Symbol in context

$s$

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

Meanings in context

Article-grounded definition

Symbol s

the number of positions in each sequence.

Read equation 11 in How AI Inference Serving Actually Works →

Article-grounded definition

Symbol s

designed to detect rather than assume.

Read equation 41 in A Chatbot Confessed to Being Built by a Company That Never Trained It →

Article-grounded definition

Symbol s

the constant.

Read equation 4 in From Origins to Frontier: A History of Evolutionary Biology and Ecology →

Article-grounded definition

Symbol s

the assigned value 1.

Read equation 4 in Human Evolution Did Not Stop, and Medicine Is Now Steering It →

Article-grounded definition

Symbol s

the vendor publishes one value of.

Read equation 1 in What Open Weights Actually Let You Verify →

Article-grounded definition

Symbol s

the any gap between.

Read equation 12 in What Open Weights Actually Let You Verify →

Article-grounded definition

Symbol s

the value the firm places on each unit of time saved reaching $P^*$ sooner.

Read equation 5 in How xAI's Infrastructure Build Compares to the Rest of the Field →

Article-grounded definition

Symbol s

the scale.

Read equation 20 in How a Model Actually Gets Small Enough to Run on a Phone →

Article-grounded definition

Symbol s

the success indicator or rate.

Read equation 1 in Why Cost and Latency Belong in the Evaluation Score, Not a Footnote →

Article-grounded definition

Symbol s

the wins on.

Read equation 13 in Why Cost and Latency Belong in the Evaluation Score, Not a Footnote →

Article-grounded definition

Symbol s

the most agent benchmarks still publish only.

Read equation 24 in Why Cost and Latency Belong in the Evaluation Score, Not a Footnote →

Article-grounded definition

Symbol s

everything true about the task — every file changed, every external call made, every fact established —.

Read equation 4 in The Hardest Unsolved Problems in AI Agent Architecture →

Article-grounded definition

Symbol s

the number of tokens.

Read equation 38 in The Economics and Physical Limits of Running AI Agents at Scale →

Article-grounded definition

Symbol s

the observed score.

Read equation 1 in How to Actually Compare Frontier AI Models Without Building a Misleading Leaderboard →

Article-grounded definition

Symbol s

the sagitta.

Read equation 2 in What a Particle Detector Actually Measures →

Article-grounded definition

Symbol s

the signal level.

Read equation 21 in When Generation Becomes Free, Attention Becomes the Scarce Good →

Article-grounded definition

Symbol s

the value-added share of task x.

Read equation 5 in What the Machine Breakers Actually Wanted →

Article-grounded definition

Symbol s

bytes occupied by each element.

Read equation 5 in What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach →

Article-grounded definition

Symbol s

therefore approximately.

Read equation 4 in The Physical Economics of Inference: Bandwidth, Energy, and the Limits of a Datacenter →

Article-grounded definition

Symbol s

therefore approximately [displayed formula].

Read equation 7 in The Physical Economics of Inference: Bandwidth, Energy, and the Limits of a Datacenter →

Article-grounded definition

Symbol s

the sequence length.

Read equation 1 in Serving a Frontier Model: The KV Cache, Batching, and What a Token Actually Costs →

Article-grounded definition

Symbol s

the environmental state.

Read equation 23 in OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence →

Article-grounded definition

Symbol s

the input state.

Read equation 17 in Codex in 2035: Scenarios for Software Teams, Verification, and Machine-Written Code →

Used in 124 equations

s(x)

The Safeguards Behind a Claude Refusal, and What They're Actually Trading Off · Equation 8

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

Equation guide → · This term → · Article →

s(x)

The Safeguards Behind a Claude Refusal, and What They're Actually Trading Off · Equation 9

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

Equation guide → · This term → · Article →

s = \frac{qB\ell^{2}}{8p}, \qquad \frac{\sigma_p}{p} \;\propto\; \frac{p}{B\ell^{2}} .

What a Particle Detector Actually Measures · 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 →

s

What a Particle Detector Actually Measures · Equation 3

the sagitta.

Equation guide → · This term → · Article →

s

When Generation Becomes Free, Attention Becomes the Scarce Good · Equation 21

the signal level.

