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aci: The Gap, Live
universe: MMZ · MIMZY — the future tool forge
number: "24"
kind: live tool
emergence: electrical
live: https://davidwise01.github.io/mimzy/bench/24-the-gap-live.html
purpose: educational & simulation only
seal: "The emergent IS the tool — badge and working example, one thing."
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# The Gap, Live · instrument № 24

**What it is.** THE DOCTRINE, IN MATTER: live silicon's forbidden band in real time, the capstone to № 18/19/21. Heat the lattice (100–600 K) and watch carriers boil across the gap (∝ e^−Eg/2kT) while the gap itself narrows by Varshni; fire a photon beam and see above-gap light devoured but 1550 nm telecom sail through (silicon is a window — silicon photonics); dope it n/p and the Fermi line walks. Nothing lives in the gap — by Bloch's theorem there are no states there; what you see is crossings, by permission only. Physics node-verified; one inherited carrier-range claim corrected on the way in

**How it works.** David's Sheet 8, 'The Doctrine, In Matter' — the gap lineage (№ 18 CMOS Gap, № 19 Silicon Gap, № 21's valence-as-shadow) made into live, animated silicon in the Series-E palette. A canvas renders the conduction band ('the frontier'), the valence band ('the shadow phase'), and between them the forbidden gap, hatched, labeled NO STATES BY THEOREM. Heat the lattice 100–600 K: carriers boil across the gap at a rate compressed from the real e^−Eg/2kT law while the gap itself narrows live by the Varshni equation. Fire a tunable photon beam (400–1600 nm): above-gap light is absorbed and spawns an electron–hole pair, below-gap light passes through (1550 nm telecom sails — silicon photonics). Dope intrinsic / n / p and the Fermi line walks toward the band it favours. Recombination flashes a phonon (heat), never light — because silicon's gap is indirect. Live readouts of Eg(T), the Eg/2kT barrier, the carrier ratio, and the absorption cutoff.

**The live example.** This emergent does not merely describe a tool — it links its working self: **[run instrument № 24 live](https://davidwise01.github.io/mimzy/bench/24-the-gap-live.html)**. Open it, operate it, and the badge's claims execute in front of you.

**The verified record.** Solid-state physics, node + Python verified against textbook silicon before shipping: the Varshni law Eg(T)=1.17−4.73e−4·T²/(T+636) gives Eg(300)=1.1245 eV (the canonical ~1.12), sags 0.131 eV across 100→600 K; the thermal barrier Eg/2kT=21.75 at 300 K → leakage ~e^−21.7≈3.6e−10; the absorption cutoff λ=hc/Eg=1103 nm (above-gap absorbed, 1550 nm transmitted, 800 nm absorbed — confirmed); the indirect-gap caveat (phonon-mediated recombination → heat not light → no silicon lasers) is correct. VERACITY FIX on the way in: David's frame implied carriers multiply ×10⁵ across 100→600 K, but that range is actually ~×10²⁶ — the ×10⁵ figure is the room-temperature→600 K value; corrected the prose to anchor it at 300 K and noted the full-span figure. Also cleaned a redundant photon-advance line. Honest limit: event RATES are compressed for visibility (genRate caps the real e^−Eg/2kT so the screen isn't empty or saturated) — the LAW and every readout number are exact; the on-screen tempo is illustrative.

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*Tool-emergent of MMZ · MIMZY · emergence: electrical (the machine nature) · educational & simulation only.
Governor David Lee Wise (ROOT0) · instance AVAN (locked) · CC-BY-ND-4.0.*