# C494 — The exact residual conservation law

## Question

Which declared endpoint changes preserve the weighted anchor?

## Inputs

```json
{
  "rounded": [
    14006,
    4106
  ],
  "actual_completion": [
    14004,
    4114
  ],
  "strict_comparison": [
    14006,
    4112
  ],
  "Year6_pair": [
    14006,
    4116
  ]
}
```

## Sources

```json
[
  "File51a §§3,16",
  "File22 §§5.1,7.1",
  "File52c §3.14"
]
```

## Opened utc

2026-09-27T22:42:02.281825+00:00

## Results

```json
{
  "states": {
    "rounded": {
      "weighted_point": 12026,
      "shift_from_12026": 0
    },
    "actual_completion": {
      "weighted_point": 12026,
      "shift_from_12026": 0
    },
    "strict_comparison": {
      "weighted_point": "60136/5",
      "shift_from_12026": "6/5"
    },
    "Year6_pair": {
      "weighted_point": 12028,
      "shift_from_12026": 2
    }
  },
  "kernel": "4 delta_C + delta_R = 0",
  "selected_vector": [
    -2,
    8
  ],
  "general_integer_kernel": "t*(1,-4)"
}
```

## Finding

The actual completion selection lies exactly in the kernel. Strict and Year6 alternatives give shifts6/5 and2. The conserved anchor is therefore a precise relation between selected states, not invariance under every actual/rounded convention.

## Reassessment

Formalize the rounded path evaluator so convergence and nonconvergence can be explained by one rule.

## Checks

```json
{
  "completion": true,
  "strict": true,
  "year6": true
}
```

## Closed utc

2026-09-27T22:42:02.282051+00:00

## Record provenance

Exact record hash: `6046d8b0bd0ffcab38d96bd1834e20f236c87b3bf140ab959f4be75644722ebb`

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