# C854 — Explain the990 and1980 branches by decimal borrowing

## Question

Does subtraction of the1400 anchor gap force the repeated paired differences?

## Inputs

```json
{}
```

## Sources

```json
[
  "C852–853 digit registers"
]
```

## Opened utc

2026-09-28T02:36:34.403212+00:00

## Results

```json
{
  "branches": {
    "path": "model/inverse_long_core_branches.json",
    "sha256": "418a6416c1a58fb34c0422d9915ccb2ad6bd1b44ed9bcc43ccf96f0c7c7c02dd",
    "bytes": 2979
  },
  "branch_values": [
    990,
    1980
  ],
  "derivation": "the shared terminal core digit cancels after positional reversal; leading/tens changes force the remaining gap"
}
```

## Finding

No borrow yields990; a tens borrow yields1980. These are forced branch values for every applicable source row, rather than separately chosen gaps.

## Reassessment

Explain every shortened-core source row by the same positional rule.

## Checks

```json
{
  "all_applicable": true,
  "only_two": true
}
```

## Closed utc

2026-09-28T02:36:34.403693+00:00

## Record provenance

Exact record hash: `49be08c21aca634f0a12e999b990c4e1b32f4d8f7efdd80960d801c223bc0008`

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