ĀRU INTELLIGENCE / INWARD MATHEMATICS™

Exact research report / certificate v2

How close is a real reversal?

One reading moves, the others stay fixed. An exact factor-root partition covers the interval [-10,40] for this odd-sized sample.

01 / Model assumptions

Stipulated inputs

5 readings. Chosen target 0. Starting winner: Median. Only one reading may change at a time; the allowed domain is the continuous real interval [-10,40].

r1 = -2r2 = -1r3 = 0r4 = 1r5 = 35

A threshold is a tie, not a strict winning move. The exact infimum can be approached from the opposing interval; the recorded witness is an explicit strict reversal.

02 / Exhaustive routes

Every movable reading

Colors summarize open intervals. Markers show the original reading (white line) and any nearest tie boundary (gold circle). Position is approximate; exact fractions below and in the certificate carry the result.

Mean winsMedian winsTie interval or boundary
Reading 01 / start -2

Move reading 1

No reversal in -10–40This reading alone cannot reverse the strict winner.
-1040
Inspect exact winning intervals
  1. (-10, 0) — Median throughout
  2. (0, 1) — Median throughout
  3. (1, 40) — Median throughout

Intervals are open. Winner at each boundary is recorded in the downloadable certificate.

Reading 02 / start -1

Move reading 2

No reversal in -10–40This reading alone cannot reverse the strict winner.
-1040
Inspect exact winning intervals
  1. (-10, 0) — Median throughout
  2. (0, 1) — Median throughout
  3. (1, 40) — Median throughout

Intervals are open. Winner at each boundary is recorded in the downloadable certificate.

Reading 03 / start 0

Move reading 3

No reversal in -10–40This reading alone cannot reverse the strict winner.
-1040
Inspect exact winning intervals
  1. (-10, -1) — Median throughout
  2. (-1, 1) — Median throughout
  3. (1, 40) — Median throughout

Intervals are open. Winner at each boundary is recorded in the downloadable certificate.

Reading 04 / start 1

Move reading 4

No reversal in -10–40This reading alone cannot reverse the strict winner.
-1040
Inspect exact winning intervals
  1. (-10, -1) — Median throughout
  2. (-1, 0) — Median throughout
  3. (0, 40) — Median throughout

Intervals are open. Winner at each boundary is recorded in the downloadable certificate.

Reading 05 / start 35

Move reading 5

Nearest route
71/2 units to tieBoundary -1/2 · strict opposing witness -3/4
-1040
Inspect exact winning intervals
  1. (-10, -3) — Median throughout
  2. (-3, -1) — Mean throughout
  3. (-1, -1/2) — Mean throughout
  4. (-1/2, 0) — Median throughout
  5. (0, 2) — Median throughout
  6. (2, 40) — Median throughout

Intervals are open. Winner at each boundary is recorded in the downloadable certificate.

03 / Reproduce

Take the evidence with you

The embedded download contains the exact bytes checked by the independent Python verifier. Its fingerprint identifies matching bytes; it does not authenticate their source or establish that the inputs reflect real measurements.

Certificate SHA-256: 3e172aee036f2c0eb08e82bbe8b13cbf1842ad870c14353e724737203b327607Download checked JSON certificate

Run python3 tools/verify_odd_sample_flip.py odd-sample-flip-certificate.json using the repository checker. Verified status: strict-baseline.