# C525 — Freeze a compact construction grammar

## Question

Which operation types are actually needed for the completed family reconstructions?

## Inputs

```json
{
  "evidence_range": "C482–C524",
  "source_objects": "ordered biographies plus tradition, frame, phase, node role and coordinate chart"
}
```

## Sources

```json
[
  "Strategy §§1,5B–5G",
  "completed sequential ledger"
]
```

## Opened utc

2026-09-27T22:53:15.913084+00:00

## Results

```json
{
  "operations": [
    {
      "operation": "row change",
      "domain": "compatible biography or admitted insertion",
      "example": "(b,r)->(b+d,r−d); Cainan130/330"
    },
    {
      "operation": "chronological projection",
      "domain": "ordered source rows and supplied terminal anchor",
      "example": "regular sums begetting intervals; cumulative sums lifespans"
    },
    {
      "operation": "round with residual",
      "domain": "declared begetting or lifespan list",
      "example": "nearest5 with retained exact residual"
    },
    {
      "operation": "evaluate reversed path",
      "domain": "source-admitted integer spans with retained segmentation",
      "example": "a+sum I(s_i)"
    },
    {
      "operation": "anchored dilation",
      "domain": "declared linear coordinate chart, source nodes and held anchor",
      "example": "a+k(x−a), with supplied E/P/J"
    },
    {
      "operation": "scoped translation/state switch",
      "domain": "source-authorized affected nodes or finite switch field",
      "example": "native/equalized frame or OFF->ON once"
    },
    {
      "operation": "reflection",
      "domain": "declared comparison chart and source roles",
      "example": "q->−q for Rounded Mirror away from origin"
    }
  ],
  "relations": [
    "L=b+r and cumulative repartition conservation",
    "weighted residual4deltaC+deltaR=0 in its selected state",
    "calendar d*K_d=8400/23",
    "affine composition/conjugacy and pivot congruences",
    "path concatenation retains segments; general additivity after forgetting them is rejected"
  ]
}
```

## Finding

Seven operation types suffice to express the reconstructed examples. Inputs still include source rows, admitted partitions, anchors and state selections. This is a useful candidate grammar; neither an unrestricted transformation group nor a proven globally smallest presentation is claimed.

## Reassessment

Map these operations onto the three family axes and their Mirrors as an explanatory topology.

## Checks

```json
{
  "no_free_anchor_operation": true,
  "finite_insertions_preserved": true,
  "count": true
}
```

## Closed utc

2026-09-27T22:53:15.913368+00:00

## Record provenance

Exact record hash: `8bf0380daa7ca26a08526ac3eaa31f15e87e78f3ff7c5393636001e8027a6f0d`

Source journal: `Research_Cycles/C0482_C0531/journal.json`