# C958 — Greatest feasible lifespan field

## Question

Why does the minimum represent shortening only as required?

## Inputs

```json
{
  "constraints": [
    "x_i≤baseline_i",
    "x_i≤capacity_i"
  ],
  "objective": "maximize sum(x_i)"
}
```

## Sources

```json
[
  "C956",
  "C957"
]
```

## Opened utc

2026-09-28T03:46:48.269850+00:00

## Results

```json
{
  "coordinate_bound": "Every feasible x_i is at most min(L_i,C_i).",
  "feasibility": "The coordinatewise minimum satisfies both upper bounds.",
  "uniqueness": "If any coordinate is smaller, the sum is smaller because no other coordinate can exceed its bound.",
  "qualification": "Conditional on the two upper bounds and fixed row meanings."
}
```

## Finding

The cap is the unique coordinatewise greatest feasible vector and uniquely minimizes total reduction. This states the model’s mechanism without inventing an optimization history.

## Reassessment

Recover death labels with each branch’s own counting convention.

## Checks

```json
{
  "upper_bound_logic": true,
  "no_increase": true
}
```

## Closed utc

2026-09-28T03:46:48.270093+00:00

## Record provenance

Exact record hash: `8d9ff13e69ac57e12fe216c71f7c1cdb31fab566310d7957925835a63d4d7329`

Source journal: `Research_Cycles/C0932_C1131/journal.json`