L8: Hamiltonian Energy Wells

Trust centers are energy wells. Moving between them costs energy. Click to drop a ball — watch it roll toward the nearest safe basin.

Challenge: Click between two wells. The ball settles into the nearest one. Now try clicking far from all wells — the ball has no safe basin and gets flagged as untrusted. The energy barrier between wells is the cost of changing trust domains.
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Kinetic Energy
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Potential Energy
Nearest Well
SAFE
Trust State
What you're seeing: A 2D energy landscape with multiple "trust wells" — safe basins of operation. Each well represents a valid operational mode (ALLOW, READ, WRITE, ADMIN). The landscape between wells has energy barriers — crossing from one mode to another costs energy proportional to the barrier height.

The physics: The ball obeys Hamiltonian mechanics. It rolls downhill, has momentum, and loses energy to friction. If you drop it IN a well, it settles quickly. If you drop it ON a barrier, it takes longer and may oscillate. If you drop it FAR from all wells, it enters an "untrusted" state.

Security implication: An attacker trying to move from READ access to ADMIN access must cross the energy barrier between those wells. The barrier height is configurable — higher barriers make privilege escalation harder. The Hamiltonian CFI (Control Flow Integrity) layer uses this to detect unauthorized transitions between trust domains.

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