candidate-1

Formulation: 2/5 — It identifies the main barriers and wallet limits, but replaces the strict daily-loss prohibition with an unverified 1% breach allowance and omits several categorical and calendar constraints.
Mathematics: 3/5 — The assessment derivative, funded kink derivation and lattice-edge formula are useful, but the claimed exact-chain corner and lot-robust optimum are not established.
Method choice: 3/5 — Scenario-based line searches are inexpensive and sensible, but the claim that they miss nothing is unsupported, and numerical lattice convergence is not checked.
Inference: 2/5 — Pairing, calendar blocks and truncation adjustment are appropriate, but testing agreement with a model difference does not establish that A beats B, and the four-block funded test exceeds the grounding’s resolution standard.
Application: 2/5 — It compares directly with the current settings, but its headline optimum relies on the no-aside cost scenario and an unjustified funded-risk restriction rather than the full operating cost and strict feasibility.

candidate-2

Formulation: 2/5 — It gives explicit objectives and several inequalities, but its general net-win constraint is algebraically wrong, strict overnight compliance remains unresolved, and important firm restrictions are missing.
Mathematics: 2/5 — The assessment derivative is correct, but funded monotonicity is largely asserted, the duration formula ignores nonzero drift, and diffusion conclusions are used to restrict a discrete search without sufficient proof.
Method choice: 3/5 — The fine funded scan is reproducible and affordable, but fixing RR through an incompletely demonstrated calendar constraint and omitting numerical convergence weaken its coverage.
Inference: 1/5 — It revives between-seed errors for account-level tests despite the shared calendar dependence and substitutes deterministic sensitivity analysis for a powered empirical test of A against B.
Application: 3/5 — It quantifies the assessment change and correctly keeps the purchase gate closed at full cost, but its conditional optimum depends on permissive accounting and incorrectly labels the fee cap binding.

candidate-3

Formulation: 4/5 — It provides the most complete pathwise, categorical, wallet and execution constraints, although the current decision’s additional funded up-step restriction appears in the rationale rather than the main formulation.
Mathematics: 5/5 — It derives the assessment corner, both funded branches, stop limitation and growth first-order condition while explicitly distinguishing diffusion results from clipped, rounded and calendar-dependent execution.
Method choice: 4/5 — It combines finite enumeration, boundary refinement and lattice-convergence checks with reproducible calls, while honestly acknowledging that the executed search does not certify a continuous optimum.
Inference: 4/5 — It declares a superiority null, paired calendar-cluster estimator, rejection threshold and planning power, but practical block independence and small-sample calibration still need specification before execution.
Application: 4/5 — Its full-cost comparison reproduces, includes the split add-on and correctly concludes no purchase among evaluated designs, but the conditional winner remains incompletely searched and unvalidated after executable lot rounding.

Recommended base: candidate-3.

candidate-3 best answers the central question: calculus supplies structure, exact computation ranks specified discrete designs, and historical inference tests model adequacy and differences at a limited resolution. It also distinguishes a conditional numerical winner from an admissible purchase. Before adopting it, move the funded up-step restriction into the formulation and make the prospective block construction and test calibration explicit.

Grafts from candidate-1:
- Keep the explicit lattice-edge formula and scenario-regret presentation as search aids and sensitivity summaries.
- Keep the assessment cap’s shadow-price interpretation.
Reject the tolerated daily-rule breach, the assertion that 1.5% maximises its proposed admissible interval, and the use of model-agreement testing as evidence of superiority.

Grafts from candidate-2:
- Keep the explicit reporting of payout probability alongside waiting time and payout frequency.
- Keep the cost/input sensitivity table as conditional model analysis, clearly separated from empirical inference.
Reject the general net-win formula, account-level between-seed tests, and the claim that deterministic chain ordering removes the need to validate that ordering against execution.

Mathematical claims checked and found wrong:

1. candidate-1’s assessment cap row: using cost_share(34.8), both clips and the default eval_chain lattice, pass probabilities at u=3.15% are 45.498%, 45.575%, 45.687% and 45.825% for RR 0.75, 1, 1.5 and 3, rather than 45.68%, 45.73%, 45.78% and 45.86%; its separate 45.57% figure for RR 1 is consistent with this check.

2. candidate-1’s claim that 1.5% gives the highest funded probability within its proposed [1.456%, 1.667%] interval is false: the stated chain gives approximately 52.543% at 1.456%, versus 52.359% at 1.5%, using cost_share(34.8).

3. candidate-2’s net-win expression RR·r·(1−γ) is wrong for general RR: with cost c=γr, the net win is (RR−γ)r; the expressions coincide only at RR=1.

4. candidate-2’s equality E[N]=TD/(ur) is the zero-drift diffusion result, not the positive-cost result used in its application; for symmetric barriers the latter is D·tanh(γD/u)/(γr).

5. candidate-2’s quoted funded comparison “52.5 ± 3.3 against 52.7” does not give z=−1.0: those displayed numbers give approximately −0.061.

6. candidate-2’s statement that the 6% wallet fee cap binds at 3.8% is false: it is slack, although the next discrete tier is excluded.

