Sundog

A sundog is a good first picture because the sky makes the idea visible. Ice crystals near the sun throw a partial pattern into view: a 22° ring, parhelia, tangent arcs, and other fragments of a larger geometry. You do not see every crystal or every ray. You see a readable projection of the hidden setup. The trick is not to treat the projection as magic, or as the whole truth; it is to ask what hidden state it reliably lets you infer.

Sundog asks whether that move generalizes: when the full system is too large, too hidden, or too expensive to inspect directly, can a smaller shadow carry enough structure to act from? In the mesa work, the hidden body is a trained policy network under selection pressure; the readable shadow is an entangled 5-dimensional subspace at net.7. In the three-body workbench, the body is the full simulated state; the shadow that survives the mechanism audit is simpler than expected: radius gates an inward reflex inside a mapped near-escape pocket. In the chat experiment, the body is the model’s whole answer process; the shadow is a trace packet that says what claim class, source, boundary, and refusal rule the answer must preserve.

The precise word for this is projection: a lower-dimensional readout of a larger object. The plain-English image is body and shadow. The shadow has less information than the body, but sometimes it is more rigid, more testable, and more useful. That is the common shape across the solar halo, cap-set and unit-distance explainers, mesa activations, three-body control, and Ask Sundog’s visible trace. The live claim is still bounded: each projection has its own failure mode, and the geometry side of the crossover remains audit-hedged while the re-derivation work clears. The point is not “one weird trick works everywhere.” The point is: publish the projection, publish where it breaks, and do not upgrade the claim past the test.