The source has eight fixed three-feature points with equal Euclidean weights. Stable Gaussian entropy search chooses each row’s bandwidth to match perplexity. Self is excluded; mathematical nonself Gaussian weights are soft. Symmetrizing conditionals and dividing by 16 gives globally normalized ordered-pair P. Heavy-tailed Student-t map affinities give globally normalized Q. This is exact full-pair t-SNE on a small toy.

The gradient is 4Σj(Pij−Qij)(yi−yj)/(1+||yi−yj||²). Each step tries learning rate 20 and halves it up to 20 times until KL does not increase, then recenters the map. If no trial is accepted the map stays fixed for that step. Two fixed A/B initializations and actual 400-step trajectories make checkpoints reproducible. No early exaggeration, momentum or Barnes-Hut approximation is included; no production-speed or global-optimum claim is made.

Changing perplexity changes source P and restarts optimization, so loss comparisons across perplexities involve different objectives. Changing initialization changes the trajectory for the same source P. Map axes, orientation, global gaps and apparent cluster sizes do not reproduce original feature units, true classes or task accuracy. The plot auto-fits with equal scales; exact current map coordinates remain in the table.

Duplicate source coordinates retain separate IDs and positive mutual affinity; excluded self is a different case. A finite map does not enforce every source distance exactly, including a duplicate pair’s zero distance. Scope excludes learned semantic labels, arbitrary input data, scalable solvers, automatic best settings, new-point transforms, inverse reconstruction and downstream evaluation. Numerical/source/initialization/checkpoint edits clear stale answers; inspection alone preserves them.