# C509 — Anchor-change and composition laws

## Question

Which affine relations explain a change of anchor without choosing a new ratio?

## Inputs

```json
{
  "E": "25/23",
  "anchors": [
    14726,
    6
  ],
  "sample_inverse_Shem": 5526
}
```

## Sources

```json
[
  "Strategy §5C",
  "File52c §3.11"
]
```

## Opened utc

2026-09-27T22:46:36.619470+00:00

## Results

```json
{
  "difference_law": "D_k,a(x)-D_k,b(x)=(1-k)(a-b)",
  "conjugacy": "T_t D_k,a = D_k,a+t T_t",
  "same_anchor_composition": "D_l,a D_k,a = D_lk,a",
  "different_anchor_order": "D_l,b D_k,a − D_k,a D_l,b = (1-l)(1-k)(b-a)",
  "Shem_Creation_held": 4726,
  "Shem_Nativity_held": 6006,
  "Nativity_minus_Creation": 1280
}
```

## Finding

Changing only the anchor shifts every output by the same amount. The14726 versus6 E-presentations differ1280 throughout. Same-anchor ratios compose multiplicatively; different anchors generally make order matter.

## Reassessment

Keep this affine geometry distinct from the two coordinate conventions used by Mirror comparisons.

## Checks

```json
{
  "shift": true,
  "Shem": true
}
```

## Closed utc

2026-09-27T22:46:36.619814+00:00

## Record provenance

Exact record hash: `7588ac0d117879aed2046e99847bf7c45d917fc46c72a3e7d32280f3b8182f93`

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