# C1143 — Express the SP changes as capacity reductions against baseline slack

## Question

Does one positive-part formula explain all three clipped rows and the six unchanged lives?

## Inputs

```json
{}
```

## Sources

```json
[
  "File18 §§2.1.3,3.1.3",
  "C1142",
  "C953–C970"
]
```

## Opened utc

2026-09-28T05:01:17.628424+00:00

## Results

```json
{
  "slack_transfer": {
    "path": "model/SP_capacity_slack_transfer.json",
    "sha256": "7f737584f8e0dd53f2a57af2a4fa39e337666e91bbc66594a19bc6f82f4d2e25",
    "bytes": 696
  },
  "capacity_reductions": [
    350,
    350,
    350,
    350,
    350,
    350,
    250,
    250,
    130
  ],
  "slack": [
    727,
    615,
    517,
    422,
    367,
    235,
    670,
    1,
    6
  ],
  "life_reductions": [
    0,
    0,
    0,
    0,
    0,
    115,
    0,
    249,
    124
  ]
}
```

## Finding

A single threshold law generates the whole SP reduction field: only capacity loss exceeding pre-existing baseline slack reduces a life. Jared crosses by115, Methuselah by249, Lamech by124; the other six retain slack.

## Reassessment

Separate the role of age-change location from its total350 capacity reduction.

## Checks

```json
{
  "three_reductions": true,
  "sum488": true,
  "identity_all_rows": true
}
```

## Closed utc

2026-09-28T05:01:17.628747+00:00

## Record provenance

Exact record hash: `1c1f33cefd0a72109baa242258edbdd5270e953b81cf795d342e13f5ff66af3c`

Source journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`