Fix inaccuracies and bugs in study notes

[Alexdruso]

Audited all six interactive study notes for factual/mathematical errors
and code bugs, then verified each finding before fixing:

• MDP: corrected the "after convergence" value vector and worked Q-value
  arithmetic ([70,80,94,106,113] → [74,84,96,107,114]) to match the values
  the embedded value-iteration demo actually produces.
• Rigged coin: theoryPower() passed the flips slider (nS) as the bias p,
  giving p>1 → sqrt of a negative → NaN in the predicted-power bar. Use the
  bias slider pS instead so the predicted bar matches the simulation.
• Options: the numeric E[payoff] integral was truncated at a fixed x<600,
  undershooting Black–Scholes by up to ~16% at high vol where the lognormal
  tail extends past 600. Integrate over a distribution-scaled domain
  (6σ above E[log S_T]) with a fixed sample count so it converges onto the
  closed form without blowing up per-redraw cost.
• Boltzmann: DEMO C legend swatch for "high energy" used --sn-bad (red) but
  the bars interpolate toward --sn-muted; aligned the swatch to --sn-muted.
• Shannon entropy: "exactly 1 bit" message fired across p∈(0.45,0.55) where
  single-outcome surprise −log2 p ranges 0.86–1.15 bits; tightened to p≈0.5.
• Temperature/entropy: "nats are bits × ln 2" read as a unit identity
  (backwards); reworded as an entropy-value conversion (1 nat ≈ 1.44 bits).

Co-Authored-By: Claude Opus 4.8 noreply@anthropic.com
Claude-Session: https://claude.ai/code/session_01MHHjQGmN3Rm3rG8XgD1R7j