# Prime Academy: the settings, and the rule that picks them

Candidate 1, 2026-09-28.

**Sources.** [P] paper; [BM] broker_map.json; [R] rules.json; [V] vault; [A] arithmetic on [R] and γ.
- **[C]** computed by me with `prime.eval_chain` and `prime.funded_chain`: γ = `cost_share(34.8)` = 2.87% of risk, target clipped, stop at the floor.
- **[W]** computed by me with `prime.wallet_mc`: $3,000 tier, $1,000 wallet, 500 trades, 6,000 paths, seed 5, P(paid) = 1.

Chain figures include the 0.5-pip spread. Broker figures charge commission only.

## 1. Settings

| setting | account A | account B |
|---|---|---|
| side, stop | EURUSD short; max(0.75 σ, 30) pips [P Cor 10] | same |
| reward-to-risk | 1, both stages | 1, both stages |
| **assessment risk** | **3.0%** | **2.5%** |
| **funded risk** | **1.5%** | **1.5%** |
| entry window | 07:00–10:00 UTC | 16:00–19:00 UTC |
| target clip, stop at the floor | on (`set_account`) | on |
| news | step aside [P §13] | step aside |
| tier | $3,000, fee $38, 70% split, no add-on | same |

Two accounts are held at once, for $76 on the first day. A dead account is replaced the next day.

**Account A.**
- **Assessment.** It passes 45.38% of the time [C]. The broker reads 47.6% against a chain of 47.7% at its cost (resolvable, z −0.03) [BM]. An assessment resolves in a median of 7 trades; a pass takes 21 days. At 4%: 46.24% and 12 days.
- **Funded stage.** The chance of any payout is 52.36%, with 1.10 payouts per account and 6.66% of the bankroll withdrawn over its life [C]. The first payout comes after a median of 46 days, and the account lives 123 days [BM].
- **Per purchase.** 23.8% of purchases return any cash. Expected value is +$25.5, 1.67 times the fee, and it breaks even at P(paid) = 60% [A on C].
- **Wallet.** Ruin 0.12%, median drawdown $276, median final wallet $1,269 after about 1,000 days. Log growth falls to zero near P(paid) = 0.8 [W].

**Account B.** Passes 44.59% [C]; broker 48.5% in 28 days [BM].

**Money.** Even with every payout honoured, one slot earns about +$134 a year and two about +$270 [A: $25.5 × 5.2 purchases a year at 2.03 days a trade, BM]. This does not solve "I need money". It is a small positive bet that tests whether the firm pays.

**Required change.** `run_live.py` runs a fixed 4% with the account rules off. It must call `set_account` with these stage risks. At 3% an unclipped target falls into the lattice trap, 40.19% against 45.38% [C].

**Payouts, by hand.** Request the full equity when all of these hold:
- 14 calendar days have passed;
- the account has 3 trading days;
- equity is at least $143 gross;
- the largest *calendar day's* realised profit is at most 35% of the request. A step-aside that spans midnight can put more than one trade's gain on one day.

**Stop buying** at the first refused request, or after 13 purchases in a row with no cash (a 2.9% chance if the model holds [A]).

**Compliance and readings assumed:**

| rule | compliance | reading assumed; what happens under the other |
|---|---|---|
| 9% static floor | stop leg at the floor | on the tick (the operator's position). On review: see §3 |
| 5% daily loss | worst trade 3.09% (A), 2.57% (B), 1.54% (funded) against ≥ 4.55% [A] | loss from entry [P Prop 18]. **Stricter reading** (from the previous day's closing equity, open profit included): an overnight trade up g/ℓ of its stop that then stops out breaches above g/ℓ = 0.51–0.67 at 3%, 0.83–1.02 at 2.5%, 0.11–0.23 at 4%, never at 1.5% [A]. B carries overnight, so runs 2.5%; §4 tests A |
| 35% daily cap | funded request ≥ max(4.76%, 1.5/0.35) | applies in the assessment too. A win at 3% is 2.91% ≤ 0.35 × 9% = 3.15%, and compliance holds up to 3.24%. At 4% every full win (3.89%) breaks it [A] |
| Expert Advisor (EA) ban [V] | one bracket a day can be placed by hand | the runner is used only after the firm confirms API placement in writing; otherwise drop B |
| 14-day clock | request rule | in days, not trades: 1.5% stays best at 14, 7 and 3 trades (52.4, 54.5 and 55.4%) [C] |

