Light nuclei climb past a wall of their own repulsion and lock into a more-bound state, spilling the difference as energy. This is the furnace of every star: not that fusion is easy, but that quantum tunnelling makes the nearly-impossible happen often enough — the Gamow peak — to keep the sky lit. Rendered, not quoted.
A fusion reaction is a walk on the binding-energy curve. Each nucleus has a binding energy B(Z,N) = (Z·mH + N·mn − M)·u, with u = 931.5 MeV. The released energy is the gain in total binding:
Q = B(products) − B(reactants)
For D + T → He-4 + n, the alpha particle (He-4) is especially bound, so Q is large and positive. Below it stand two barriers: the Coulomb wall Z₁Z₂e²/r that classical thermal energy cannot clear, and beneath it the tunnel — the reverse of alpha decay — that quantum mechanics opens.
Light side of the curve: merging climbs toward the Fe-56 peak from below, so it pays. (The heavy side pays by splitting — that is the-nuclear-fission.)
Neighbour: the-binding-energy. Fusion is climbing that curve from the light side; the reactants are less bound than the product, and the height climbed is exactly Q.
Also touching: the-quantum-tunnelling (the same barrier-penetration that lets alpha particles out lets fusing nuclei in), and the-nuclear-fission — its uphill mirror on the heavy side. Bethe 1939 wired all of this to why stars shine.
Re-runs the engine's core invariants live and independently of the panel. If the machine is tampered, this flips red.
status: …
Checks: Q>0 (release), He-4 most-bound of the set, barrier ≫ kT, tunnelling nonzero, Gamow-peak location matches theory.
Measured atomic masses (u) and physical constants — the only inputs. Everything else is computed.
The live engine: Q-value from binding gain, the Coulomb barrier, and the Gamow-peak tunnelling that makes stars burn.
Curve: the Maxwell tail exp(−E/kT) falls, the tunnelling factor exp(−√(EG/E)) rises; their product is the Gamow peak — the narrow window of energies where fusion actually happens.
D + T → He-4 + n …
WALL — "If the barrier is ~1 MeV and the Sun's core is only ~1 keV, classically the two protons never touch. Rate should be zero. Stars can't fuse."
Rebuttal: classically, yes — the rate would be astronomically suppressed. But the barrier is penetrated, not cleared. The Gamow factor exp(−√(EG/E)) is small but strictly nonzero, and the Maxwell tail supplies a thin population at the Gamow-peak energy (~keV). The product is tiny per pair and enormous per star. The engine reports both: barrier/kT ≫ 1 and tunnelling > 0.
Fusion works because the product is lighter, and lightness itself is the fuel. → It is the binding, not the mass alone: Q = B(products) − B(reactants). Mass defect is the accountant, not the cause.
Hotter is always enough; just raise T until thermal energy exceeds the barrier. → Stellar cores never reach barrier temperatures (~1010 K). Fusion runs at ~107 K only because of tunnelling.
Helium-4 sits at the top of the binding curve. → The peak is near Fe-56 (~8.8 MeV/nucleon). He-4 is a local standout (~7.07), which is why its Q is large — but the climb continues past it.
Planted void (disclosed): flip the sign of Q so the product is less bound than the reactants — fusion would absorb energy and no star could shine. The Witness (7) catches it live.
tamper flag: off