# Rationale and numerical provenance

The choice is deliberately conditional. The user's need for cash does not turn a model whose compliant transaction cost is unknown into a demonstrated income source. A single $38 account is the proposed deployment unit, but zero purchases is the present decision because the supplied broker does not implement all required equity/calendar behavior and the measured news intervention is large enough to erase the candidate's base-cost expected surplus. This distinction avoids both claiming validation and discarding a plausible setting solely because its broker cell is unresolved.

## How the settings follow

The decision rule is a policy choice, not a global mathematical optimum. It gives priority to a simple symmetric bracket and a single small account, then optimizes risk inside that restricted family. RR 1 has the strongest symmetry justification and the existing operational precedent. Different RR values are not assumed to have a forecasting edge; the fair probability is 1/(1+RR), or b/(a+b) after clipping. The broker's non-unit ratios depend more on the shared historical path. A broker-unresolved rival is not a loser, but it cannot establish the small superiority needed to complicate deployment.

On the mapped RR-1 assessment grid, 3% is the highest risk below the conservative 3.15% daily-profit ceiling. This also requires at least four net winning contributions to reach the cost-inclusive 9% target, so the three-day minimum is not evaded. The daily ledger still matters: partial news exits and overnight marked equity are not represented by a simple two-point close-to-close chain. Setting risk once per stage is accepted by the user; losses never trigger an increase, and lot changes respond only to stop distance and account safety.

On the funded grid, 1.5% is the RR-1 payout-probability maximum, although its difference from 1% is economically tiny and empirically unresolved. Its much shorter waiting time supplies the useful distinction. The $100 minimum stops the payout hurdle falling below 4.7619% at this tier. Reducing risk indefinitely therefore increases cost and time, not safety in every sense.

The approximately 6% fee screen comes from the paper's older wallet experiments, not a guarantee for the new strategy. $38 is 3.8% of the $1,000 wallet; the next tier costs $99, 9.9%. One account avoids importing the old pooling estimates into a new two-risk, tick-floor policy. The $300,000 allocation cap remains binding if the policy is ever expanded. EA/HFT bans mean the broker is a research executor, not permission to automate the live account.

## Computations C: exact chains and permitted wallet comparison

Read module: `/root/Projects/trading-framework/src/notebooks/reports/topics/prime_academy/modules/prime.py`. Ran with bytecode writing disabled; no notebook or broker replay. Parameters:

```python
g = PA.cost_share(34.8)  # (5/10 + 0.5)/34.8
PA.eval_chain(ra, g*ra, rr=1, clip_up=True, clip_dn=True)
PA.funded_chain(rf, g*rf,
    PA.payout_threshold(rf, 1, 3000, .70), rr=1, clip_dn=True)
PA.wallet_mc(PA.Tier(3000,38,51), .03, g*.03, .70, 1, 1000,
    horizon_days=500, n=6000, seed=5, rr=1,
    funded_risk=rf, funded_cost=g*rf, clip_up=True, clip_dn=True)
```

Exact-chain outputs, base cost, floor clipped throughout:

| Stage/risk | Pass or any-payout probability | Mean trades to resolve/lifetime | Conditional median first payout | Expected lifetime gross |
|---|---:|---:|---:|---:|
| Assessment 3% | 0.453773 | 9.652674 | — | — |
| Assessment 4% | 0.462414 | 5.901076 | — | — |
| Funded 1% | 0.522125 | 106.094673 | 30 | 0.059518 |
| Funded 1.5% | 0.523595 | 54.311490 | 18 | 0.066590 |
| Funded 2% | 0.463059 | 36.227041 | 16 | 0.069180 |
| Funded 4% | 0.293734 | 15.414543 | 14 | 0.072314 |

Per purchase at 3%/1.5%, chain arithmetic gives P(cash)=0.23759297, expected receipts=3000×0.70×P(pass)×E[W]=$63.45498, surplus=$25.45498, and EV payment breakeven=38/63.45498=0.5988498. Payout eligibility is distinct from cash honoured by the firm.

Wallet outputs below are conditional simulations, not exact-chain results or full-rule deployment forecasts. No spread-free broker result is substituted into them.

| Funded risk | Ruin | Median maximum wallet drawdown | 90th percentile drawdown | Median first cash, model trades among cash recipients | Expected log growth |
|---|---:|---:|---:|---:|---:|
| 1% | 0% observed | $228.00 | $453.85 | 99 | 0.030969 |
| 1.5% | 0.1167% | $276.40 | $532.00 | 66 | 0.166519 |
| 2% | 0.2667% | $342.00 | $608.90 | 65 | 0.247681 |
| 4% | 3.8333% | $532.00 | $912.00 | 78 | 0.263009 |

The chosen funded risk improves this wallet drawdown comparison against 4%, while giving up growth. It does not minimize drawdown absolutely: 1% has smaller drawdown and much longer first cash. The funded account still ultimately fails under the model; lower per-trade risk does not remove its 9% terminal floor. Nor does 0% observed ruin mean zero probability.

Using broker_map.json's RR-1 pace, 2.02508 calendar days/trade, 66 model trades would be about 134 days; that is only a rough clock conversion, not a lifecycle cash median estimate. The older section-23 114-day claim used a cheaper cost and another pace and cannot establish a 120-day promise here. A failed assessment and another purchase must be included in wallet time; adding conditional assessment and funded medians is not a wallet median. The 120-day preference in section 23 was explicitly operator-adjustable, not one of this brief's hard constraints. This decision makes no near-term income promise.

