Three bodies pulling on each other have no general formula for where they end up — and this is that fact, told over three days. A rare few beginnings keep their exact shape for ever (the promise). Nudge two starts a hair apart and their futures fly apart (the betrayal). Run the numbers, and the computer can only rule futures out — never pick the one that is ours (the question).
Two special answers keep their shape. Eleven nearby beginnings do not. Five calculations fail the instrument; six survive it and disagree. The witnesses can reject a future. They cannot choose ours.
equal massequal massequal mass
simulation time0.0000 periods
centre of mass0.00e+0
total momentum0.00e+0
relative energy error0.00e+0
angular momentum0.00e+0
measured initial state · G = m = 1
referenceshadow · δ = 10⁻⁷
simulation time0.0target · 150
shadow separation1.00e−7
max relative energy error0.00e+0
total momentum0.00e+0
angular-momentum drift0.00e+0
same equations · two states 10⁻⁷ apart
accepted futureinstrument refused
simulation time0.0target · 150
initial interval1.00e−7
resolved fan diameter0.00e+0
accepted11 / 11
instrument refused0 / 11
eleven beginnings inside one invisible interval
Special answers exist
Lagrange's equilateral triangle rotates exactly. The figure-eight returns periodically. The three-body problem is not the absence of answers; it is the absence of one general shortcut that turns every beginning into a closed-form future.
exact islands · no general map
The witnesses cannot elect
Energy and distance gates reject five under-resolved close encounters. Six distinct futures remain physically admissible over the measured interval. Passing the witnesses means the calculation earned a place in the question. It does not make that future ours.