# C901 — Unify endpoint interpolation and extrapolation

## Question

Can one span and one generated coordinate retain the entire source pair?

## Inputs

```json
{}
```

## Sources

```json
[
  "C892",
  "C831 weighted Creation bridge"
]
```

## Opened utc

2026-09-28T02:54:05.215910+00:00

## Results

```json
{
  "basis": {
    "path": "model/endpoint_coordinate_basis.json",
    "sha256": "47b0713d83431b05bb871bd6fd461cc179ef1d3d5de57403a84c8f817a06e7d7",
    "bytes": 391
  },
  "symbolic_coefficients": {
    "R_recovered": [
      0,
      1
    ],
    "C_recovered": [
      1,
      0
    ]
  }
}
```

## Finding

The pair (D,W_lambda) is an exact coordinate system for (C,R), for every fixed lambda. The old weighted bridge and new twelvefold head use the same endpoint algebra with different source-appointed coefficients and roles.

## Reassessment

Recover every macro source pair and both inherited weighted Creation pairs from this basis.

## Checks

```json
{
  "determinant": true,
  "R_coefficients": true,
  "C_coefficients": true
}
```

## Closed utc

2026-09-28T02:54:05.216450+00:00

## Record provenance

Exact record hash: `7fd7b24f3969631c5c1071c6eef86b55f1226912df43c3452060b7e55239fefc`

Source journal: `Research_Cycles/C0832_C0931/journal.json`