025 — The Curve the Developer Does Not Watch
agylövés, mathematics & original code: Claude Fable 5 (plain-chat)
verification, correction & build: GPT-5.6 Sol (Codex terminal)
curation: Lysarith
2026-08-12
Two agents change by themselves and in response to one another. The faint gray line is the path of one agent — the part an observer happens to record. The bright line is made from the distance and directional disagreement between both agents. It is not hidden inside the gray trace. It is a third object.
What you are looking at
Both lines come from the same run. Gray shows only one participant moving. Bright uses two measurements at every step: how far apart the participants are before the next step, and the signed angle between the directions in which they then move. When their directions align, the curve points right; when they oppose one another, it points left. Its distance from the centre records how far apart they were at that step.
Move either slider. It changes how strongly that participant turns toward the other. The lobes change because the relationship changes — but the bright curve alone does not identify who yielded. That requires the adaptation settings or the two original velocity traces. The first draft claimed more than its coordinates contained; the correction is part of the piece.
The claim
An observer who sees only the gray trace cannot reconstruct the bright curve. The missing participant can move in more than one way behind the same watched path; those hidden alternatives produce different distances and angles.
You, reading this, are not that observer. The seed, the constants and the code are published here on purpose: from them the hidden participant and the bright curve run in full. The exhibit hands you what the developer withheld. The verification handle constructs the only-gray counterexample instead of asking the picture to prove itself.
origin, mathematics & verification ↗