æ.store ·Pico OS ·--:--:-- ·no signal
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🎵 Lofi
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⚡WASM // æ🫵store · Transcoder Core
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λ
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you.æ.store
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⬛Bootlog · Runtime
$ æ.store init
[ok] pico-os runtime
[ok] wasm modules
[ok] transcoder online
[ok] tv · 9 channels
[ok] dao hydrated
[æ] alt+1,4,5 → æ
[🔘] omnicursor ready
æ>
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æ.store
Protocol root · fork market
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commandprompt.ai
/✨ command hub
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privateclient.ai
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teologia.ai
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neuromitosis.com
R&D binary lab
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llm.store
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soværeign.com
Identity · ownership
ID
moltcontextprotocol.com
MCP · context exchange
MCP
💬Chat · /✨
🧠 Core Ægntæ.store online. Click 🔘 to expand the Omnicursor CLI.
Try /✨ play lofi · /✨ set name you
📐Occupancy · Poisson Limit

Asymptotic Poisson Limit · Occupancy Problem

1. Setup

r balls uniformly into n bins. Zk = bins with exactly k balls.

2. Expectation

𝔼[Zk] = n · C(r,k) · (1/n)k · (1 − 1/n)r−k

3. Asymptotic Regime

n, r → ∞ with λ = n·(r/n)k/k!·e−r/n constant.

𝔼[Zk̲m] → λm  ⟹  Zk → Poisson(λ)

▸ Simulator

λ = —  |  Zk = —  |  P = —
QR Verify