Findings

Outcomes, with their limits attached

A finding is a checked outcome. A claim is the exact sentence that outcome supports. “Discovery” is only a badge after a fresh novelty review—not a separate pile of content.

Supported findingNOVEL VERIFIEDChecked 2026-07-27

K7 rainbow stacking conditional machine proof

The result: All nine frozen machine cases for the seven-vertex rainbow-stacking problem are closed as unsatisfiable. Six have direct checked certificates. Three have checked symmetry-reduced certificates plus a reviewed transfer argument. This is a conditional resolution pending human review of the encoding and mathematical reductions.

What it means: A seven-vertex math problem was closed by machine: all nine required cases are proven impossible, six directly and three through a checked symmetry argument. Pending one human review of the setup, the question is resolved.

What it is NOT: Not yet a finished theorem, because a human mathematician must still validate the encoding and the reduction steps. Not a general method claim, because the certificates cover exactly these nine formulas.

Next test that could settle it: Human mathematician review of the full reduction from Question 3.3 to the nine formulas.

Open question: Does human mathematical review confirm that the nine checked formulas exactly resolve Question 3.3 for n=7?

Receipts (exact limits and evidence records)

Claim ceiling (the strongest sentence this evidence supports): The nine machine cases are closed; resolution of Question 3.3 at n=7 remains conditional on human validation of the encoding, split, R3 semantics, small-weight closures, and symmetry transfer.

Novelty: Aletheia closes the nine-case machine search for n=7 with checked certificates; the theorem-level translation remains under human review.

Question: Q-K7-N7-RAINBOW

Evidence grade: G3_MACHINE_CERTIFIED_CONDITIONAL

Evidence records: ART-030, ART-031