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C1306 — Register coherent translation through Rounded residuals

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Study sequence: Four-part grammar and complete-family registers (C1282–C1331) · Family grammar & reading guides

C1306 — Register coherent translation through Rounded residuals

Question

How does exactsourcechange remaincompatiblewiththeRoundedrepresentation?

Inputs

{}

Sources

[
  "C1305",
  "C1218–C1221",
  "C1278"
]

Opened utc

2026-09-28T06:10:25.090906+00:00

Results

{
  "residual_relation": {
    "path": "model/relation_rounded_residuals.json",
    "sha256": "1c0b4aa4f98bb9e353a968eb99533277ba860ce60b040fe488a24060ad35574e",
    "bytes": 839
  }
}

Finding

TheRoundedplusresidual representation carries exactsourcechanges coherently, anditsaccumulatedresiduals recovercompletepaths. Itworks byretaininginformation, notby makingroundingadditive.

Reassessment

Register uniformKeycompatibility withsums andthelimitforcomponent-specificKeys.

Checks

{
  "two_applications": true,
  "proof_bound": true
}

Closed utc

2026-09-28T06:10:25.091366+00:00

Record provenance

Exact record hash: cd8423799fd21e6fc407edabdcdb75d6a5b7bbb127020996a63de30f268b80c9

Source journal: Research_Cycles/C1132_C1431_Recovered/journal.json

Linked sources and evidence

Edition and provenance

C1306.md

SHA-256 cde9b5d9f39b370cb31b866cf8c0190da888a11bfeb7ab1e657a16c9b312a9df

C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1306