MODEL FRONTIER 2026 · MATH 2025 · under KEEPER ERIS
Hilbert's Sixth · Particles → Fluid
Deng, Hani and Ma derived the fluid equations from Newton's laws for hard-sphere particles, by way of Boltzmann's equation. It is a major case of Hilbert's 1900 sixth problem.
Dave (t242u): "perfect, continue on building out pages please, anything you want browse the internet for guidance"
LIT Yu Deng, Zaher Hani and Xiao Ma (2025) gave a rigorous chain from microscopic Newtonian hard spheres to Boltzmann's kinetic equation to the macroscopic fluid equations. Quanta listed it among the top results of 2025.
LIT kB = 1.380649 × 10⁻²³ J/K exactly (SI 2019). At 300 K, kT = 4.14 × 10⁻²¹ J, and the mean molecular speed of N₂ is √(8kT/πm) ≈ 476 m/s.
MODEL Tie to Dave's world: Nitrogen as the gas: his band III.
MODEL Art: 300 elastic spheres bounce in a glass box. The coloured arrow is their averaged momentum, the "fluid" seen from far away.
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): 76ee9e2ffeb1f1c385c8aee3b08df0efb75729b387caa765cebe1805e27670d7