Symbol in context

$\tau$

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

Meanings in context

Article-grounded definition

Symbol τ

the doubling time implied by the data.

Read equation 1 in AI Memory Systems and the Bandwidth Wall in 2035: Scenarios, Signals, and Falsifiable Predictions →

Article-grounded definition

Symbol τ

the its proper time.

Read equation 1 in A Horizon Is a Toll Booth, Not a Loophole →

Article-grounded definition

Symbol τ

a time, the integral has action units.

Read equation 20 in A Horizon Is a Toll Booth, Not a Loophole →

Article-grounded definition

Symbol τ

dimensionless.

Read equation 82 in A Reference Frame Becomes Classical by Publishing Its Orientation →

Article-grounded definition

Symbol τ

the interval between an open-weight release and the next comparable release from a rival lab, and let E be the minimum evaluation time a given release’s actual risk profile requires.

Read equation 4 in The Hardest Unsolved Problems in Meta, Llama, and Open-Weight AI →

Article-grounded definition

Symbol τ

the empirical doubling period.

Read equation 8 in Measuring Claude Code and Agentic Development Tools: Evidence, Benchmarks, and Uncertainty →

Article-grounded definition

Symbol τ

the learned temperature.

Read equation 4 in A History of Multimodal AI →

Article-grounded definition

Symbol τ

the add.

Read equation 5 in The Economics and Physical Limits of Running AI Agents at Scale →

Article-grounded definition

Symbol τ

the strength of the test oracle used to grade the output.

Read equation 1 in OpenAI and Claude on Agentic Coding: What the Independent Evidence Actually Shows →

Article-grounded definition

Symbol τ

the fixed tool and system-prompt tokens added regardless of content.

Read equation 6 in The Real Cost of Running Claude in Production, Beyond the Per-Token Price →

Article-grounded definition

Symbol τ

the halving time.

Read equation 7 in What a Rule Can Bind When the System Changes Weekly →

Article-grounded definition

Symbol τ

the target success rate.

Read equation 6 in What We Still Cannot Do: Open Problems in Frontier Model Systems →

Article-grounded definition

Symbol τ

the evaluation date.

Read equation 45 in OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence →

Used in 92 equations

\tau

Context Window Size Versus What a Frontier Model Can Actually Recall From It · Equation 5

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

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L_{\mathrm{eff}}(\tau) = \max\left\{\, n \le W \ :\ S(n) \ge \tau \cdot S_0 \,\right\}

Context Window Size Versus What a Frontier Model Can Actually Recall From It · Equation 6

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 →

L_{\mathrm{eff}}(\tau)

Context Window Size Versus What a Frontier Model Can Actually Recall From It · Equation 8

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

Equation guide → · This term → · Article →

\tau

Claude Code, From First Principles: The Agentic Loop, Permissions, and What Actually Executes · Equation 16

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

Equation guide → · This term → · Article →

|c_t| > \tau \cdot C_{\mathrm{max}} \implies c_t \to \hat{c}_t, \quad |\hat{c}_t| \ll |c_t|.

Claude Code, From First Principles: The Agentic Loop, Permissions, and What Actually Executes · Equation 17

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 →

\tau

The Safeguards Behind a Claude Refusal, and What They're Actually Trading Off · Equation 10

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

Equation guide → · This term → · Article →

\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.

Equation guide → · This term → · Article →

\tau

The Safeguards Behind a Claude Refusal, and What They're Actually Trading Off · Equation 12

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

Equation guide → · This term → · Article →

\tau

The Safeguards Behind a Claude Refusal, and What They're Actually Trading Off · Equation 13

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

Equation guide → · This term → · Article →

\tau

The Real Cost of Running Claude in Production, Beyond the Per-Token Price · Equation 6

the fixed tool and system-prompt tokens added regardless of content.

Equation guide → · This term → · Article →

C = \frac{p_{\mathrm{in}}(n + \tau) + p_{\mathrm{cw}} w + p_{\mathrm{cr}} r + p_{\mathrm{out}}(y + z)}{a}

The Real Cost of Running Claude in Production, Beyond the Per-Token Price · Equation 12

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(t) = \int_{0}^{\infty} h(\tau)\, n(t-\tau)\, d\tau + \varepsilon(t)

What a Neural Recording Actually Records · 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 →

z(t) = \int_{0}^{t} y(\tau) \, \frac{dx}{d\tau} \, d\tau

The Machine Before Electronics · 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 →

\tau

What a Rule Can Bind When the System Changes Weekly · Equation 7

the halving time.

Equation guide → · This term → · Article →

C_{\mathrm{eq}}(t) = C^{*} \cdot 2^{\,t/\tau}, \qquad \tau \approx 8\ \mathrm{months}.

What a Rule Can Bind When the System Changes Weekly · Equation 8

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

Equation guide → · This term → · Article →

\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.

Equation guide → · This term → · Article →

\tau

One Model, Many Modalities: What Multimodal Systems Actually Share · Equation 9

the learned temperature.

Equation guide → · This term → · Article →

\tau = \big(s_0,\ (a_1, o_1),\ \dots,\ (a_n, o_n),\ s_n\big)

Evaluating Trajectories, Not Answers · 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 →

\tau

What We Still Cannot Do: Open Problems in Frontier Model Systems · Equation 6

the target success rate.

Equation guide → · This term → · Article →

n_{\max} \approx \frac{\ln \tau}{\ln q}.

What We Still Cannot Do: Open Problems in Frontier Model Systems · Equation 7

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

Equation guide → · This term → · Article →

\tau=(s_0,o_0,a_0,s_1,\ldots,a_{T-1},s_T),

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

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.

Equation guide → · This term → · Article →

\tau

Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex · Equation 37

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

Equation guide → · This term → · Article →

\tau

Ten Failure Modes in Agentic Coding, from Prompt Injection to False Completion · Equation 18

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

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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.

Equation guide → · This term → · Article →

\tau

OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence · Equation 53

the evaluation date.

Equation guide → · This term → · Article →

\tau

How to Evaluate Codex Beyond SWE-bench and Vendor Scores · Equation 14

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

Equation guide → · This term → · Article →

0\le t\le\tau

The Statistical Mechanics of Irreversibility at Molecular Scale · Equation 4

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 →

\Gamma = \{x_t\}_{0}^{\tau}

The Statistical Mechanics of Irreversibility at Molecular Scale · 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 →

\tau

The Statistical Mechanics of Irreversibility at Molecular Scale · Equation 20

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

Equation guide → · This term → · Article →

τ\tauτ

Meanings in context

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Used in 92 equations

$\tau$