# C974 — Local regular-to-cumulative response

## Question

What map transmits a begetting change through fixed active caps?

## Inputs

```json
{
  "active_indices": [
    5,
    7,
    8
  ],
  "condition": "fixed Noah/Flood relation, baseline lives and active support"
}
```

## Sources

```json
[
  "C954",
  "C956",
  "C972"
]
```

## Opened utc

2026-09-28T03:50:09.862441+00:00

## Results

```json
{
  "matrices": {
    "path": "model/sp_cap_response_matrices.json",
    "sha256": "46a93aa1039bf6f918fa8511df197bc50256963e14539212d68c1522c2d3f709",
    "bytes": 2641
  },
  "last_begetting_response_regular": [
    1,
    1,
    1,
    1,
    1,
    1,
    1,
    1,
    1
  ],
  "last_begetting_response_cumulative": [
    3,
    3,
    3,
    3,
    3,
    3,
    2,
    2,
    1
  ]
}
```

## Finding

Within one active region, the maps are U, A·U, and U·A·U. A regular-row change can alter three capped lives and hence several cumulative coordinates; this is a sensitivity model, not an admitted variant.

## Reassessment

Test the local formula against a controlled one-unit perturbation.

## Checks

```json
{
  "upper_rows_accumulate_three": true,
  "last_row_one": true,
  "masked_unchanged_rows": true
}
```

## Closed utc

2026-09-28T03:50:09.863113+00:00

## Record provenance

Exact record hash: `75189292abe14af86c0d373f69e84299bf326a8bf60139818d74e809a03d0482`

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