What does this equation mean?

The compute ledger has a plausible, if unproven, path downward. $C_{\mathrm{SAE}}$ $\approx$ 2dnT is a cost that infrastructure and algorithmic improvements — sparser encoders, better initialization that reaches convergence at lower n , transcoders that replace rather than merely observe a component — can attack directly, the same way serving-side engineering rather than raw parameter growth has driven most within-generation price reduction for inference elsewhere in this field. TopK autoencoders were themselves exactly this kind of improvement over the softer, less efficient sparsity penalties they replaced [ 1 ] . There is no comparable engineering lever visible yet for the labor ledger. $H_{\mathrm{verify}}$ is bounded below by the number of independent lines of evidence a claim needs before it stops being a good story and starts being a checked fact, and every fully triangulated example this field has published — induction heads, indirect object identification — got there by adding more human-driven checks, not fewer. Automated circuit discovery and attribution graphs are real progress against that floor, but on their own authors’ published numbers they currently trade a large fixed compute cost for partial coverage — a quarter of prompts yielding satisfying insight, half of ordinary completions matched, whole mechanism classes still out of reach — rather than for full replacement of the manual check [ 5 , 6 ] .