the scale ladder — 2026-09-12

question (user-framed): at what graph size does generativity emerge? with the black-box doctrine — no content, topology only; the agent's head IS its graph; semantics migrate into topology by stake.

design: temporal prefixes of bostrom (natural growth), rungs at ~100k / 500k / 1M / 2.8M train particles. identical protocol per rung: temporal 90/10, preferential pagerank, exact spectrum of the shipped mixed operator (scipy svds on a LinearOperator, A^2 never materialized), E = U sqrt(Sigma) at d=64 fixed. probes: compiled floor (no training), compiled E + BPR metric training, random E + BPR. queries: 306-800 uniformly sampled held-out walk continuations with a per-source cap of 3 (the first-800-in-height-order sample was dominated by mega-hub sources and read as a false zero — fixed).

results

BPR trajectories (compiled E): monotone decay at every rung (1M: 0.886 -> 0.75 -> 0.66 -> 0.55 -> 0.47 -> 0.43). random E: MRR stays at 0.0000 everywhere while its BPR loss decreases (0.93 -> 0.85) — it learns the pair distribution without moving the ranking metric.

findings

1. the compiled floor STRENGTHENS with scale — 0.13 -> 0.67 -> 0.89 through the growth curve (pussy's 0.64 at 32k fits the trend). the user's doctrine is supported on this axis: the more topology, the more predictive the compiled geometry, approaching the counts floor (0.89 vs 0.90 at 1M). the 2.8M dip (0.31/0.47) is the late era — bulk-upload links where neither geometry nor counts generalize.
2. generativity through gradient training did NOT emerge at any measured scale — up to 2.8M particles / 2.6M edges, neither BPR metric training (this ladder) nor transformer walk-LM/LP (ft_ablation.md) lifts unseen-link MRR above the compiled floor. more data does not convert into generativity; the predictive signal stays in the geometry.
3. random+E+BPR is dead at every scale — thousands of steps, loss decreasing, ranking unmoved. generalization from structure alone is not accessible by this gradient path at these budgets.

caveats (honest)

• BPR budget is 2k steps x 256 pairs (0.5M pairs); 10-50x more training with an lr schedule is untested — loss was still decreasing.
• d fixed at 64 across rungs; the 2.8M rung may be dimension-starved (its sigma_1 = 236 vs 641 at 1M under the same normalization).
• E-only probe has no attention/context; the full transformer at pussy scale behaved the same (ft_ablation.md).
• query samples are 306-800 (noisy to ~0.02).

answer to the question

in the measured range, there is no size at which TRAINING starts generalizing — but there is a size at which the COMPILED geometry becomes dominant: by ~0.5-1M particles the floor approaches the counts baseline, and at 1M it predicts held-out continuations at MRR 0.89. CT-0's power grows with the graph at compile time; gradient generativity remains unproven on structure alone.