# C813 — Integrate the primary File52c component paths

## Question

How do the primary regular and cumulative inverse paths meet in the shared path model?

## Inputs

```json
{
  "regular": [
    1650,
    1050
  ],
  "cumulative": [
    9170,
    3430
  ],
  "anchor": 1406
}
```

## Sources

```json
[
  "latest File52c §§3.3–3.4; inherited C731"
]
```

## Opened utc

2026-09-28T02:10:44.686801+00:00

## Results

```json
{
  "paths": {
    "regular": {
      "source_components": [
        1650,
        1050
      ],
      "single_pass_components": [
        5610,
        5010
      ],
      "endpoint": 12026,
      "unsplit_single_pass_endpoint": 8606
    },
    "cumulative": {
      "source_components": [
        9170,
        3430
      ],
      "single_pass_components": [
        7190,
        3430
      ],
      "endpoint": 12026,
      "unsplit_single_pass_endpoint": 63506
    }
  },
  "status": "integration check of established File52c constructions; no second inversion"
}
```

## Finding

Both admitted subdivided paths evaluate to12026. Their unsplit totals yield different endpoints, confirming why the component list belongs to the source object. This integrates an established result rather than adding another independent hit.

## Reassessment

Compare the retained-component and whole-span Key paths at their shared completion.

## Checks

```json
{
  "primary_endpoint": true,
  "subdivision_required": true
}
```

## Closed utc

2026-09-28T02:10:44.687068+00:00

## Record provenance

Exact record hash: `6030f78645e32795e8736429f2c55facd2d5ca73af2e288dfebc663e3032a34c`

Source journal: `Research_Cycles/C0732_C0831/journal.json`