# C1466 — Measure stage–Key interaction

## Question

Does translating a spine by2700 commute with the existing anchored Key relations?

## Sources

```json
[
  "Universal stage law",
  "C1432 Covenant map",
  "LXX paired join"
]
```

## Opened utc

2026-09-29T01:19:39.213431+00:00

## Results

```json
{
  "Covenant_two_stage_image": "257168/23",
  "SP_two_stage_target": 11416,
  "Covenant_two_stage_residual": "-5400/23",
  "LXX_two_stage_regular_join": "14278/23",
  "LXX_two_stage_cumulative_join": "14278/23",
  "positive_stage_commutator": "5400/23",
  "correction": "The first expectation used the positive-stage sign. Reducing both heads by2700 gives residual−5400/23, not+5400/23; no input changed."
}
```

## Finding

Keeping Covenant1866 fixed sends the two-stage LXX head5400/23 later than the SP target (signed residual−5400/23). The LXX paired join remains equal between modes at14278/23.

## Reassessment

Group successful equalities and exact misses into a compact explanatory dependency structure.

## Checks

```json
{
  "negative_residual_exact": true,
  "LXX_pair_still_equal": true
}
```

## Closed utc

2026-09-29T01:20:19.733340+00:00

## Record provenance

Exact record hash: `df68b26433259fb63de992932047d66f9d1f759ea57a6f5802937d7aa7162783`

Source journal: `Research_Cycles/C1433_C1482/journal.json`