ĀRU INTELLIGENCE / INWARD MATHEMATICS™

Exact research report / certificate v3

How close is a real reversal?

One reading moves, the others stay fixed. An exact factor-root partition covers the interval [0,100] for this even-sized sample.

01 / Model assumptions

Stipulated inputs

4 readings. Chosen target 50. Starting winner: Median. Only one reading may change at a time; the allowed domain is the continuous real interval [0,100].

r1 = 40r2 = 45r3 = 50r4 = 80

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 40

Move reading 1

5 units to tieBoundary 35 · strict opposing witness 25
0100
Inspect exact winning intervals
  1. (0, 15) — Median throughout
  2. (15, 35) — Mean throughout
  3. (35, 45) — Median throughout
  4. (45, 75) — Median throughout
  5. (75, 80) — Mean throughout
  6. (80, 85) — Mean throughout
  7. (85, 100) — Median throughout

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

Reading 02 / start 45

Move reading 2

Nearest route
5/3 units to tieBoundary 130/3 · strict opposing witness 125/3
0100
Inspect exact winning intervals
  1. (0, 10) — Median throughout
  2. (10, 40) — Mean throughout
  3. (40, 130/3) — Mean throughout
  4. (130/3, 70) — Median throughout
  5. (70, 80) — Mean throughout
  6. (80, 90) — Mean throughout
  7. (90, 100) — Median throughout

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

Reading 03 / start 50

Move reading 3

5/3 units to tieBoundary 145/3 · strict opposing witness 265/6
0100
Inspect exact winning intervals
  1. (0, 5) — Median throughout
  2. (5, 40) — Mean throughout
  3. (40, 145/3) — Mean throughout
  4. (145/3, 75) — Median throughout
  5. (75, 80) — Mean throughout
  6. (80, 85) — Mean throughout
  7. (85, 100) — Median throughout

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

Reading 04 / start 80

Move reading 4

5 units to tieBoundary 75 · strict opposing witness 65
0100
Inspect exact winning intervals
  1. (0, 35) — Median throughout
  2. (35, 40) — Mean throughout
  3. (40, 45) — Mean throughout
  4. (45, 50) — Median throughout
  5. (50, 55) — Median throughout
  6. (55, 75) — Mean throughout
  7. (75, 100) — 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: a27b09068d467a37be81c749baaaf8e689c85a67df5b7e78bfa34c478e906791Download checked JSON certificate

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