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Equation 8 · Part 3 · The Hidden Infrastructure Bill Behind Every RAG Answer

Symbol p_in

CLC(Q)=Q⋅pin⋅EC_{\mathrm{LC}}(Q) = Q \cdot p_{\mathrm{in}} \cdot E
pinp_{\mathrm{in}}

What this part means

the applicable — possibly long-context-tiered — input price.

Its job in the formula

pip_in is one factor in the product that computes the quantity on the left.

Where the article explains it

where E is the number of extra context tokens each call would need to carry in place of what retrieval would otherwise have selected, and pinp_{\mathrm{in}} is the applicable — possibly long-context-tiered — input price.

The passage around this formula

where S is index size in gigabytes, r(S) is Pinecone’s documented read units per query as a function of that size, Q is monthly query volume, and pstorep_{\mathrm{store}} , prup_{\mathrm{ru}} , and prerankp_{\mathrm{rerank}} are the published per-unit rates given earlier. Set against it, the cost of skipping retrieval and instead inlining a fixed block of extra context on every single call is CLC(Q)=Q⋅pin⋅EC_{\mathrm{LC}}(Q) = Q \cdot p_{\mathrm{in}} \cdot E. where E is the number of extra context tokens each call would need to carry in place of what retrieval would otherwise have selected, and pinp_{\mathrm{in}} is the applicable — possibly long-context-tiered — input price.

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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