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Equation 2 · Codex vs Claude Code: A Systems Comparison, Not a Benchmark Beauty Contest

What does this equation mean?

Aj=(Mj,Cj,Tj,Pj,Ej,Sj,Oj),\mathcal A_j=(M_j,C_j,T_j,P_j,E_j,S_j,O_j),

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Inputs and operations(M_j,C_j,T_j,P_j,E_j,S_j,O_j)
Result or conditionmathcal A_j
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

AjA_j

Symbol A_j

AjA_j is part of the quantity the equation computes from the expression on the right.

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MjM_j

Symbol M_j

MjM_j is an input to the expression that computes the quantity on the left.

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CjC_j

Symbol C_j

CjC_j is an input to the expression that computes the quantity on the left.

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TjT_j

Symbol T_j

TjT_j is an input to the expression that computes the quantity on the left.

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PjP_j

Symbol P_j

PjP_j is an input to the expression that computes the quantity on the left.

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EjE_j

Symbol E_j

EjE_j is an input to the expression that computes the quantity on the left.

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SjS_j

Symbol S_j

SjS_j is an input to the expression that computes the quantity on the left.

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OjO_j

Symbol O_j

OjO_j is an input to the expression that computes the quantity on the left.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

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What the article says around this equation

Represent a deployed system j as Aj=(Mj,Cj,Tj,Pj,Ej,Sj,Oj)\mathcal A_j=(M_j,C_j,T_j,P_j,E_j,S_j,O_j). where M is model policy, C context and state, T tools and extensibility, P permissions, E execution isolation, S surfaces and handoff, and O organizational controls. Comparing only M discards most of what users buy and most of what defenders must secure.

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