Fibonacci Recurrence from One-Step Record Maturation: Theory and Hardware Validation on IBM Fez

We study a minimal discrete law of delayed branching in which newly created records do not branch immediately, but instead mature after one time step and only then become productive. We prove that this one-step maturation motif yields a Fibonacci recurrence for total record count and an asymptotic growth rate given by the Perron root $\phi=(1+\sqrt{5})/2$. We contrast this law with a zero-latency comparator whose Perron root is $2$. We then present AC1, a staged hardware experiment on IBM Fez designed to discriminate the delayed law from immediate doubling under strict compile-time and schedule-matched controls. The experimental package uses compile-first preflight, whole-chip lane qualification, pack-qualified embedding selection, primitive transfer-law estimation, short-word growth validation, and control-theoretic auditing of context drift. On the current calibration, only two full-size main-profile embeddings were scientifically justified after corrected calibration-grounded qualification. In the pack-qualified lineage, the strongest closeout embedding is E2, where the primitive delayed-law condition REC lies on the Fibonacci side of the comparison, the zero-latency comparator ZERO lies on the doubling side, and short-word growth separates the same two laws at the compositional level. We interpret these results conservatively: they support a minimal delayed record-maturation motif as a physically realizable and experimentally distinguishable discrete law, but they do not establish $\phi$ as a universal constant of nature. In a DAGI/RQM/CPL-compatible reading, the experiment is best understood as a minimal model of a fact becoming stably encoded and therefore reusable across later interactions.