# C888 — Join the NT lattice to the general Key domain theorem

## Question

Why are integer years weaker than return to an NT70-year slot?

## Inputs

```json
{
  "NT_grid_h": 70
}
```

## Sources

```json
[
  "C866–867",
  "C873–874"
]
```

## Opened utc

2026-09-28T02:50:15.593174+00:00

## Results

```json
{
  "domain_transfer": {
    "path": "model/NT_grid_domain_transfer.json",
    "sha256": "8dab8c8f0f0df5055ecf650a69e8f256eeac08bfc956fd91e82019e7da83e1f8",
    "bytes": 519
  },
  "same_slots": {
    "E": [
      0,
      23,
      46,
      69
    ],
    "P": [
      0,
      69
    ],
    "J": [
      0
    ]
  }
}
```

## Finding

The NT return rule is the h=70 instance of the general theorem. E/P returns remain0,23,46,69 and0,69; J has only the fixed hinge in this finite domain. Integer output and return to a named slot are different requirements, even when these particular finite index sets coincide.

## Reassessment

Integrate the operator results as grid and anchor registers.

## Checks

```json
{
  "E_matches": true,
  "P_matches": true,
  "J_fixed_only": true
}
```

## Closed utc

2026-09-28T02:50:15.594580+00:00

## Record provenance

Exact record hash: `63fba02f36b2aa6acd92946a06403651b8e2d867f633998bc627341448bcdacd`

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