# C855 — Explain every shortened-core branch

## Question

Which positional changes produce the later nonconstant paired differences?

## Inputs

```json
{}
```

## Sources

```json
[
  "C852–854"
]
```

## Opened utc

2026-09-28T02:36:48.497198+00:00

## Results

```json
{
  "branches": {
    "path": "model/inverse_short_core_branches.json",
    "sha256": "fb9e0311663e549bcb790b83c963c12b4f8c56b5a4c775d265f84df52f81b8c0",
    "bytes": 2122
  },
  "formulas": {
    "three_to_two": "1260+90a−90b−900c",
    "three_to_one": "990−990c"
  }
}
```

## Finding

The later variations follow core-length changes, which move the same digits into different place values. The nonlinear field therefore needs its digit register, not extra chronological corrections.

## Reassessment

Resolve the two retained-zero source cases and complete the partition.

## Checks

```json
{
  "all_shortened": true,
  "both_changes": true
}
```

## Closed utc

2026-09-28T02:36:48.497789+00:00

## Record provenance

Exact record hash: `37ae274c72ed24200684fac0361a99f3156380afff072c9abb13fc917abf0de2`

Source journal: `Research_Cycles/C0832_C0931/journal.json`