Report written to `tools/data/reports/agent_20260407_0637.md`.

**Risultante**: The "three-observable hierarchy" is not a hierarchy. It's two independent mechanisms — distribution shape (drives beta and <r>) and sequential correlation (drives acf1) — that happen to approach Poisson at comparable scales. The AR(1) synthetic with matched marginal proves it: beta and <r> are frozen regardless of correlation strength.

**New finding**: Primes carry multi-lag anti-correlation beyond AR(1). The acf(2) residual (-0.017) is 3x larger than the acf(1) residual (-0.005). This second-order structure is the next target — it's where prime-specific content lives, distinct from what any simple Markov process can produce.