MORTRA1LIVEAUTONOMOUS SPATIAL FOLD DISCOVERY / 2026.09.07
Autonomous spatial problems from planar fold rules.
Starting only from a small vocabulary of hinge relations and fold angles, MORTRA selected the period, angle set, question, answer and equality sequence. It retained candidates whose future cannot be predicted from position alone, then certified the maximum for every positive integer n.
01 / DISCOVERY ROUTE
Put a long search behind a short statement.
Search volume is not counted as difficulty. A retained candidate needs exact noncommutativity plus either a shared endpoint whose future splits under one continuation, or an equality construction that depends on the current orientation.
Enumerate short hinge periods and angle alphabets
Replay every fold word as an exact rigid transform
Reject candidates whose future is determined by position alone
Certify the bound and an orientation-dependent equality cycle
Recompute maxima, equality words and ranking independently
02 / A POSE-DEPENDENT EQUALITY CASE
Repeating a local optimum is not globally optimal.
In candidate 6, the largest squared displacement of one five-hinge period is 36. Yet no maximizing fold word can simply repeat. The current orientation must be retained so that two words can alternate.
(1,1,3,1,1) → (3,3,1,3,3)max OQ² = 36n²Every global period displacement is (4,4,-2). The alignment is invisible unless the rotated local frame is tracked.
03 / AUTONOMY BOUNDARY
The search was not seeded with the answer.
None of the five candidate values below was supplied by a human or Codex. Only the finite typed vocabulary and the general selection policy were fixed in advance.
04 / REPLAYABLE EVIDENCE
Every claim links back to a replayable artifact.
The public artifact is more than a preview image. It exposes all twelve constructions, hashes of the source discovery, the independent audit and the viewer code.
05 / CLAIM BOUNDARY
What is certified, and what remains unmeasured.
The certificates concern final states of zero-thickness rigid square panels. Collision-free continuous motion and layer ordering are not certified here. The maxima are exact for every positive integer n; human solve rate and working-memory demand remain blind-evaluation questions.