I reproduced candidate-3’s three main pass/payout comparisons at its stated finer lattice and found no discrepancy in those figures. No web browsing or file writes were performed.
tokens used
44,201
candidate-1

Formulation: 2/5 — It identifies the main barriers and wallet limits, but replaces the strict daily-loss prohibition with an unverified 1% breach allowance and omits several categorical and calendar constraints.
Mathematics: 3/5 — The assessment derivative, funded kink derivation and lattice-edge formula are useful, but the claimed exact-chain corner and lot-robust optimum are not established.
Method choice: 3/5 — Scenario-based line searches are inexpensive and sensible, but the claim that they miss nothing is unsupported, and numerical lattice convergence is not checked.
Inference: 2/5 — Pairing, calendar blocks and truncation adjustment are appropriate, but testing agreement with a model difference does not establish that A beats B, and the four-block funded test exceeds the grounding’s resolution standard.
Application: 2/5 — It compares directly with the current settings, but its headline optimum relies on the no-aside cost scenario and an unjustified funded-risk restriction rather than the full operating cost and strict feasibility.

candidate-2

Formulation: 2/5 — It gives explicit objectives and several inequalities, but its general net-win constraint is algebraically wrong, strict overnight compliance remains unresolved, and important firm restrictions are missing.
Mathematics: 2/5 — The assessment derivative is correct, but funded monotonicity is largely asserted, the duration formula ignores nonzero drift, and diffusion conclusions are used to restrict a discrete search without sufficient proof.
Method choice: 3/5 — The fine funded scan is reproducible and affordable, but fixing RR through an incompletely demonstrated calendar constraint and omitting numerical convergence weaken its coverage.
Inference: 1/5 — It revives between-seed errors for account-level tests despite the shared calendar dependence and substitutes deterministic sensitivity analysis for a powered empirical test of A against B.
Application: 3/5 — It quantifies the assessment change and correctly keeps the purchase gate closed at full cost, but its conditional optimum depends on permissive accounting and incorrectly labels the fee cap binding.

candidate-3

Formulation: 4/5 — It provides the most complete pathwise, categorical, wallet and execution constraints, although the current decision’s additional funded up-step restriction appears in the rationale rather than the main formulation.
Mathematics: 5/5 — It derives the assessment corner, both funded branches, stop limitation and growth first-order condition while explicitly distinguishing diffusion results from clipped, rounded and calendar-dependent execution.
Method choice: 4/5 — It combines finite enumeration, boundary refinement and lattice-convergence checks with reproducible calls, while honestly acknowledging that the executed search does not certify a continuous optimum.
Inference: 4/5 — It declares a superiority null, paired calendar-cluster estimator, rejection threshold and planning power, but practical block independence and small-sample calibration still need specification before execution.
Application: 4/5 — Its full-cost comparison reproduces, includes the split add-on and correctly concludes no purchase among evaluated designs, but the conditional winner remains incompletely searched and unvalidated after executable lot rounding.

Recommended base: candidate-3.

candidate-3 best answers the central question: calculus supplies structure, exact computation ranks specified discrete designs, and historical inference tests model adequacy and differences at a limited resolution. It also distinguishes a conditional numerical winner from an admissible purchase. Before adopting it, move the funded up-step restriction into the formulation and make the prospective block construction and test calibration explicit.

Grafts from candidate-1:
- Keep the explicit lattice-edge formula and scenario-regret presentation as search aids and sensitivity summaries.
- Keep the assessment cap’s shadow-price interpretation.
Reject the tolerated daily-rule breach, the assertion that 1.5% maximises its proposed admissible interval, and the use of model-agreement testing as evidence of superiority.

Grafts from candidate-2:
- Keep the explicit reporting of payout probability alongside waiting time and payout frequency.
- Keep the cost/input sensitivity table as conditional model analysis, clearly separated from empirical inference.
Reject the general net-win formula, account-level between-seed tests, and the claim that deterministic chain ordering removes the need to validate that ordering against execution.

Mathematical claims checked and found wrong:

1. candidate-1’s assessment cap row: using cost_share(34.8), both clips and the default eval_chain lattice, pass probabilities at u=3.15% are 45.498%, 45.575%, 45.687% and 45.825% for RR 0.75, 1, 1.5 and 3, rather than 45.68%, 45.73%, 45.78% and 45.86%; its separate 45.57% figure for RR 1 is consistent with this check.

2. candidate-1’s claim that 1.5% gives the highest funded probability within its proposed [1.456%, 1.667%] interval is false: the stated chain gives approximately 52.543% at 1.456%, versus 52.359% at 1.5%, using cost_share(34.8).

3. candidate-2’s net-win expression RR·r·(1−γ) is wrong for general RR: with cost c=γr, the net win is (RR−γ)r; the expressions coincide only at RR=1.

4. candidate-2’s equality E[N]=TD/(ur) is the zero-drift diffusion result, not the positive-cost result used in its application; for symmetric barriers the latter is D·tanh(γD/u)/(γr).

5. candidate-2’s quoted funded comparison “52.5 ± 3.3 against 52.7” does not give z=−1.0: those displayed numbers give approximately −0.061.

6. candidate-2’s statement that the 6% wallet fee cap binds at 3.8% is false: it is slack, although the next discrete tier is excluded.

I reproduced candidate-3’s three main pass/payout comparisons at its stated finer lattice and found no discrepancy in those figures. No web browsing or file writes were performed.