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Equation 13 · The Hidden Infrastructure Bill Behind Every RAG Answer

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EE

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the number of extra context tokens each call would need to carry in place of what retrieval would otherwise have selected. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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EE

Symbol E

the number of extra context tokens each call would need to carry in place of what retrieval would otherwise have selected.

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Filling in the billion-chunk illustration used throughout: at a hundred thousand queries a month, CRAGC_{\mathrm{RAG}} comes to roughly 2,195 dollars of storage plus about 11,500 dollars of combined query and rerank cost, or approximately 13,700 dollars a month, not counting the one-time ingestion charge. If the same workload instead pasted 100,000 tokens of context into every call to substitute for what retrieval would have selected, at OpenAI’s gpt-5.6-sol long-context input rate of ten dollars per million tokens, CLCC_{\mathrm{LC}} comes to one dollar per query, or 100,000 dollars a month — about seven times the retrieval pipeline’s bill. This is arithmetic on a stated hypothetical workload, not…
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Filling in the billion-chunk illustration used throughout: at a hundred thousand queries a month, CRAGC_{\mathrm{RAG}} comes to roughly 2,195 dollars of storage plus about 11,500 dollars of combined query and rerank cost, or approximately 13,700 dollars a month, not counting the one-time ingestion charge. If the same workload instead pasted 100,000 tokens of context into every call to substitute for what retrieval would have selected, at OpenAI’s gpt-5.6-sol long-context input rate of ten dollars per million tokens, CLCC_{\mathrm{LC}} comes to one dollar per query, or 100,000 dollars a month — about seven times the retrieval pipeline’s bill. This is arithmetic on a stated hypothetical workload, not a measurement of either approach in production, and it depends entirely on the size of E , the amount of context a given task would actually need without retrieval; a task where the relevant evidence is small, or where the corpus fits comfortably inside the window, tilts the comparison the other way.

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