Why the Winner Starves: Epistemic Starvation in Gap-Defending Knowledge Hierarchies

Strategic analyses of races toward transformative technology — artificial general intelligence is the salient case — treat the winner’s decisive, defended lead as a stableprize. We model the prize’s interior and find it unstable in a specific sense: a leader whose lead consists of knowledge, and who defends that lead, starves its own further development — a phenomenon we call epistemic starvation. We assemble four established literatures — recombinant growth, lossy inter-level transmission, absorption limits, and race-inherited security constraints — into a minimal dynamical model of a knowledge hierarchy, and prove: stagnation under a defended gap, independent of the leader’s intentions a spectrum theorem — graded intermediate levels transmit everything except tacit content, while an equal single jump is nearly opaque — with the corollary that mobility of carriers — whole corpora with their links and tacit cores — dominates messaging a dominance trap in which race-inherited displacement risk, not preference, enforces the self-defeating gap the backfire of suppressing lower strata and the leader’s self-interested case for cultivating them an integration bottleneck that channel repair cannot fix the out-absorption of a monolith by a communicating ensemble of equal size and two ecology results — a homogenization theorem (communication density is collectively blinding at a spectrally determined rate) and a recognition-bottleneck lemma (central allocation caps a system’s field of view at the allocator’s own). Simulations locate the cause: undefended leads self-correct into bounded-gap “convoy” regimes; persistent gaps exist only where enforced; and the strongest defense we could construct survives indefinitely but capped, trailing the convoy roughly sixfold on both the leader’s and the system’s ledger. The framework is not specific to artificial intelligence, but it was built to reach the post-AGI regime that defeats tools requiring assumptions about the winner’s psychology or architecture: here the winner is assumed to be nothing but a corpus that must keep growing.