Watch the GeoNum kernel flag the digits a silent IEEE-754 subtraction quietly throws away.
See it run - a worked example, 100% in this browser tab
The problem
A standard f64 subtraction of two nearly equal numbers loses significant digits silently - the result looks fine but is wrong. Engineers and scientists rarely see when their floating-point math has quietly collapsed.
The local-first solution
This plugin sweeps the textbook f=(1-cos x)/x^2 toward x->0 and runs the cancelling subtraction through the real GeoNum substrate kernel client-side: as the f64 relative error blows up, the GeoNum drift compartment rises in lock-step and honestly flags the loss. Every figure is cited and computed in your browser.
What it does
Logarithmic sweep of x from a mild regime down to deep cancellation
Naive f64 form (1-Math.cos(x))/(x*x) that cancels catastrophically
Cancellation-free half-angle reference 0.5*(sin(x/2)/(x/2))^2 for ground truth
Measured f64 relative error at each sweep point
Real GeoNum drift compartment read directly from the substrate kernel
Worst-case drift mapped to a VALID / DEGRADED / UNRELIABLE trust verdict
Honest scope
GeoNum is a conditioning-based uncertainty signal, NOT extra precision: the f64 value is exactly what f64 computes and GeoNum does not make it more accurate - it tells you not to trust it. A red UNRELIABLE badge at strong cancellation is the kernel working correctly. If the GeoNum import is unavailable, trust falls back honestly to untracked.
Authorities cited
Goldberg, D. (1991). What Every Computer Scientist Should Know About Floating-Point Arithmetic. ACM Computing Surveys 23(1), 5-48. DOI 10.1145/103162.103163.
Higham, N. J. (2002). Accuracy and Stability of Numerical Algorithms, 2nd ed. SIAM. (Catastrophic cancellation; conditioning of subtraction.) DOI 10.1137/1.9780898718027.
See your floating-point error honestly
Run the sweep in your browser with nothing uploaded, then save the drift-vs-error curve to a Sandbox workspace or attach it to a Worklog case as a reproducibility record.