## 2. The optimization rule

**Rule.** Admit a cell only if it complies with every rule under the stricter reading of each unverified one: the floor on the tick, the 35% cap in both stages, one trade a day with the news step-aside on, and, for an account whose trades usually carry across the firm's day boundary, the daily loss measured from the previous day's closing equity with open profit included for any overnight gain up to the full stop. Fix reward-to-risk at 1 unless another ratio beats it by more than 2 points plus its per-trade shortfall through the broker [P T28]. Choose the funded risk that maximises the exact chain's chance of any payout at the tier's own minimum request, breaking ties within 1 point on the larger gross withdrawn, then the faster first payout. Choose the assessment risk that maximises the clipped pass rate with the broker's median days to pass at or under 30, breaking ties within 1 point toward fewer days to pass (risks on a 0.5-point grid, funded on 0.25). Buy the largest tier whose fee is at most 6% of the wallet with simulated ruin at most 5%, and add accounts one staggered entry window at a time while the first-day outlay stays at or under 10% of the wallet and the outcome correlation between windows at or under 0.3. A cell the broker cannot resolve (fewer than 10 calendar blocks of twice the account span) is ranked on the chain, admitted only at RR 1, where each trade is an exact coin [P §14.10], and only if the broker reads no more than 2 block standard errors below the chain under its protocol; a resolvable cell below that line is dropped.

**The one sentence.** Re-run the rule whenever a reading, the live spread or the payout record changes, and stop buying the moment a payout is refused.

**Applied.**
- **Funded.** 1.5% (52.36%) ties 1% and 1.25% and wins on gross withdrawn (6.66% against 5.95% and 6.36%) [C]. The broker reads 50.0% against 52.7% under its protocol, z −1.0 [BM].
- **Assessment.** The cap limits A to 3.24%, and the overnight carry limits B to 2.5% [A].
- **Tier.** $10,000 carries 8.2% ruin [W].

## 3. What would change the choice

| open question | direction and size |
|---|---|
| 35% cap is funded-only **and** §4's downward threshold is met | A goes to 4%: +0.86 points of pass rate, 9 fewer days, growth +0.203 against +0.167 [C, W, BM] |
| floor on review, not on the tick | A goes to 4% if the cap allows (+5.1 points). Funded stays 1.5% (54.0% against 34.8%) [C] |
| live spread | at 0.25–1.0 pip funded stays 1.5% (54.0% / 48.7%). At 0.0 pip it moves to 1.0% (57.0% against 55.4%). Expected value breaks even at P(paid) 49% (0.0 pip) to 73% (1.0 pip) [C] |
| a recurring funded charge | funded risk goes up (2%: life 36 trades against 54) [C] |
| wallet ≥ $1,650 with payouts honoured | $10,000 tier; funded 1% there gives 61.7% chance of any payout and 1.61 payouts per account [C] |
| correlation between windows > 0.45 | drop B [P §11.6] |
| firm objects to two accounts or to the runner | A only, placed by hand |

## 4. Falsification test (declared before any number is seen)

**Engine.** `PrimeAcademyStrategy` on `HistoricalBarBroker`, vendor hourly EURUSD bars 2023-11-24 to 2026-09-10:
- `set_account` on, CYCLE_EVAL, step-aside on;
- commission $5 a side through the runner's instrument override (not meta.json), which carries the 0.5-pip spread;
- 20 coin seeds plus the short path.

**Arms.** A3 enters 07–10 UTC at 3%. A4 enters 07–10 UTC at 4%.

**Scoring.** The strategy marks the open position at each bar's adverse extreme. An account is **strict-daily-eliminated** when equity falls more than 5% below its equity at the previous 21:00 UTC, open profit included (00:00 UTC reported, not acted on).

**Statistic.** S is the share of assessments strict-daily-eliminated, pooled over seeds. Its error is clustered in calendar blocks, as in notebook §24.

**Null.** S(A3) ≤ 2%.

**Thresholds.**
- **Upward.** If S(A3) ≥ 3.0%, A goes to 2.5%. The alternative is to build a boundary stop-tightening (fair by [P] Prop 20–21) and re-test it.
- **Downward.** If S(A4) ≤ 3.0% and S(A4) − S(A3) ≤ 1.0 point, A goes to 4% once the firm confirms the cap is funded-only.
- Otherwise the choice stands.

**Power** [A]. The block errors in [BM] match binomial errors on about 860 accounts (3%) and 1,730 (4%).
- Upward: a false rejection at S = 2% has a 1.8% chance. Power is 93% at 4% and 99.6% at 5%.
- Downward: power is 96% if both arms sit at 2%. A false move when A4 is 3 points worse has a 0.2% chance.
- If the realised block error exceeds 1.5× the binomial, act only on S(A3) ≥ 5%.
- The funded 1.5% cell is unresolvable on 2.8 years (4 blocks); its test is the live payout record.