# Large-scale fragility study: cross-paradigm report

## Claim scope (mandatory)

- Uncertainty channels: gas/electricity unit_price trajectories only.
- Response metric: fixed-first-stage expected TAC.
- Fragility construct: primary: second-order/convexity sign of multi-delta response around per-design nominal anchor; secondary: asymmetry shares and F_s.
- GSA: PAWN only (raw TAC and re-anchored F_s); Sobol exploratory/omitted.
- epsilon_exc threshold: 0.05.
- Tier: final_lite; namespaces pooled: 44.

## Completeness gate

- Claim status: **complete**.
- Active paradigms: antifragile, regret, robust, stochastic.

## Headline: multi-delta curvature (self-anchored)

| Cell | n factors | mean a | a 95% CI | fragile | robust | antifragile |
|------|----------:|-------:|:--------:|--------:|-------:|------------:|
| vone/antifragile | 144 | -0.0015 | n/a | 0.05 | 0.58 | 0.37 |
| vone/regret | 144 | -0.0004 | n/a | 0.00 | 0.81 | 0.19 |
| vtwo/regret | 144 | -0.0007 | n/a | 0.00 | 0.67 | 0.33 |
| vone/robust | 144 | -0.0004 | n/a | 0.00 | 0.59 | 0.41 |
| vtwo/robust | 144 | -0.0007 | n/a | 0.00 | 0.67 | 0.33 |
| vone/stochastic | 144 | -0.0005 | n/a | 0.00 | 0.58 | 0.42 |
| vtwo/stochastic | 144 | -0.0007 | n/a | 0.00 | 0.67 | 0.33 |

## Corroborating: fragility F_s (bootstrap 95% CI)

| Cell | F_s mean | F_s CI | F_s CVaR | CVaR CI | n scen |
|------|---------:|:------:|---------:|:-------:|-------:|
| vone/antifragile | 0.0003 | [0.0003, 0.0004] | 0.0058 | [0.0051, 0.0066] | 3888 |
| vone/regret | 0.0001 | [0.0001, 0.0001] | 0.0012 | [0.0011, 0.0014] | 1728 |
| vtwo/regret | 0.0003 | [0.0002, 0.0003] | 0.0036 | [0.0029, 0.0041] | 432 |
| vone/robust | 0.0002 | [0.0002, 0.0002] | 0.0029 | [0.0025, 0.0033] | 3456 |
| vtwo/robust | 0.0002 | [0.0002, 0.0002] | 0.0033 | [0.0029, 0.0036] | 1728 |
| vone/stochastic | 0.0002 | [0.0002, 0.0002] | 0.0035 | [0.0030, 0.0039] | 3888 |
| vtwo/stochastic | 0.0001 | [0.0001, 0.0001] | 0.0021 | [0.0018, 0.0023] | 3888 |

## Table 8.1 stress resilience metrics

| Cell | phi_ret | phi_ret CI | phi_struct | phi_struct CI | epsilon_exc | epsilon_exc CI | U_095_Z | U_095_Z CI |
|------|--------:|:----------:|-----------:|:-------------:|------------:|:--------------:|--------:|:----------:|
| vone/antifragile | 1.0000 | [1.0000, 1.0000] | 0.0000 | [0.0000, 0.0000] | 0.0000 | [0.0000, 0.0000] | 12320.0870 | [12314.9672, 12327.7674] |
| vone/regret | 1.0000 | [1.0000, 1.0000] | 0.0000 | [0.0000, 0.0000] | 0.0000 | [0.0000, 0.0000] | 13495.0905 | [13493.3732, 13496.3255] |
| vtwo/regret | 1.0000 | [1.0000, 1.0000] | 0.0000 | [0.0000, 0.0000] | 0.0000 | [0.0000, 0.0000] | 12230.4741 | [12216.0909, 12244.0998] |
| vone/robust | 1.0000 | [1.0000, 1.0000] | 0.0000 | [0.0000, 0.0000] | 0.0000 | [0.0000, 0.0000] | 12563.8593 | [12562.4097, 12565.6488] |
| vtwo/robust | 1.0000 | [1.0000, 1.0000] | 0.0000 | [0.0000, 0.0000] | 0.0000 | [0.0000, 0.0000] | 12315.2517 | [12307.7106, 12319.8037] |
| vone/stochastic | 1.0000 | [1.0000, 1.0000] | 0.0000 | [0.0000, 0.0000] | 0.0000 | [0.0000, 0.0000] | 12300.7130 | [12298.0341, 12302.7955] |
| vtwo/stochastic | 1.0000 | [1.0000, 1.0000] | 0.0000 | [0.0000, 0.0000] | 0.0000 | [0.0000, 0.0000] | 12212.0505 | [12211.3360, 12213.0321] |

