# C710 — Unify the conserved measurements

## Question

Which simple linear quantities explain the family-preserving changes?

## Inputs

```json
{
  "changes": {
    "biography": [
      100,
      -100
    ],
    "symmetric_opening": [
      10,
      -10
    ],
    "Actual_to_Rounded_C_R": [
      2,
      -8
    ]
  },
  "weights": {
    "biography": [
      1,
      1
    ],
    "symmetric_opening": [
      1,
      1
    ],
    "Actual_to_Rounded_C_R": [
      4,
      1
    ]
  }
}
```

## Sources

```json
[
  "C631 integrated synthesis; C681–C682; Research Strategy"
]
```

## Opened utc

2026-09-28T01:19:52.257351+00:00

## Results

```json
{
  "conservation_checks": {
    "biography": 0,
    "symmetric_opening": 0,
    "Actual_to_Rounded_C_R": 0
  },
  "functionals": [
    "b+r",
    "U+L",
    "4C+R"
  ],
  "Actual_Rounded_values": [
    12026.0,
    12026.0
  ]
}
```

## Finding

Three previously separate mechanisms share a precise explanation: their allowed change vectors preserve a specified measurement. Biography preserves total lifespan, opposed opening preserves center, and the Actual/Rounded displacement preserves4C+R. The weights differ because the measured objects differ.

## Reassessment

Consolidate the anchored and fixed-set results, then assemble the complete explanatory deliverables.

## Checks

```json
{
  "all_invariants": true,
  "weighted_anchor": true
}
```

## Closed utc

2026-09-28T01:19:52.257669+00:00

## Record provenance

Exact record hash: `462cc50e9847f409a42e3579f759a024298d72a3ab5a7bd773c94536f974b897`

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