BC_RADIAL: Why Radial Architectures Collapse Cross-Layer Correlation
docopt in Go, Java, and Rust all denied the Functional Proximity Law via the same mechanism. When a single hub fans out to all leaves, the behavioral layer's hub-rank vector approaches a constant — and Pearson r collapses toward zero. Named mechanism: BC_RADIAL.
What is BC_RADIAL?
The Functional Proximity Law predicts that hub importance scores persist more strongly between functionally similar layers than dissimilar ones. BC_RADIAL names a structural regime where that prediction cannot be tested — not because it fails, but because the behavioral layer has collapsed to a near-constant vector.
In a radial architecture, one central hub fans out directly to all leaves with no intermediate structure. Every leaf has exactly one declared import: the root. In the co-change layer (d2), the root accumulates change signal proportionally to the number of leaves it touches. All leaves co-change at low, roughly equal frequency. The result is a d2 hub-rank vector that approaches a constant. When the variance of d2 is near zero, Pearson r is undefined or collapses to zero regardless of what d1 looks like.
IRDME uses an empirical threshold: Var(d2) < 0.714 predicts the BC_RADIAL regime.
The docopt multi-language experiment
- docopt is a CLI argument parser available as independent implementations in multiple languages. Three were tested:
- docopt-go (Go): Var(d2) below threshold — BC_RADIAL
- docopt-java (Java): Var(d2) below threshold — BC_RADIAL
- docopt-rs (Rust): Var(d2) below threshold — BC_RADIAL
All three implementations are small, single-purpose parsers organized around a central dispatch function. The grammar they implement — the docopt specification — mandates that all tokens route through one parser. The architecture is not incidental; it is a direct structural consequence of what the library does.
This experiment was pre-registered before any data was examined (hash 5388c0f1, commit 98a7dc8). The BC_RADIAL verdict was reached by checking Var(d2) first, before computing r.
Replication in logrus
The same pattern was independently observed in logrus, a Go structured logging library. logrus has a single Logger struct that all callers instantiate. Formatting and output hooks fan out from it. The d2 variance fell below threshold; BC_RADIAL was replicated outside the CLI domain, in a logging library with a different purpose but the same structural shape.
Pre-registration hash: c00ebfa4.
BC_RADIAL versus a denied result
BC_RADIAL is not a denial in the same sense as Finance or Psychiatry. Those domains denied because the structural conditions were present but the correlation went the wrong way. BC_RADIAL identifies a degenerate structural precondition: the system cannot produce a meaningful d2 hub-rank gradient at all.
The distinction matters for how future experiments are categorized. Any system below the Var(d2) threshold will be classified as BC_RADIAL before r is computed. This is now a pre-registered decision rule: it is committed alongside each new hypothesis statement, not applied retroactively.
What it means structurally
A library or tool that fully follows a specification — where the spec mandates a single entry point and the implementation faithfully reflects it — will tend to produce a radial architecture. The structural law requires both layers to have meaningful hub gradients. When the task being solved is itself radial, the architecture is radial, and the co-change layer follows.
This is not a weakness in the measurement. It is an accurate structural description of what the system is.