# Independent Wolfram validation — Misery Index v3

**Checked:** August 11, 2026  
**Purpose:** independent arithmetic reproduction outside the Python scoring implementation

The Wolfram Language evaluator was given Detroit's frozen cumulative inputs, its five season-level records, and the formulas from the precomputed-lock version of `V3_SPEC.md`. It did not read `misery_results_v3.csv` or reuse Python-generated component values.

## Detroit at the 2025 cutoff

Inputs:

- titles: 1935, 1952, 1953, 1957;
- 96 seasons, 49 losing seasons, 9 playoff wins, 19-game longest losing streak;
- one relocation and one durable nickname change;
- recent records, newest first: 2025 9–8, 2024 15–2, 2023 12–5, 2022 9–8, 2021 3–13–1;
- recent postseason: two wins in 2023, a winless berth in 2024, no berth in the other three seasons.

| Component | Wolfram | Python CSV | Difference after display precision |
|---|---:|---:|---:|
| L1 championship legacy | 25.484163857073 | 25.484164 | 0.000000 |
| L2 historical postseason scarcity | 12.187500000000 | 12.187500 | 0.000000 |
| L3 sustained futility | 6.862500000000 | 6.862500 | 0.000000 |
| L4 identity disruption | 3.000000000000 | 3.000000 | 0.000000 |
| C1 recent regular season | 7.828235274365 | 7.828235 | 0.000000 |
| C2 recent postseason non-closure | 17.245325648197 | 17.245326 | 0.000000 |
| Legacy /60 | 47.534163857073 | 47.534164 | 0.000000 |
| Current /40 | 25.073560922562 | 25.073561 | 0.000000 |
| **Total /100** | **72.607724779635** | **72.607725** | **0.000000** |

The small apparent differences before rounding are only the six-decimal CSV display precision.

## Campbell-era change

Wolfram independently computed:

| Cutoff | Total | Tier |
|---:|---:|---|
| 2020 | 79.658411764784 | Severe |
| 2021 | 81.487809074398 | Historic |
| 2022 | 80.778733739245 | Historic |
| 2023 | 74.573725406902 | Severe |
| 2025 | 72.607724779635 | Severe |

The 2020-to-2025 change is **−7.050686985149 points**. The headline crossed from Historic back to Severe at the **2023 completed-season cutoff**, when Detroit's 12–5 season and two playoff wins entered the five-season window. This agrees with `misery_history_v3.csv`.

## Exact Wolfram construction

The independent calculation used exact rational values for 0.5, 0.6, 0.4, 0.10, 0.25, and 0.85, and applied numeric approximation only to the final output. Its operations were:

1. sum the four discounted half-weight pre–Super Bowl titles;
2. calculate the cumulative playoff-win, losing-season, losing-streak, and identity fractions;
3. build the five weights `2^(-Range[0,4]/3)` from newest to oldest;
4. calculate each season's `(wins + ties/2) / games`;
5. calculate recent postseason relief from berth, win, and championship fields only;
6. sum the six published components.

No playoff-round label, near-miss count, v2 score, or current-team rank entered the evaluation.