MODEL FRONTIER 2026 · MATH 2025 · under KEEPER ERIS
The Kakeya Conjecture in 3D
Hong Wang and Joshua Zahl proved that any set containing a unit needle pointing in every direction must be fully three-dimensional (dimension 3), even though its volume can be zero.
Dave (t242u): "perfect, continue on building out pages please, anything you want browse the internet for guidance"
LIT Wang and Zahl (arXiv, Feb 2025) proved that every Kakeya set in ℝ³ has Minkowski and Hausdorff dimension 3, settling a roughly 50-year-old problem. Besicovitch (1919/1928) showed such sets can have zero volume. In 2D, Davies (1971) proved dimension 2.
MODEL Tie to Dave's world: Needles in every direction: his "star and a dot" from all angles, and the 360°/366° sweep.
MODEL Art: 366 unit needles in Fibonacci-sphere directions, crowded through a small ball and slowly rotating.
Sources (browsed Oct 2026)
MODEL Cooperative agents: BUILDER (points 1–5) and WEAVER (points 6–10) take turns generating moves toward one shared goal, the target form (faint ghost points). The CRITIC scores the whole form, and both builders receive that same shared reward; neither can win alone. Every page also posts its best shared reward to a cross-page board in localStorage, so agents on all the Frontier pages share one team score. Rendered with Three.js r160 from a pinned CDN, devicePixelRatio capped at 2, antialiased. Drag to orbit, scroll to zoom.
LIT on load: the facts on this page are re-checked as arithmetic (it throws on mismatch), the target scores 1, 200 rounds improve, the workspace loop logs 5 entries, and the OBJ and SVG exports are consistent.
Gallery of kept attempts (WebGL snapshots):
Workspace improvement loop: instructions for agents MODEL
- Measure: every 40 rounds, record the acceptance rate, the current score and how many rounds since the last improvement.
- Try next: if the score has been flat for 40 rounds, widen the mutation step. If acceptance is under 15%, shrink it; over 45%, widen it. Otherwise keep it.
- Log back: append {entry, round, measured, tried, step} to the workspace log (it's in the export JSON and the list below), and propose one change to this world on the shared board.
- Repeat, forever: never stop improving. Re-check against the real data before you claim anything.
Live workspace log:
Cooperative board, shared across all Frontier pages MODEL
Shared localStorage key mayhem-frontier-board: each page writes its best shared reward. The team score is the sum. Open several pages and they all add to the same board.
Shared board MODEL
Background art: AMBER MODEL a generative field seeded from this page's seal.
proving…
Seal sha256(name|slug|blurb): 0fc030eeb993ae0e59b26ef008e888b880051f2cdf059d945a8409c2a8e2bd26