Companion Note B v2: The Apparatus Authors the Load — Outflow-Side Orientation to the Homelessness Convergence

Companion Note B introduces the obligation-authorship side of the Obligation Density Programme. The paper argues that the apparatus is the principal author of the obligation density it subsequently measures the failure of. Integrating the Geometry of Administrative Amnesia (DOI:10.5281/zenodo.20017659), the paper formalises the quadratic burden geometry, fiduciary-memory decay, mimicry memory, and the misdiagnosis loop through which structural overload is repeatedly interpreted as individual misconduct. The paper positions homelessness as the realised outflow surface of obligation density and argues that the apparatus's linear discharge mechanisms cannot keep pace with the quadratic burden geometry produced across multiple administrative layers. Programme function: Outflow-side account of obligation-density overproduction. Core structural question: How does a system become unable to perceive the burden it is itself producing? This is v2 of Companion Note B. v1 oriented the reader to the obligation-authorship recognition. v2 adds the geometric mechanism: the quadratic burden geometry that the apparatus cannot perceive from inside its layers; the decay law for non-load-bearing fiduciary memory; the mimicry-memory substitution; the misdiagnosis loop; and the structural foreclosure of internal restoration.