| Cell | phi_s | phi_s CI | cvar_ell_095 | cvar_ell_095 CI |
|------|------:|:--------:|-------------:|:---------------:|
| vone/antifragile | 0.0001 | [0.0001, 0.0002] | 0.0058 | [0.0050, 0.0065] |
| vone/regret | -0.0000 | [-0.0000, 0.0000] | 0.0012 | [0.0011, 0.0014] |
| vtwo/regret | -0.0000 | [-0.0002, 0.0001] | 0.0036 | [0.0029, 0.0041] |
| vone/robust | -0.0000 | [-0.0000, 0.0000] | 0.0029 | [0.0025, 0.0033] |
| vtwo/robust | -0.0000 | [-0.0001, 0.0000] | 0.0033 | [0.0029, 0.0036] |
| vone/stochastic | -0.0000 | [-0.0001, 0.0000] | 0.0035 | [0.0030, 0.0039] |
| vtwo/stochastic | -0.0000 | [-0.0000, 0.0000] | 0.0021 | [0.0018, 0.0023] |

## Cross-paradigm significance

### variant one

| Pair | mean a (A,B) | curvature perm p | F_s mean (A,B) | F_s perm p |
|------|:------------:|-----------------:|:--------------:|-----------:|
| antifragile vs regret | (-0.0015, -0.0004) | 0.378 | (0.0003, 0.0001) | 0.000 |
| antifragile vs robust | (-0.0015, -0.0004) | 0.365 | (0.0003, 0.0002) | 0.000 |
| antifragile vs stochastic | (-0.0015, -0.0005) | 0.410 | (0.0003, 0.0002) | 0.000 |
| regret vs robust | (-0.0004, -0.0004) | 0.960 | (0.0001, 0.0002) | 0.000 |
| regret vs stochastic | (-0.0004, -0.0005) | 0.318 | (0.0001, 0.0002) | 0.000 |
| robust vs stochastic | (-0.0004, -0.0005) | 0.164 | (0.0002, 0.0002) | 0.284 |

### variant two

| Pair | mean a (A,B) | curvature perm p | F_s mean (A,B) | F_s perm p |
|------|:------------:|-----------------:|:--------------:|-----------:|
| regret vs robust | (-0.0007, -0.0007) | 0.981 | (0.0003, 0.0002) | 0.232 |
| regret vs stochastic | (-0.0007, -0.0007) | 0.966 | (0.0003, 0.0001) | 0.000 |
| robust vs stochastic | (-0.0007, -0.0007) | 0.986 | (0.0002, 0.0001) | 0.000 |

## GSA drivers (PAWN, grouped to trajectory factors)

Two responses: raw stressed TAC (in-run, anchor-independent) and re-anchored F_s (offline). Sobol is omitted (invalid on these non-Saltelli designs).
- vone/antifragile raw-TAC top: gas_S1=0.249, gas_S2=0.243, gas_S3=0.241
- vone/regret raw-TAC top: gas_S1=0.247, gas_S2=0.241, gas_S3=0.239
- vtwo/regret raw-TAC top: gas_S1=0.247, gas_S2=0.242, gas_S3=0.237
- vone/robust raw-TAC top: gas_S1=0.247, gas_S2=0.241, gas_S3=0.238
- vtwo/robust raw-TAC top: gas_S1=0.247, gas_S2=0.242, gas_S3=0.238
- vone/stochastic raw-TAC top: gas_S1=0.249, gas_S2=0.243, gas_S3=0.240
- vtwo/stochastic raw-TAC top: gas_S1=0.246, gas_S2=0.242, gas_S3=0.238

## Caveats (mandatory)

- Sobol indices are not reported; they are invalid on OAT/default designs (require Saltelli sampling).
- The response metric is expected TAC, not each paradigm's own objective (worst-case / max-regret).
- Degeneracy: variant_two regret~stochastic (design rel diff 3.57e-05); pairwise claims withdrawn.