# C499 — Where path evaluation is compatible with affine geometry

## Question

Which operations commute with the path evaluator without losing segmentation?

## Inputs

```json
{
  "parts": [
    1650,
    1050
  ],
  "anchor": 1406,
  "test_translation": 215,
  "decimal_scale": 10
}
```

## Sources

```json
[
  "File52c §1.2",
  "Strategy §§5C–5F",
  "C495"
]
```

## Opened utc

2026-09-27T22:43:19.757713+00:00

## Results

```json
{
  "translated_endpoint": 12241,
  "scaled_endpoint": 120260,
  "original_endpoint": 12026,
  "whole_span_inverse": 7200,
  "segmented_inverse_sum": 10620,
  "general_rules": [
    "all dates and anchor translated together: V shifts by same t",
    "all durations and anchor scaled by10^k: V scales by10^k",
    "I(s+t) need not equal I(s)+I(t)"
  ]
}
```

## Finding

The module respects a change of origin and decimal rescaling when the entire declared object moves. It does not respect erasing segmentation. These are mathematical compatibility rules, not permission to translate source chronologies outside their admitted domains.

## Reassessment

Connect the actual field to the three calendar Keys through their common measure.

## Checks

```json
{
  "translation": true,
  "scale": true,
  "nonadditive": true
}
```

## Closed utc

2026-09-27T22:43:19.757928+00:00

## Record provenance

Exact record hash: `ce6d76fb4adda85cc41fc08521f6dbacb1b1aeffd236bf259317221b9aae69fa`

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