C994 — An equal total can hide internal change

Question

What is the vector defect when partial and uniform transformations share one total?

Inputs

{
  "S": 483,
  "selected_fraction": "1/6",
  "selected_factor": "25/23"
}

Sources

[
  "C993",
  "File63 §1.3",
  "C609 inherited example"
]

Opened utc

2026-09-28T03:54:03.786038+00:00

Results

{
  "source_parts": [
    "805/2",
    "161/2"
  ],
  "partial": [
    "805/2",
    "175/2"
  ],
  "uniform": [
    "1225/3",
    "245/3"
  ],
  "defect": [
    "-35/6",
    "35/6"
  ],
  "general_selected_first_defect": "(k−1)f(1−f)S·(1,−1)"
}

Finding

The inherited490 equality loses an internal displacement of35/6 in opposite directions. The general zero-sum defect explains why equal totals do not identify the same path.

Reassessment

Find a complete nonredundant measurement basis for retained-part families.

Checks

{
  "same_total": true,
  "nonzero_shape": true,
  "criterion_fails": true
}

Closed utc

2026-09-28T03:54:03.786371+00:00

Record provenance

Exact record hash: 15cc695fa2dd8c10163b7a33c74a3ac607d7e682b0642e224d4d4e586b7d65d0

Source journal: Research_Cycles/C0932_C1131/journal.json