For the news sensitivity only, substitute `g *= 2.33`, from the rounded 1.33 extra round trips/trade in paper §13. This treats episode frequency as constant across risk and ignores any swap credit; it is an illustrative adverse cost case, not a measured fact for the new cell. Outputs:

| Risk | Assessment pass | Funded any payout | Funded gross withdrawn |
|---|---:|---:|---:|
| 1% | — | 0.400591 | 0.035333 |
| 1.5% | — | 0.418074 | 0.044586 |
| 2% | — | 0.393314 | 0.049169 |
| 3% | 0.393111 | — | — |
| 4% | 0.415985 | 0.251232 | 0.054356 |

For 3%/1.5%, expected receipts fall to $36.80711, surplus −$1.19289, EV payment breakeven 1.0324093. Even within RR 1, choosing 2% or 4% funded risk merely to rescue a slim expected surplus would change the payout/drawdown objective; neither has a fully compliant positive wallet-growth result at these costs. Zero allocation is the defensible current gate outcome. No claim is made that every possible cell is unprofitable.

## Alternatives rejected or deferred

- **Today's 4%/1.5% unchanged:** almost the same pass probability, faster assessment, but a full assessment win exceeds 35% of the target. It becomes the fallback only on confirmation that this cap excludes assessment. Target clipping alone does not repair daily concentration.
- **4% funded:** a 22.99-percentage-point reduction in payout probability relative to 1.5%, and markedly larger wallet drawdown in C. Faster lifetime extraction is not the user's first objective.
- **1% funded:** virtually identical payout chance but 30 versus 18 conditional trades to payout and roughly twice mean life. Lower drawdown is real in the wallet comparison; it remains the alternative if the user prioritizes that over cash timing.
- **RR 3/0.5% funded:** paper §14 gives 55.7% payout chance versus 52.4%, but 37 versus 18 trades to payout; broker pace is 3.51 versus 2.03 days/trade. Its cell is unresolved. Do not convert a few chain points into empirical superiority or call its low raw broker rate a refutation.
- **RR below 1:** paper §10's wallet drawdown advantage is under another floor/cost/same-risk setup. At the present funded map, RR 0.5/2% gives about 50.1% versus 52.4%; its broker row has material shortfalls in resolvable cells. Neither finding proves a universal ban on low RR, but neither establishes a reason to replace the default.
- **Larger tier, multiple accounts, 90% add-on:** more money committed before firm payment is observed. The old $1,000-wallet pooling choice was two $3,000 accounts and $76 upfront, with correlations measured between 07:00 and 16:00 only. That result does not transfer automatically. The add-on costs $51 and may lower a binding $100 hurdle, so the paper's simple 'never helps' statement is not treated as a universal dominance proof; it needs its own small-tier wallet calculation. Keep the lower fee until such evidence exists.
- **No target clip, soft floor or postmortem clamp:** obsolete for the operator's stated assumptions. An equity floor truncates the price path and changes the chance of a win; changing only the final booked loss does not simulate that mechanism. Sections 14 and 24 supersede older claims that account clipping was absent, but completed-trade accounting still cannot test floating-equity enforcement.
- **News rule off or naked through releases:** explicitly incompatible with the rulebook or daily floor. The observed 53.8% news-aside bootstrap rate is not a trading edge: it resamples a different set of lucky trades. Retain the extra costs.
- **Carry harvesting, another instrument, volatility timing, GARCH:** no reliance on positive swap drift. NDX100 is only a cost-ranking candidate lacking its own pace/walk-forward validation; volatility timing was a recorded dead end; GARCH did not beat the existing filter out of sample. Keep the tested stop floor and entry window.
- **Mirroring Maven or another account:** the vault explicitly identifies opposing exposure and reverse arbitrage as prohibited. Its attractive simulated ruin reduction is irrelevant to a compliant plan.

## Evidence strength and test power

Read all listed grounding files end to end, with paper.txt as the paper's text representation. The newest map is the appropriate numerical base. Section 23's 60-pip cost is superseded by the 34.8-pip calculation; older vault entries also contain superseded ruin and floor claims. broker_results.json is a useful accounting check, not independent validation of today's tick-floor, low-risk funded plan.

The original map test failed: 39.0625% of 192 cells outside two between-seed standard errors. The later 13.6986% of 73 resolvable cells is a post hoc diagnosis, still above the old 10% acceptance threshold, not a clean successful preregistration. Seeds share prices, long accounts reduce independent history, and dropping terminal accounts biases payout statistics. At 1.5% funded, broker_map.json's seed-average 52.496% differs from its pooled 50%; compare the latter to the protocol expectation 52.709%, not interchange denominators. Four calendar blocks cannot justify precise payout-rate confidence.

The prospective test's commission-only null comes directly from agreement rows: 0.5543180161 − 0.3072258701 = 0.2470921461. Design SE=√(0.25/100+0.25/100)=0.0707107; critical margin=1.96×SE=0.1385929. At Δ=0, normal-design power is Φ(0.2470921/SE−1.96)+Φ(−0.2470921/SE−1.96), about 94%; the upper symmetric alternative has the same power. The test levels and sample targets are declared design choices, not quantities estimated from the grounding. Calendar dependence can reduce effective sample size below actual account counts, so the SE target and block minimum both apply; 20 random seeds cannot manufacture 100 independent market accounts. At adequate power, loss of the payout advantage can reject the reason for the chosen funded risk. Until then, report inconclusive rather than 'passed'.

A historical broker test also cannot establish the firm's willingness to pay or its discretionary interpretation of gambling. The operator's investor information is a prior only. One honoured payout, if eventually observed, would be evidence about that request, not a guarantee against correlated future refusals. No web access, data pull, notebook execution, broker replay, or modifying git command was used.