# C1065 — Symbolic branch support conditions

## Question

How do the source branch formulas constrain a common integer pivot?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1064",
  "C850–C858"
]
```

## Opened utc

2026-09-28T04:10:50.964993+00:00

## Results

```json
{
  "branch_conditions": [
    {
      "branch": "three-to-two core",
      "gap": "90(14+a−b−10c)",
      "remaining_divisors": [
        23,
        23,
        299
      ]
    },
    {
      "branch": "three-to-one core",
      "gap": "990(1−c)",
      "remaining_divisors": [
        23,
        23,
        299
      ]
    },
    {
      "branch": "retained-zero Jacob",
      "gap": 0,
      "difference_obstruction": false
    },
    {
      "branch": "retained-zero Adam",
      "gap": 7200,
      "difference_obstruction": true
    }
  ],
  "qualification": "difference compatibility never supplies the missing pivot residue or source authorization"
}
```

## Finding

The paired-branch law gives divisibility conditions before any pivot placement is considered. A zero gap removes only the difference obstruction; it does not appoint a pivot.

## Reassessment

Represent the complete paired field and inherited nine-member field by their difference meshes.

## Checks

```json
{
  "reduced_divisors": true,
  "Adam_obstructed": true
}
```

## Closed utc

2026-09-28T04:10:50.965550+00:00

## Record provenance

Exact record hash: `309e21350a593f4dddd6f9a5bb209e9cabc5f795296d812a3fed0bf52aba35ca`

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