Code decides, models suggest.

In Moye, grades, difficulty placement, streak resilience and rewards are computed by pure, tested functions in lib/mastery.ts, lib/honey.ts, and lib/streak.ts: never an opaque LLM prompt.

Interactive Live Sandbox

Bayesian Single-Step Update Simulator

66%p_known

Tier 2: just-right

Prior Knowledge Probability (p_prior):p = 0.25

0.05 (Beginner)0.60 – 0.85 (Target Zone)0.95 (Mastered)

Student Attempt Outcome:

p_learn

0.25

p_guess

0.25

p_slip

0.10

target zone

0.60–0.85

Proof Trace: Strong Learner5 Steps

Smooth advancement from Tier 1 to Tier 3 within 4 steps

Step 1 (Correct):p = 0.6053 (Tier 2)

Step 2 (Correct):p = 0.885 (Tier 3)

Step 3 (Correct):p = 0.9739 (Tier 3)

Step 4 (Correct):p = 0.99 (Tier 3)

Step 5 (Correct):p = 0.99 (Tier 3)

Proof Trace: Struggling Learner4 Steps

Gentle descent to remedial Tier 1 without shame or buzzer

Step 1 (Not Yet):p = 0.5109 (Tier 1)

Step 2 (Not Yet):p = 0.3417 (Tier 1)

Step 3 (Not Yet):p = 0.2985 (Tier 1)

Step 4 (Not Yet):p = 0.2903 (Tier 1)

Zero Signup Proof Surface

Client-Side Verification Ledger

INV-1 · BKT

Mathematical convergence in bounded interval [0, 1].

Pass0ms

INV-2 · Honey Cap

Hard cap strictly clamped at 50 drops daily.

Pass0ms

INV-3 · Streak Rest

No guilt copy; Spark rests at 1 on break.

Pass0ms

INV-4 · Theme Engine

Deterministic re-skinning across all curriculum lenses.

Pass0ms

Last audit verification timestamp: checkingAll 4 Invariants Green

Code decides, models suggest.

In Moye, grades, difficulty placement, streak resilience and rewards are computed by pure, tested functions in lib/mastery.ts, lib/honey.ts, and lib/streak.ts: never an opaque LLM prompt.

Interactive Live Sandbox

Bayesian Single-Step Update Simulator

66%p_known

Tier 2: just-right

Prior Knowledge Probability (p_prior):p = 0.25

0.05 (Beginner)0.60 – 0.85 (Target Zone)0.95 (Mastered)

Student Attempt Outcome:

p_learn

0.25

p_guess

0.25

p_slip

0.10

target zone

0.60–0.85

Proof Trace: Strong Learner5 Steps

Smooth advancement from Tier 1 to Tier 3 within 4 steps

Step 1 (Correct):p = 0.6053 (Tier 2)

Step 2 (Correct):p = 0.885 (Tier 3)

Step 3 (Correct):p = 0.9739 (Tier 3)

Step 4 (Correct):p = 0.99 (Tier 3)

Step 5 (Correct):p = 0.99 (Tier 3)

Proof Trace: Struggling Learner4 Steps

Gentle descent to remedial Tier 1 without shame or buzzer

Step 1 (Not Yet):p = 0.5109 (Tier 1)

Step 2 (Not Yet):p = 0.3417 (Tier 1)

Step 3 (Not Yet):p = 0.2985 (Tier 1)

Step 4 (Not Yet):p = 0.2903 (Tier 1)

Zero Signup Proof Surface

Client-Side Verification Ledger

INV-1 · BKT

Mathematical convergence in bounded interval [0, 1].

Pass0ms

INV-2 · Honey Cap

Hard cap strictly clamped at 50 drops daily.

Pass0ms

INV-3 · Streak Rest

No guilt copy; Spark rests at 1 on break.

Pass0ms

INV-4 · Theme Engine

Deterministic re-skinning across all curriculum lenses.

Pass0ms

Last audit verification timestamp: checkingAll 4 Invariants Green