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The precision ladder

Short answer to "should we go to float128?" — no, and the numbers say why. The framework computes in IEEE-754 float64 (what JavaScript, and every browser/Node/desktop target, actually has in hardware). float128 does not exist in JS and is software-emulated on every CPU you'd target. More importantly, at the framework's tolerances float64 rounding is not the limiting error.

Where accuracy actually binds (measured, 10⁶ steps)​

Error sourceMagnitude
KO42 tolerance10⁻³
Integrator truncation (default Verlet)5.3×10⁻⁵
float64 rounding (vs 106-bit double-double, same algorithm)2.6×10⁻¹³
CODATA uncertainty of G2.2×10⁻⁵

Rounding sits 8–9 orders of magnitude below the truncation error. Moving the word size buys zero correctness. If you want better numbers, integrator order is the lever, not precision — a 4th-order step buys ~10³× accuracy for ~3× cost; double-double buys nothing here for ~35× cost.

The ladder (opt-in; default is unchanged)​

The nano-zeqond engine exposes three upgrades. The default path is byte-identical to the audited engine.

  1. Kahan-compensated energy ledger (always on) — compensated summation for the energy/driftPct diagnostic only; the dynamics are untouched. Near-free.
  2. integrator: 'yoshida4' — 4th-order symplectic composition of the same KDK kernel. Measured: 501× lower truncation error at 1.4× cost, convergence order 4.00. Use for accuracy-critical runs.
  3. precision: 'dd' — double-double (~106-bit, "float128-class") state, pure JS, identical on web/Node/desktop. ~30× cost; agrees with float64 to 3.5×10⁻¹⁵ over 1000 steps. The one legitimate niche is long-horizon chaotic dynamics (three-body class), where extra digits extend the trustworthy horizon — not accuracy of ordinary runs.
new ZeqNanoEvolver({ integrator: "yoshida4" });      // 501× accuracy, 1.4× cost
new ZeqNanoEvolver({ precision: "dd" });             // 106-bit, chaotic-horizon research

The GPU note​

The GPU field engine is float32 — below float64. It is a visualization layer (documented tolerance: max ϕ diff 3.3×10⁻⁷ vs the CPU reference), never the compute source of truth. Native desktop compute inherits the same float64 CPU engine, so results stay consistent across every surface.

Claim discipline​

Do not market "float128 accuracy": at these tolerances it is indistinguishable from float64 by nine orders of magnitude, and reviewers will check exactly that way (run both, diff). The defensible claims are: integer-nanosecond time base, symplectic integrators with measured drift ≤0.1%, compensated energy ledger, and — with quad mode — 106-bit option for chaotic-horizon research.

Full study: PRECISION-FLOAT128-DESIGN.md and audits/phase5-precision-ladder/ (7/7).