Look closer.
The Bitcoin Signature
Anyone can see your Bitcoin address. No one should see your private key. So how can the network verify that you authorized a payment without learning the secret that authorizes all payments?
Distributions
A probability is one guess. A distribution is the whole shape of uncertainty. The thing softmax produces, the thing a histogram is, the thing a return is drawn from. Most quantities a model predicts or a portfolio holds are distributions before they are numbers.
Equilibrium
Two opposing forces, one point where they cancel. The shape underneath the pendulum, the falling raindrop, and the optimal portfolio: name the forces, write the balance equation, solve for where the net change vanishes.
Where Change Vanishes
One question — *where does change vanish?* — under three physics applications.
Proof-of-system stage. 16 live applications span 4/4 pillars; 10/10 modules are consumed by at least one application; 116 bilingual terms backfill the gaps. Still early — most of math is missing — but the graph now has working evidence. The bar remains one question: does this make a curious learner understand something they could not understand before? Yes — it ships. No — it doesn't, however polished.