add pool sizing calculator to reserved browsers overview

[dprevoznik]

Summary

• New interactive calculator at the bottom of browsers/pools/overview.mdx that recommends a reserved pool size from acquisition rate, average acquired duration, and fill rate.
• Calculator assumes reuse: false on release (every acquisition triggers a refill). It computes both the concurrency floor (Little's Law with a 1.25× safety factor to match the FAQ's 10–20% headroom guidance) and the refill floor (driven by the 25%-per-minute fill ceiling), and returns the larger of the two with a "binding constraint" indicator.
• Docs section explains the equation, the ~3.2-minute crossover between the two constraints, and a small worked-examples table.

Formula

concurrency_floor = ceil(λ × d × 1.25)
refill_floor      = ceil(100 × λ / fill_rate)
N                 = max(concurrency_floor, refill_floor)

Test plan

• Mintlify preview renders the calculator inside the overview page
• Inputs update the recommended size live and flash on change
• Fill rate clamps to 1–25
• Worked-examples table values match the calculator output
• URL query params (acquisitionRate, sessionDuration, fillRate) update on interaction, matching the existing pricing calculator pattern

[mintlify]

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Project	Status	Preview	Updated (UTC)
Kernel	🟢 Ready	View Preview	Jun 2, 2026, 3:29 PM

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[cursor]

Risk assessment: Low risk.

Evidence from the diff: this PR modifies browsers/pools/overview.mdx and adds an isolated snippets/pool-sizing-calculator.jsx Mintlify snippet for a docs-page calculator. The change is user-facing documentation UI, but it doesn't modify production runtime code, auth, permissions, billing, infrastructure, shared libraries, or data/schema behavior. I also found no CODEOWNERS file in the repo and no existing approvals on the PR, so approval is appropriate under the requested rules.

  

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[cursor]

Risk assessment: Low risk.

Evidence from the diff: this PR modifies browsers/pools/overview.mdx and adds snippets/pool-sizing-calculator.jsx, an isolated Mintlify docs-page calculator. The change is user-facing documentation UI, but it doesn't touch production application code, auth, permissions, billing, infrastructure, shared libraries, data/schema behavior, or deployment configuration. The snippet only performs local calculator state updates and URL query/hash replacement in the browser.

I found no CODEOWNERS file in the repo. The PR is already approved on the current head commit, so I did not add another approval.

  

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[cursor]

Risk assessment: Low risk.

Evidence from the current diff: the PR only updates browsers/pools/overview.mdx and snippets/pool-sizing-calculator.jsx. The added/updated JSX is an isolated Mintlify docs calculator that uses local React state, numeric input handling, simple sizing math, and window.history.replaceState for URL parameters. It doesn't touch production application runtime code, backend logic, auth, permissions, billing, infrastructure, shared libraries, schema/data behavior, or deployment configuration.

The new commit changes the calculator inputs and copy, but it doesn't increase the blast radius relative to the prior approved version. I found no CODEOWNERS file, and the PR already has an active approval, so I did not add another approval or dismiss the existing one.

  

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[cursor]

Risk assessment: Low risk.

Evidence from the current diff: this PR only updates browsers/pools/overview.mdx and adds snippets/pool-sizing-calculator.jsx. The JSX is an isolated Mintlify docs-page calculator using local React state, bounded numeric inputs, simple pool-sizing arithmetic, and window.history.replaceState to persist URL parameters. It doesn't modify production runtime code, backend logic, auth, permissions, billing, infrastructure, shared libraries, schema/data behavior, or deployment configuration.

I found no CODEOWNERS file in the repo. The PR already has an active approval, so I did not add another approval. The synchronized changes do not increase the risk level, so I did not dismiss the existing approval.

  

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