# C495 — Rounded chronology as path evaluation

## Question

Can one rule explain both convergence and the LXX miss?

## Inputs

```json
{
  "anchor": 1406,
  "paths": {
    "MT_regular": [
      1650,
      1050
    ],
    "MT_cumulative": [
      9170,
      3430
    ],
    "LXX_regular": [
      2250,
      1830
    ]
  }
}
```

## Sources

```json
[
  "File52c §3.3",
  "C489"
]
```

## Opened utc

2026-09-27T22:42:21.243193+00:00

## Results

```json
{
  "rule": "V_a(path)=a+sum I(segment); chi(path)=sum(I(segment)-segment)",
  "paths": {
    "MT_regular": {
      "raw_total": 2700,
      "reversal_gain": 7920,
      "evaluated_endpoint": 12026
    },
    "MT_cumulative": {
      "raw_total": 12600,
      "reversal_gain": -1980,
      "evaluated_endpoint": 12026
    },
    "LXX_regular": {
      "raw_total": 4080,
      "reversal_gain": 4950,
      "evaluated_endpoint": 10436
    }
  },
  "composition": "chi(P followed by Q)=chi(P)+chi(Q), for an admitted concatenation"
}
```

## Finding

Path gains are additive over retained segment lists. The MT regular gain7920 and cumulative gain−1980 offset their original9900 difference; LXX has different gains. Forgetting the partition discards necessary input.

## Reassessment

Measure the exact effect of only the source-admitted Noah and Shem refinements.

## Checks

```json
{
  "MT_convergence": true,
  "LXX_miss": true
}
```

## Closed utc

2026-09-27T22:42:21.243412+00:00

## Record provenance

Exact record hash: `8a4cd775dc33fc52edf7cde89eb38e1dff9f3e623e580d94d57784d9a342abdf`

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