ĀRU INTELLIGENCE / INWARD MATHEMATICS™

Your data / exact continuous search

How far to flip the result?

Enter 3–21 readings and a chosen target. Odd samples use their middle reading; even samples average the central pair. Set the permitted movement range, including signed values. The lab checks every real position using exact fractions, then exports a certificate for independent verification.

01 / Model assumptions

Set the readings and bounds

The target and allowable range are stipulated by you. The result establishes a conditional mathematical statement, not which estimate should be trusted for real measurements.

The calculation runs in this browser. Values are not put into a URL or sent to an application server. The certificate contains every input; share it only if those values may be disclosed.

02 / Exact result

Every one-reading route

The starting estimate and exact routes will appear here.

Mean winsMedian winsTie

03 / Reproduce

Take the evidence with you

The partition includes every median transition and exact factor root. Each open interval has a constant winner; the printed positions of the bars are approximate, while the exported fractions are exact. A nearest threshold is a tie and is an infimum of movement, usually not an attained smallest strict reversal.

Check a downloaded certificate independently, browse your local Research Archive, or run the Python checker from the repository root:

python3 tools/verify_odd_sample_flip.py odd-sample-flip-certificate.json

Saving rechecks the certificate with a separate browser verifier and keeps it in this device's local archive. A passing checker verifies the mathematical claim under the entered inputs. The download itself does not authenticate measurements or prove an empirical theory. Explore the checked even-sample report, the signed example, or read the proof argument and limits.