multiplication

The passage around this formula

That combinatorial framing is worth making explicit, as a stylized model rather than a measured cost curve. Call the number of distinct model-facing client applications M and the number of distinct external tools or data sources N . Absent any shared protocol, a connector is needed for each pairing that is actually wanted, so the number of bespoke integrations that must be built and separately kept current scales as $I_{\mathrm{bespoke}} \approx M \times N$. A protocol that both sides target once, instead, lets each side write a single adapter to the shared standard, so the count becomes

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