Symbol in context

$C$

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

Meanings in context

Article-grounded definition

Symbol C

constants fixed by the microscopic couplings.

Read equation 6 in Every Crystal Has Its Own Speed of Light →

Article-grounded definition

Symbol C

the covariance.

Read equation 26 in The Bend an Elevator Cannot Fake →

Article-grounded definition

Symbol C

the independent of.

Read equation 41 in The Bend an Elevator Cannot Fake →

Article-grounded definition

Symbol C

their dimensionless decohering flux.

Read equation 27 in How Fast Can a Horizon Learn Which Path You Took? →

Article-grounded definition

Symbol C

the polar moment of inertia.

Read equation 4 in How Planetary Science and Exploration Actually Work →

Article-grounded definition

Symbol C

the current concentration.

Read equation 1 in How Earth Systems and Climate Dynamics Actually Work →

Article-grounded definition

Symbol C

the model’s usable context window.

Read equation 11 in The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol →

Article-grounded definition

Symbol C

copied from one run into the other.

Read equation 17 in Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared →

Article-grounded definition

Symbol C

sufficient to restore the behaviour.

Read equation 23 in Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared →

Article-grounded definition

Symbol C

the model’s evaluated capability on a specific threat class.

Read equation 1 in A History of Anthropic and the Claude Model Line →

Article-grounded definition

Symbol C

the nameplate capacity.

Read equation 4 in Power Density and What It Permits →

Article-grounded definition

Symbol C

the consumption rate of a force in the field and T(r) the sustained throughput that can be delivered to it at distance r from the last high-capacity transfer point.

Read equation 10 in The Logistics Tail: Sustainment as the Binding Constraint on Organised Force →

Article-grounded definition

Symbol C

the parameters.

Read equation 20 in Why Materials Fail: Fracture, Flaws and the Inspection Interval →

Article-grounded definition

Symbol C

the agent’s completion claim and V as external task success.

Read equation 24 in Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex →

Article-grounded definition

Symbol C

computational and human-review cost.

Read equation 22 in Reliable AI Agents Are Control Systems, Not Chatbots →

Article-grounded definition

Symbol C

technical capability.

Read equation 21 in Humanity Has Always Been a Human–Technology System →

Used in 80 equations

C

The Main Technical Approaches to AI Alignment, Compared · Equation 6

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

Equation guide → · This term → · Article →

C \geq 0

Why Average Success Rate Hides the Failures That Matter Most · Equation 3

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 →

q_\tau = \Pr(\text{failure and severity} > \tau) = (1-p)\cdot \Pr(C > \tau \mid \text{failure})

Why Average Success Rate Hides the Failures That Matter Most · Equation 5

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 →

\Pr(C > \tau \mid \text{failure})

Why Average Success Rate Hides the Failures That Matter Most · Equation 8

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 →

C

Why Average Success Rate Hides the Failures That Matter Most · Equation 9

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

Equation guide → · This term → · Article →

C

Shrink It, Train It Small, or Search for It: The Main Strategies for Small Models, Compared · Equation 11

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

Equation guide → · This term → · Article →

E[C] = c_{\mathrm{local}} + (1-p)\, c_{\mathrm{cloud}}.

Shipping an On-Device AI Feature That Actually Works in the Field · 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 →

\log_2 C

How a Model Actually Gets Small Enough to Run on a Phone · Equation 12

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

Equation guide → · This term → · Article →

C

How a Model Actually Gets Small Enough to Run on a Phone · Equation 13

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

Equation guide → · This term → · Article →

C(t) = \mathbb{1}\!\left[U(t) \ge u^{*}\right] \cdot \mathbb{1}\!\left[R(t) \ge r^{*}\right]

Multimodal 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.

Equation guide → · This term → · Article →

C(t)

Multimodal AI in 2035: Scenarios and Falsifiers · Equation 4

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

Equation guide → · This term → · Article →

C(\mathbf{r}) = \int_{t_n}^{t_f} T(t)\, \sigma(\mathbf{r}(t))\, \mathbf{c}(\mathbf{r}(t), \mathbf{d})\, dt, \qquad T(t) = \exp\!\left(-\int_{t_n}^{t} \sigma(\mathbf{r}(s))\, ds\right),

How Multimodal Models Actually Handle Video, Audio, and Space · Equation 13

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

Equation guide → · This term → · Article →

\text{score}(\mathcal C) = \frac{m_{\text{patch}}(\mathcal C) - m_{\text{corrupt}}}{m_{\text{clean}} - m_{\text{corrupt}}},

Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared · Equation 17

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_{\text{patch}}(\mathcal C)

Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared · Equation 20

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

Equation guide → · This term → · Article →

\mathcal C

Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared · Equation 21

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

Equation guide → · This term → · Article →

\mathcal C

Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared · Equation 22

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

Equation guide → · This term → · Article →

\mathcal C

Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared · Equation 23

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

Equation guide → · This term → · Article →

\mathcal C

Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared · Equation 24

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

Equation guide → · This term → · Article →

C(t)

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them · Equation 1

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

Equation guide → · This term → · Article →

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.

Equation guide → · This term → · Article →

C(k) \approx k\bar{c}

Why Cost and Latency Belong in the Evaluation Score, Not a Footnote · Equation 27

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

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 →

C(\text{model}) \ge \tau_k \;\Longrightarrow\; \text{deploy only if safeguards} \ge S_k,

A History of Anthropic and the Claude Model Line · Equation 1

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 →

C(\text{model})

A History of Anthropic and the Claude Model Line · Equation 2

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

Equation guide → · This term → · Article →

C

Power Density and What It Permits · Equation 4

the nameplate capacity.

Equation guide → · This term → · Article →

P_d = \frac{E}{A\,t} = \frac{C}{A} \times f = C_d\,f

Power Density and What It Permits · 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 →

C

The Logistics Tail: Sustainment as the Binding Constraint on Organised Force · Equation 10

the consumption rate of a force in the field and T(r) the sustained throughput that can be delivered to it at distance r from the last high-capacity transfer point.

Equation guide → · This term → · Article →

\frac{dS}{dt} = T(r) - C, \qquad T(r_c) = C .

The Logistics Tail: Sustainment as the Binding Constraint on Organised Force · Equation 13

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

Equation guide → · This term → · Article →

C

The Logistics Tail: Sustainment as the Binding Constraint on Organised Force · Equation 15

the consumption rate of a force in the field and T(r) the sustained throughput that can be delivered to it at distance r from the last high-capacity transfer point.

Equation guide → · This term → · Article →

\frac{\mathrm{d}a}{\mathrm{d}N} = C\,(\Delta K)^{m}.

Why Materials Fail: Fracture, Flaws and the Inspection Interval · Equation 20

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

Equation guide → · This term → · Article →

CCC

Meanings in context

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Used in 80 equations

$C$