Explore
Research A · B · C · X · Y · ZForm hypotheses, construct representations and develop arguments.
HORIZON organizes several artificial intelligence roles around the same research.
Propose, challenge, connect and integrate: the method begins with this separation.
The roles below illustrate the organization described in the HORIZON presentation. The sequence animates automatically.
Form hypotheses, construct representations and develop arguments.
Seek counterexamples and reconstruct the steps that must hold.
Condense knowledge, connect research and guide the next questions.
Incorporate admissible results with their checks and provenance.
“This formula always produces a prime number.”
What about n = 40?
1,681 = 41 × 41.
The universal claim falls.
The first forty cases remain true.
This discussion is a teaching scenario based on a classical example, not a history of agent messages.
Keeping the discovered limitation makes it possible to ask a better question: identify a missing hypothesis, define a method’s scope or change direction.
The idea. In a Research Z case with n = 160,229, the expected period was 18 steps.
The challenge. Referee finds a return after 9 steps.
The crucial detail. The ratio between coordinates evolves with −n: modulo 19, that sign halves the period.
The correction. The assumptions are strengthened and the period recalculated using the correct transformation.
HORIZON is an independent program led by Geoffrey Muller in France. The showcase presents its organization and dated overviews; it does not display the roles’ current operational activity.