💻 Computer Science — TFT_3Pack Example Suite

Problem 1 — Resonant Algorithm Runtime

T = D₆ τ_r log(X)

If \( τ_r \) is halved, how does the runtime \( T \) change?

Problem 2 — Data Throughput

R = F₃ T_f D₃

If \( D₃ \) triples and \( T_f \) decreases by 10%, what is the net effect on \( R \)?

Problem 3 — Error Correction

p = e^{-ΛΘ τ_r}

If error probability must be reduced by 50%, how must \( τ_r \) change?

Solution 1 — Runtime

Halving \( τ_r \) halves the runtime.

Solution 2 — Throughput

\( R' = 2.7R \) → a 170% increase.

Solution 3 — Error Correction

Increase \( τ_r \) by \( \ln(2)/(ΛΘ) \).

Problem 4 — Pipeline Latency

L_tot = τ_r (D₃ + D₆ + D₉)

Analyze how latency changes when τ_r decreases by 20%.

Problem 5 — Cache Resonance Coherence

C = X / (1 + e^{-D₃ τ_r})

Sketch C(τ_r) and describe how coherence changes with τ_r.

Problem 6 — Resonant Hashing

H = D₆(key) + X sin(τ_r)

Describe how doubling τ_r affects hash dispersion.

Problem 7 — Network Packet Delay

D = (D₃ + τ_r) / T_f

Analyze the effect of increasing T_f and decreasing τ_r.

Problem 8 — Gradient Resonance

g' = g e^{-D₆ / τ_r}

Describe how increasing τ_r affects gradient magnitude.

Diagram 1 — Algorithm Runtime

D₆ × τ_r × log(X) → T
        

Diagram 2 — Data Throughput

F₃ × T_f × D₃ → R
        

Diagram 3 — Error Correction

ΛΘ × τ_r → exponent → e^{-ΛΘ τ_r} → p