C1063 — Allocation identity versus available source cuts

Question

Can the1/6 or1/26 allocation be made from whole components of the completed paths?

Inputs

{
  "duration": 14720,
  "fractions": [
    "1/6",
    "1/26"
  ]
}

Sources

[
  "C991",
  "C1058–C1062"
]

Opened utc

2026-09-28T04:10:00.880635+00:00

Results

{
  "required_selected_amounts": [
    "7360/3",
    "7360/13"
  ],
  "whole_component_realization": false,
  "proof": "All original components and their one-pass values are integers; any sum of whole components is integral, while both required amounts are nonintegral.",
  "scope": "does not refute source allocations on other paths; a new fractional cut would need source support"
}

Finding

The factor identities transfer algebraically, but neither allocation can select whole components of these four paths. A named subdivision is additional source information.

Reassessment

Use paired endpoint gaps to test common-pivot integrality without searching pivots.

Checks

{
  "noninteger_amounts": true,
  "values": true,
  "integer_source_components": true
}

Closed utc

2026-09-28T04:10:00.881122+00:00

Record provenance

Exact record hash: 33639af14c299054b0ed518aa9468c255e77b29e480910f4478353b18ef28553

Source journal: Research_Cycles/C0932_C1131/journal.json