Formal Extensions to Structural Probe Domain and Authority-Safety Theory for Latent-Space Predictive Architectures

This deposit contains two technical reports establishing formal extensions to structural governance theory for adaptive socio-technical systems operating with latent-space predictive architectures, specifically Joint Embedding Predictive Architectures (JEPA) of the kind developed by LeCun et al. TR-LSPD-1.0 extends the Structural Probe Domain (SPD) fail-closed deployment instrument to JEPA-class systems. It introduces the Latent-Space Structural Limit Theorem (L-SLT), which proves that causal non-identifiability in latent predictive systems is a function of representation geometry rather than interventional geometry alone. The theorem establishes Representation Indeterminacy (RI) as a formally novel failure mode — an encoder's abstraction collapse can produce rank-deficient latent Jacobians even when the observable Jacobian is full-rank. The L-SLT reduces to the observable-space SPD condition when the encoder is the identity map. TR-SA-1.1 extends authority-safety theory to named-integrator multi-agent topologies where agents may be JEPA-class systems subject to RI. It introduces the distinction between nominal authority — structural reference graph connectivity — and substantive authority — geometric identifiability of an agent's causal structure under the human integrator's available probe set. The Integrated Authority-Safety Theorem proves that containment boundary enforcement requires both topological connectivity and geometric identifiability along every path from the human integrator to the executing agent. The theorem reduces to the Maffeis-Mitchell-Taly authority-safety result in the special case where all agents are observable-space systems with no RI. Both results are formally grounded using Clarke generalized Jacobians to accommodate neural network non-smoothness. Open problems are explicitly identified and distinguished from established results.