allow} \mid \text{harmful}).

The Safeguards Behind a Claude Refusal, and What They're Actually Trading Off · 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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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 →

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

Measuring What a RAG System Retrieves, Not Just What It Answers · Equation 23

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

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P(r) = L_0 - \frac{2rf}{v}, \qquad r_{\max} = \frac{v\,L_0}{2f}.

The Logistics Tail: Sustainment as the Binding Constraint on Organised Force · Equation 7

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

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P(L \mid D) = \frac{P(D \mid L)\, P(L)}{P(D \mid L)\, P(L) + P(D \mid \overline{L})\, P(\overline{L})},

What a Biosignature Has to Rule Out · Equation 2

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

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PPP

Meanings in context

Symbol P

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Used in 78 equations

$P$