# C510 — Mirror requires a declared coordinate chart

## Question

How can Mirror join the affine grammar without confusing civil and rounded crossings?

## Inputs

```json
{
  "civil": "q(BC B)=1−B; q(AD Y)=Y",
  "rounded": "q(BC B)=1−B; q(AD Y)=Y−1",
  "sample_pair": [
    601,
    1351
  ]
}
```

## Sources

```json
[
  "File51a coordinate clarification",
  "File52c §§1,3.12,6"
]
```

## Opened utc

2026-09-27T22:46:59.304698+00:00

## Results

```json
{
  "civil_crossing": 1951,
  "rounded_crossing": 1950,
  "rounded_reflection": "q -> −q carries BC B to AD B in this display",
  "affine_compatibility": "M D_k,a = D_k,M(a) M for M(q)=−q",
  "source_roles": "ordinary same-side reflection, cross-polarity Mirror, and decimal reversal remain distinct operators"
}
```

## Finding

Reflection is affine once its coordinate chart is declared. Civil and rounded opposite-side spans differ by one; they cannot be pooled as one metric. The rounded origin is a comparison convention, not a historical year zero.

## Reassessment

Reconstruct the rounded macro529 endpoint ladder in that declared chart.

## Checks

```json
{
  "civil": true,
  "rounded": true,
  "difference": true
}
```

## Closed utc

2026-09-27T22:46:59.305012+00:00

## Record provenance

Exact record hash: `16f8158e97927dc5e61fb5fbb7c7421013a0a36a07eee44dee6714b0280ceec0`

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