# C1012 — Alternative complete walk basis

## Question

Do the clean and unclean ordered walks together recover the same list?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1008",
  "File58 §§13.3–13.4"
]
```

## Opened utc

2026-09-28T03:57:57.876332+00:00

## Results

```json
{
  "measurements": [
    20,
    40,
    50,
    250,
    450,
    490,
    20,
    50,
    60
  ],
  "determinant": -1,
  "recovered": [
    200,
    20,
    200,
    20,
    40,
    10,
    30,
    20,
    10
  ]
}
```

## Finding

The two complete walks form another integer basis. The same accumulation-and-difference operation used for genealogical paths reconstructs this counted list.

## Reassessment

Separate universal register dependencies from source-specific equalities.

## Checks

```json
{
  "unimodular": true,
  "prefixes": true
}
```

## Closed utc

2026-09-28T03:57:57.881574+00:00

## Record provenance

Exact record hash: `7465c438c9beef8f72a018ea0ef5741b7ea5d31d8053999b2787768448e96202`

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