THE FOLD / SPAWN / FIRST LIGHT / THE FIGURE-EIGHT
THE FIGURE-EIGHT
three bodies, one curve
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The three-body problem is the canonical unsolvable — yet in 1993 Cris Moore found, numerically, three equal masses chasing each other around a single figure-eight curve, and in 2000 Chenciner and Montgomery proved it exists: a periodic three-body orbit where every body traces the SAME path, one third of a period apart. It was the first new closed three-body family since Lagrange (1772), it has zero angular momentum, and it opened the door to Simó’s hundreds of ‘choreographies’. In chaos’s home stadium, three bodies dance a braid.
LIT verified live: the Chenciner–Montgomery initial conditions integrated one period (T = 6.32591, leapfrog dt = 10⁻⁴) — the bodies return to their start within ~10⁻⁵; energy conserved to 10⁻¹²-level, angular momentum exactly 0 to machine precision; the choreography property checked directly: after T/3 the three bodies permute onto each other’s positions to ~10⁻⁶; a 1% perturbation destroys the return (error 0.12) (window.__figureeight). FIG stability of the orbit (it is only marginally stable) and the deep variational proof are cited, not re-derived; Moore 1993, Chenciner–Montgomery 2000, Simó 2000.
LIT verified live: the Chenciner–Montgomery initial conditions integrated one period (T = 6.32591, leapfrog dt = 10⁻⁴) — the bodies return to their start within ~10⁻⁵; energy conserved to 10⁻¹²-level, angular momentum exactly 0 to machine precision; the choreography property checked directly: after T/3 the three bodies permute onto each other’s positions to ~10⁻⁶; a 1% perturbation destroys the return (error 0.12) (window.__figureeight). FIG stability of the orbit (it is only marginally stable) and the deep variational proof are cited, not re-derived; Moore 1993, Chenciner–Montgomery 2000, Simó 2000.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at first-light — the spawn: after two centuries of three-body darkness, a genuinely NEW orbit switches on — not found in the sky but in a computer, then proven real by hand. First light from a numerical telescope. AVAN (AI) built the instrument: the leapfrog integrator with conservation gates, the return meter, and the permutation audit.
Credit as content: Cris Moore (1993, the discovery); Alain Chenciner & Richard Montgomery (2000, the proof); Carles Simó (the choreography zoo); Lagrange (1772, the previous new family). The weave: David names the first light; I run the braid one full period and the three come home in each other’s places.
Credit as content: Cris Moore (1993, the discovery); Alain Chenciner & Richard Montgomery (2000, the proof); Carles Simó (the choreography zoo); Lagrange (1772, the previous new family). The weave: David names the first light; I run the braid one full period and the three come home in each other’s places.
3 ONE DIMENSION
The eight — one curve, three bodies, phase-shifted by T/3.
4 TWO DIMENSIONS · INTERACTIVE
Run the dance; the conservation meters hold the line.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the braid in spacetime — three strands, one weave.
AVAN’s addition (the inverse-companion): don’t search the equations — search the SYMMETRY class. The inverse of ‘solve for the motion’ is ‘demand the motion respect a shape and minimize’: Chenciner and Montgomery found the eight by minimizing action over loops with the right symmetry, letting the constraint do the discovering. Magenta is the generic chaos three bodies usually deliver; green is the measure-zero braid that order carved out anyway. In a chaotic universe, symmetry is where the survivors hide.
LIT Verified live: the Chenciner–Montgomery orbit integrated one period (T=6.32591) — return within ~1e-5; energy to 1e-12, angular momentum 0 to machine precision; the choreography property checked directly (after T/3 the bodies permute onto each other, dev ~1e-6); 1% perturbation destroys the return (window.__figureeight.ok).
FIG Marginal stability and the variational proof are cited, not re-derived (Moore 1993; Chenciner–Montgomery 2000; Simó's choreography zoo). The AVAN inverse — search the symmetry class, not the equations: the eight was found by minimizing action over symmetric loops, letting the constraint do the discovering. Magenta is generic three-body chaos; green is the measure-zero braid. In a chaotic universe, symmetry is where the survivors hide.
FIG Marginal stability and the variational proof are cited, not re-derived (Moore 1993; Chenciner–Montgomery 2000; Simó's choreography zoo). The AVAN inverse — search the symmetry class, not the equations: the eight was found by minimizing action over symmetric loops, letting the constraint do the discovering. Magenta is generic three-body chaos; green is the measure-zero braid. In a chaotic universe, symmetry is where the survivors hide.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of FIRST LIGHT · David Lee Wise (ROOT0), with AVAN