| Clean re-run of out/analysis.py (results.json deleted first) reproduces byte-identical results.json |
PASS (cmp identical) |
| budget_identity_residual = 0 ( |
r |
| mrs_at_optimum = price_ratio (tangency) |
PASS (0.625 = 0.625) |
| expenditure_share_good1 = alpha |
PASS (0.35) |
| indirect_utility equals α ln(αm/p1)+(1−α) ln((1−α)m/p2) |
PASS |
| Numerical max does not exceed closed-form utility (beyond 1e-12) |
PASS (gap 0.0) |
| Grid, Brent and SLSQP demands agree with closed form |
PASS (max |
| SLSQP with inequality constraint finds binding budget (monotonicity) |
PASS (slack 2.8e-14) |
| Counts: n_input_rows 4 − removed 0 = n_analysed 4 |
PASS |
| Magnitude vs baseline: closed-form v vs numerical baseline v |
PASS (identical to float precision) |