Observer-Modifying Contagion on Networks

This paper develops a finite-horizon axiomatic and compositional certificate framework for observer-modifying contagion on networks: a regime in which exposure changes not only transmissibility, but also the receiver’s later ability to notice, diagnose, contest, remember, or safely audit related exposures. Rather than proposing a universal law of semantic hazard or contagion dynamics, the paper gives a narrower and constructive support-phase certificate framework for relative self-concealment under explicit comparison semantics. The framework separates four layers that are often conflated: the primitive networked state process, protocol-relative descriptors used for diagnosis claims, external audit experiments used for recovery claims, and attribution ledgers used only for accounting. Its exact structural layer is built on intrinsic node-level active-support counts, selected collision-free witness bundles, entry-window growth of total active support, and primitive one-step persistence certified on the same selected bundles rather than on attribution conventions. Internal blindness is treated through a branch-separated screened-state factorization and comparator-uniform contraction on the declared internal diagnostic channel. External recovery is treated experiment-relatively, with exact monotonicity for portfolio augmentation over single-anchor marginals, while stronger portfolio gains require separate certification rather than unjustified minimax interchange. Delayed audit is modeled as an optional external-only bounded-difference evidence process with null calibration and post-onset positive drift. The central result is a finite-horizon assembly theorem that combines declared active families and type partitions, downstream support margins, nonempty-support entry conditions, primitive persistence factors, active-support blindness inequalities, and phase-conditioned external recovery certificates on comparator-stable realizations. Operationally, the paper advances executable fail-closed semantics: deployment claims weaken automatically when required comparator declarations, metadata, or budgets are missing. The theory is positioned for future human and AI systems that must reason about when spread degrades diagnosis, when that degradation persists through primitive lineages, when external audits can still recover contestability, and how such claims can remain sound under explicit downgrade rules. The manuscript does not claim a universal truth theory for misinformation, a full theory of adaptive rewiring or optimal intervention, a universal portfolio-synergy theorem, an asymptotic quickest-detection theory, or an empirical identification result.