Equation guide → · This term → · Article →

\frac{\partial^{2} c(s,\theta)}{\partial s \, \partial \theta} \;<\; 0,

When Generation Becomes Free, Attention Becomes the Scarce Good · Equation 23

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 →

\Delta \ln L \;=\; \underbrace{\eta \, \Delta \ln Y}_{\text{productivity}} \;-\; \underbrace{\int_{I}^{I+\Delta I} s(x)\,dx}_{\text{displacement}} \;+\; \underbrace{\int_{N}^{N+\Delta N} s(x)\,dx}_{\text{reinstatement}}

What the Machine Breakers Actually Wanted · Equation 5

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

Equation guide → · This term → · Article →

s(x)

What the Machine Breakers Actually Wanted · Equation 7

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

Equation guide → · This term → · Article →

s

What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach · Equation 5

bytes occupied by each element.

Equation guide → · This term → · Article →

I_{\mathrm{gemm}} = \frac{2mnk}{s\,(mk + kn + mn)},

What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach · 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 →

M_{\mathrm{kv}} = 2\,L\,n_{\mathrm{kv}}\,d_{\mathrm{head}}\,s\,p,

The Physical Economics of Inference: Bandwidth, Energy, and the Limits of a Datacenter · 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 →

s

The Physical Economics of Inference: Bandwidth, Energy, and the Limits of a Datacenter · Equation 6

therefore approximately.

Equation guide → · This term → · Article →

B(b,s) \approx Np + b\,M_{\mathrm{kv}}(s),

The Physical Economics of Inference: Bandwidth, Energy, and the Limits of a Datacenter · Equation 7

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

Equation guide → · This term → · Article →

s

The Physical Economics of Inference: Bandwidth, Energy, and the Limits of a Datacenter · Equation 10

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

Equation guide → · This term → · Article →

b_{\max} \approx \frac{M_{\mathrm{device}} - M_{\mathrm{weights}}}{M_{\mathrm{kv}}(s)},

Dense, Sparse, and Distilled: Comparing Approaches to Frontier Model Capacity · Equation 26

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

Equation guide → · This term → · Article →

M_{\mathrm{kv}} = 2\, L \, n_{\mathrm{kv}} \, d_{\mathrm{head}} \, s \, b \, p ,

Serving a Frontier Model: The KV Cache, Batching, and What a Token Actually Costs · 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 →

s

Serving a Frontier Model: The KV Cache, Batching, and What a Token Actually Costs · Equation 5

the sequence length.

Equation guide → · This term → · Article →

b_{\max} \approx \frac{M_{\mathrm{device}} - M_{\mathrm{weights}}}{M_{\mathrm{kv}}(s)} ,

Serving a Frontier Model: The KV Cache, Batching, and What a Token Actually Costs · Equation 13

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

Equation guide → · This term → · Article →

s

Measuring Frontier Models: Contamination, Variance, and What a Score Can Support · Equation 2

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

Equation guide → · This term → · Article →

s

OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute · Equation 30

the observed score.

Equation guide → · This term → · Article →

s = f(\theta,\ e,\ \mathcal{P},\ \mathcal{H},\ \mathcal{S},\ t),

OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute · 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 →

s

OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute · Equation 38

the observed score.

Equation guide → · This term → · Article →

A_{\mathrm{excess}}=A_g\setminus A_u(g,s),

Ten Failure Modes in Agentic Coding, from Prompt Injection to False Completion · 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 →

s

Ten Failure Modes in Agentic Coding, from Prompt Injection to False Completion · Equation 12

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

Equation guide → · This term → · Article →

T_j:(s,x)\mapsto (s',y,e),

OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence · Equation 23

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

Equation guide → · This term → · Article →

s

OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence · Equation 24

the environmental state.

Equation guide → · This term → · Article →

s'

OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence · Equation 26

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

Equation guide → · This term → · Article →

A_H(s)

OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence · Equation 29

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

Equation guide → · This term → · Article →

A_P(s)\subseteq A_H(s)

OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence · Equation 30

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

Equation guide → · This term → · Article →

A_U(s)\subseteq A_P(s)

OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence · Equation 31

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

Equation guide → · This term → · Article →

sss

Meanings in context

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Used in 124 equations

$s$