C1028 — General reflection descent criterion

Question

When does a source grouping carry an existing involution?

Inputs

{}

Sources

[
  "C1025",
  "C1027"
]

Opened utc

2026-09-28T04:00:42.389009+00:00

Results

{
  "point_quotient": "q(x)=q(y) implies q(Rx)=q(Ry).",
  "boundary_subset": "Selected boundaries must be invariant under R.",
  "interval_coarsening": "R must permute complete coarse blocks.",
  "proof": "The proposed map q(x)↦q(Rx) is well-defined exactly when representatives of one class have a common image class."
}

Finding

Reflection can pass to a grouped object only when the grouping respects its action. Point identification, interval coarsening and boundary selection require their own checks.

Reassessment

Test the source NT490 coarsening as a contrasting complete field.

Checks

{
  "Toledot_counterexample": true,
  "representative_condition_explicit": true
}

Closed utc

2026-09-28T04:00:42.389353+00:00

Record provenance

Exact record hash: 5653889cd9b0ba5b0bdabd7dffa729ca3c51cbf82040188864e6115170a16e11

Source journal: Research_Cycles/C0932_C1131/journal.json