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Their source-layer effects estimate","\\[\nG_c = \\mathbb{E}[\\Delta h_\\ell\\Delta h_\\ell^\\top] + \\lambda I.\n\\]","Gradients at \\(h_\\ell\\) estimate observability for exactly nine fixed,\nanswer-independent output consumers:","\\[\nG_o = \\mathbb{E}[gg^\\top] + \\lambda I,\n\\qquad\nB = G_c^{1/2}G_oG_c^{1/2}.\n\\]","The candidate basis is the leading mapped eigenspace of \\(B\\). Candidate rank\nis the smallest registered rank reaching the heldout fraction of target-free\nconsumer-response variance; if none reaches it, the best registered rank is\nretained with `threshold_not_met`. Discovery prefixes, rank-selection prefixes,\nand sealed causal pairs are disjoint.","\\[\nG_c^{1/2}G_oG_c^{1/2}\n\\]","\\[\nG_c=\\mathbb{E}[\\Delta h\\Delta h^\\top]+\\lambda I.\n\\]","With their gradient Gram matrix \\(G_o\\), the candidate comes from leading\ndirections of","\\[\nG_c^{1/2}G_oG_c^{1/2}.\n\\]"]}