Vis-Viva

analytical · neon · twelve laws · under keeper eris

neon

{{ act || react || change }} · the sculpture

analytical

On an ellipse with a at 2 and e at 1/2, the speed law v squared equals GM times (2/r minus 1/a), and the energy matches minus GM over 2a.

LIT GM = 1, a = 2, e = 1/2. Mean anomaly M = 1 is turned into eccentric anomaly by Newton on Kepler's equation. Radius r = a(1 − e cos E). Then v² = GM(2/r − 1/a) and the specific energy v²/2 − GM/r equals −GM/(2a). The circular case r = a is checked beside it: v² = GM/a, same energy.

AMBER The vis-viva equation is classical orbital mechanics. The name is Latin for living force. No ephemeris is fitted here.

MODEL The sun sits at the focus, not the center. The ship advances by mean anomaly, so it really does move faster near the sun. The ellipse uses a = 2 and e = 1/2, the same numbers as the proof. One unit on the page is one unit in the formula.

Sources AMBER

  1. Vis-viva equation (reference)

LIT on load: the identity is recomputed (it throws on mismatch), the training target scores 1, 200 rounds improve the shared sketch, the workspace loop logs 5 entries, and the OBJ and SVG exports match the sketch.

Gallery of kept sketches:

Workspace improvement loop MODEL

  1. Measure: every 40 rounds, record the acceptance rate, the current score and how many rounds since the last improvement.
  2. 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.
  3. Log back: append {entry, round, measured, tried, step} to the workspace log (it is in the export JSON and the list below).
  4. Repeat: re-check the identity before claiming it. The seal stays write-if-missing.

Live workspace log:

    Shared board MODEL

    localStorage key mayhem-twelve-laws-board. Each page writes its best shared reward.

      Attempt board MODEL

        ← The Remainder Bell · Twelve Laws · Golden Icosahedron → · ERIS

        Background wash: AMBER MODEL a field seeded from this page's seal. The viewport is a deep colour, not black, over a vivid page.

        proving…

        Seal sha256(name|slug|blurb): 7698748a2d74e32d35e552d0e0dab28d7f21d1509ecf10f25b311fdcef643208