# C1202 — Derive the composite cap-plus-round inverse set

## Question

What original lifespans can produce a fixed rounded capped value when capacity is known?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1201",
  "C1143",
  "C1131 cap analysis"
]
```

## Opened utc

2026-09-28T05:26:09.238998+00:00

## Results

```json
{
  "fibre_law": {
    "path": "model/cap_round_fibre_law.json",
    "sha256": "4ff7af76d04d05a1559f9918457b5a1ea19a6369cf01f0740073105104291fbf",
    "bytes": 2166
  }
}
```

## Finding

At the rounded capacity, a finite rounding cell joins an unbounded cap tail. The rounded capped output can therefore forget even whether clipping occurred.

## Reassessment

Apply the threshold formula to the three SP clipped capacities.

## Checks

```json
{
  "thresholds": true,
  "tails": true
}
```

## Closed utc

2026-09-28T05:26:09.239508+00:00

## Record provenance

Exact record hash: `df5e09d75d05022c7bc20ea540505645c79ac555ed0492221773a5d49d1198f6`

Source journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`