# C674 — Unify the micro Key outputs

## Question

How do35,37.5 and40 relate to the source’s34.5 input?

## Inputs

```json
{
  "source_scalar": "69/2",
  "normalization_residual": "5/2"
}
```

## Sources

```json
[
  "Supplement A §§4.1,4.3"
]
```

## Opened utc

2026-09-28T01:10:47.985243+00:00

## Results

```json
{
  "P_output": 35,
  "E_output": "75/2",
  "output_gap": "5/2",
  "normalized": 40,
  "affine_continuation": 40
}
```

## Finding

The normalization residual2.5 equals the gap between E and P outputs. The source-defined40 therefore equals2E(34.5)−P(34.5). This compresses the two-stage calculation without promoting it to a new universal Key.

## Reassessment

Relate the scalar completion to the whole before/after phase envelopes.

## Checks

```json
{
  "keys": true,
  "residual": true,
  "completion": true
}
```

## Closed utc

2026-09-28T01:10:47.985485+00:00

## Record provenance

Exact record hash: `2441183bdc17f95c6de29513d0ee9f899375f5fc6731f27a16d936adc0c4e126`

Source journal: `Research_Cycles/C0632_C0731/journal.json`