ĀRU INTELLIGENCE / INWARD MATHEMATICS™

Exact conjecture laboratory / Research instrument 05

Try to break the claim.

Search four registered statements, then build your own conditional claim about mean, median, and target. Exact counterexamples can refute it. A reviewable algebraic certificate proves only those claims that follow for every real input.

01 / Define the search

A reproducible finite domain

The engine visits every sorted five-reading multiset from your values. Each target is tested against it. The midpoint claim also checks its exact constructed midpoint, even when that point is not on the chosen target grid.

Ready for an exact finite search.

Sorted values and reduced fractions are written into the certificate. The work stays on this device. No customer data, target interval, or reading is sent to an application server.

03 / Your claim

Build a statement. Test its limits.

Use the reading and target grids above. Choose 3 through 7 readings, a precise target condition, and a predicted error ordering. The engine checks exact eligible cases on your grid, then classifies every supported claim using either a general algebraic proof or a constructed, exact endpoint counterexample.

Choose a claim to test.

For even samples, the median is the exact average of the two central sorted readings; for odd samples it is the central reading. The proof covers the two resulting real estimates and target for the selected sample size; the finite grid only supplies examples. The v6 checker independently replays the selected grid, the endpoint construction, and any algebraic argument. An older receipt may have only a finite-grid result. Inputs stay in this browser until you choose to export them.

04 / Research discipline

A mathematical claim has a status.

A displayed counterexample includes exact readings, target, mean, median, and winner. The independent replay reconstructs the enumeration and rejects altered counts or witnesses. A selected grid can remain unrefuted on that finite grid even when a separate exact witness refutes its universal claim. This experiment says nothing about which estimator is best for a real-world data set.