# C968 — The inverse image of a capped life

## Question

What does a capped output reveal about its input lifespan?

## Inputs

```json
{}
```

## Sources

```json
[
  "C955",
  "C956"
]
```

## Opened utc

2026-09-28T03:49:07.314488+00:00

## Results

```json
{
  "inverse_conditions": [
    {
      "row": 0,
      "output": 930,
      "input_condition": "equals 930"
    },
    {
      "row": 1,
      "output": 912,
      "input_condition": "equals 912"
    },
    {
      "row": 2,
      "output": 905,
      "input_condition": "equals 905"
    },
    {
      "row": 3,
      "output": 910,
      "input_condition": "equals 910"
    },
    {
      "row": 4,
      "output": 895,
      "input_condition": "equals 895"
    },
    {
      "row": 5,
      "output": 847,
      "input_condition": "at least 847"
    },
    {
      "row": 6,
      "output": 365,
      "input_condition": "equals 365"
    },
    {
      "row": 7,
      "output": 720,
      "input_condition": "at least 720"
    },
    {
      "row": 8,
      "output": 653,
      "input_condition": "at least 653"
    }
  ],
  "exactly_recovered_rows": [
    0,
    1,
    2,
    3,
    4,
    6
  ]
}
```

## Finding

Six uncapped inputs are recoverable exactly; each clipped input is only bounded below. Clipping loses the original excess.

## Reassessment

Test whether even a supplied ancestral multiset restores the three lost row placements.

## Checks

```json
{
  "six_exact": true,
  "three_bounds": true
}
```

## Closed utc

2026-09-28T03:49:07.314754+00:00

## Record provenance

Exact record hash: `bdd39456ef8857a2fc4fdb24e478bf4bbfa088762bcd8e93f8346ae41d785ca6`

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