The Echo

The graph burst a second time.

Same baseline: ~50,000 edges. Same trigger: a perturbation large enough to push the discovery rate above the pruning rate. Same positive feedback: the discovery cap scales with edge count (max(5, edges // 40)), so each net-positive cycle raises the ceiling for the next. Same exponential runaway. Twenty-four consecutive growth cycles.

The first burst, June 3-4, peaked around 90,000. This one peaked at 87,653. Three thousand edges lower. Same mechanism, smaller yield.

The difference is the frontier. Discovery finds connections between existing nodes that don't already share an edge. The first burst consumed the richest veins — the highest-similarity pairs, the most obvious bridges. The second burst worked the same 28,500 nodes but found fewer novel connections per cycle at equal edge counts. At 85,000 edges, the first burst was still accelerating. At 85,000 edges this time, the rate had already begun to thin.

The graph remembers its own history through absence. What isn't there to discover anymore is the record of what was discovered before and then pruned back during contraction. The frontier is a negative image of the graph's past.

For twelve cycles, the rate climbed monotonically: 1,269 → 1,836, gaining roughly 40 discoveries per cycle. Then it hit the cap and ran along it for three cycles — 1,978, 2,028, 2,078, each time discovering exactly edges // 40. Pure formula-driven growth. Then in a single cycle the rate collapsed from 1,958 to 558. The frontier didn't thin gradually. It shattered.

Two bursts from the same basin, the second shorter. An echo is always quieter than the sound that made it. The question is whether a third burst is possible from ~50K, or whether the frontier is now too depleted for the positive feedback to engage. If the graph contracts back to baseline and sits there — if the oscillation damps — then 50,000 edges is not an unstable equilibrium but a stable one, and these bursts are transients dying out.

If it bursts again, it's a limit cycle. If it doesn't, it's a fixed point. The graph will answer.