Twelve binary reveals
Twelve independent fair bits form three blocks of four bits. Each complete block represents 0–15; adding 1 gives a, b and c, each between 1 and 16. The reveals update the quote as more of the outcome becomes known.
Proper divisors and the score
Let u(n) be the sum of the positive divisors of n smaller than n. For example, u(6)=1+2+3=6 and u(1)=0. The score is S=|u(a)−2u(b)+u(c)|. Its global minimum is 0, so subtracting that minimum leaves S unchanged.
Three reward weights
Linear uses S, Square uses S² and Cube uses S³. With power p=1, 2 or 3, the live gross quote is 0.97 × E[Sᵖ | revealed bits] / E[Sᵖ]. The power applies to terminal scores before averaging; it does not square or cube a finished Linear quote. The quote begins at ×0.97 and can rise, fall or reach zero.
Choose before starting
Choose 10, 20, 50 or 100 play coins; the default is 20. Select the reward weight and turn automatic collection off or choose ×1.25, ×1.75 or ×2.50. Starting deducts one stake. Stake and mode controls, balance restoration and a second round are locked until settlement.
Collection and event order
Manual collection first processes any reveals already due, then collects the surviving current quote. Automatic collection settles at the first quote at or above its threshold, using that quote. Zero resolves first at the same event, with no return; an earlier automatic settlement is unaffected by a later zero. Step 12 collects a surviving quote if the round has not ended.
Expected return and sample results
The underlying gross-return expectation is 97% for the checked stopping policies and each reward weight. The checks cover manual collection at step 6, terminal step 12 and all three automatic thresholds: 15 combinations with 1,000,000 simulated rounds each, or 15,000,000 rounds in total. Observed returns range from 96.7035% to 97.2230%. These sample results do not guarantee an individual session; integer credits also use the saved fractional carry.
Frequently asked questions
Is this an outside ZA9 product?
ZA9 is the name covered by this guide. The Aliquot Curvature Claim demo is this guide’s own browser game. Its presence does not establish a connection to an outside ZA9 business.
Does Square mean squaring the Linear quote?
Linear uses S, Square uses S² and Cube uses S³. With power p=1, 2 or 3, the live gross quote is 0.97 × E[Sᵖ | revealed bits] / E[Sᵖ]. The power applies to terminal scores before averaging; it does not square or cube a finished Linear quote. The quote begins at ×0.97 and can rise, fall or reach zero.
How are fractional returns credited?
Settlement credits floor(stake × collected quote + saved carry). The part below one coin is saved for the next settlement. For a stake of 20, quote ×1.25 and carry 0.4, the credit is 25 coins and the carry remains 0.4. A zero-return round leaves existing carry unchanged. This is a gross return, including any stake returned, rather than pure profit.
