# C741 — Recover SP local changes from its boundary profile

## Question

Which source rows and counting terms generateSP’s entire displacement staircase?

## Inputs

```json
{
  "profile": "SPminusMT",
  "Lamech_regular": "53counted versus52completed"
}
```

## Sources

```json
[
  "C739; File18 §§3.1–3.2,6C"
]
```

## Opened utc

2026-09-28T01:44:42.031795+00:00

## Results

```json
{
  "nonzero_edge_changes": {
    "R": {
      "Jared": -100,
      "Methuselah": -120,
      "Lamech": -130,
      "Arphaxad": 100,
      "Shelah": 100,
      "Eber": 100,
      "Peleg": 100,
      "Reu": 100,
      "Serug": 100,
      "Nahor": 50
    },
    "C_lower": {
      "Jared": -115,
      "Methuselah": -249,
      "Lamech": -124,
      "Eber": -60,
      "Terah": -60
    },
    "G": {
      "Jared": -15,
      "Methuselah": -129,
      "Lamech": 6,
      "Arphaxad": -100,
      "Shelah": -100,
      "Eber": -160,
      "Peleg": -100,
      "Reu": -100,
      "Serug": -100,
      "Nahor": -50,
      "Terah": -60
    }
  },
  "Lamech_regular_decomposition": [
    -129,
    -1
  ]
}
```

## Finding

TheSP profile localizes its regular130-yearLamech difference as129 from the nominal age plus one completed-year correction. Cumulative support remains the five lifespan changes. The whole staircase therefore explains both the shared plateaus and the different mode response.

## Reassessment

Test the entire post-ShelahLXX/SP family where births agree but cumulative coordinates differ.

## Checks

```json
{
  "Lamech_regular": true,
  "cumulative_support": true,
  "support_locality": true
}
```

## Closed utc

2026-09-28T01:44:42.032103+00:00

## Record provenance

Exact record hash: `11bd6ee787eb179e42d7df33609e7119948470bbaa6808679f8696da8e44c2f2`

Source journal: `Research_Cycles/C0732_C0831/journal.json`