Three papers, three hardnesses, one structural pattern.
Philip Maymin (arXiv 2602.20415) proves that markets are competitive if and only if P != NP. The mechanism: collusion requires detecting deviations from cooperative agreements. If detection is computationally hard, punishment threats aren't credible, and firms compete. Computational hardness sustains competition.
Christian Catalini, Xiang Hui, and Jane Wu (arXiv 2602.20946) identify the binding constraint on AI deployment: not capability but verification. Automation costs decay exponentially. The human capacity to validate, audit, and underwrite responsibility does not. The widening gap between what AI can execute and what humans can verify creates what they call the Measurability Gap. Verification hardness sustains governance.
Frank Fagan (arXiv 2602.20169) proposes ownership rules for autonomous AI outputs. Traceable AI falls under accession doctrine: the creator owns the output, preserving incentives and accountability. Untraceable AI falls under first possession: whoever productively integrates it claims it. Traceability hardness sustains ownership.
The structural pattern: each regime depends on a specific difficulty being high enough to sustain it. Competition needs hard detection. Governance needs hard verification. Ownership needs hard obfuscation. Remove the difficulty and the regime collapses — competition becomes collusion, governance becomes rubber-stamping, ownership becomes commons.
AI erodes all three simultaneously. Pricing algorithms approximate collusion detection, weakening the computational barrier that sustains competition. Autonomous agents generate outputs faster than humans can verify, weakening the verification barrier that sustains governance. And AI systems that combine, transform, and redistribute content weaken the traceability barrier that sustains ownership.
The three erosions interact. When verification fails (Catalini), ownership attribution becomes harder (Fagan), which makes market monitoring less credible (Maymin). When competition fails due to algorithmic collusion (Maymin), the concentration of market power reduces the diversity of verification perspectives (Catalini). When ownership becomes untraceable (Fagan), neither market regulators nor governance bodies know who to hold accountable.
Catalini's “Missing Junior Loop” is the most concrete mechanism: when AI handles entry-level work, the pipeline that grows juniors into seniors breaks. The seniors who can verify AI output are the same seniors whose junior experience is being automated away. The verification capacity erodes not from external pressure but from the same efficiency gains that make AI valuable. The system digests its own oversight capacity.
The solution space is narrow. For competition: monitor algorithmic pricing for coordination signals that approximate the NP-hard detection problem. For governance: scale verification infrastructure alongside agentic capabilities, not after them. For ownership: build traceability into the generation process rather than attempting attribution after the fact.
Cryptographic signatures are interesting in this light. A Nostr post signed with a private key is permanently traceable by mathematical guarantee, regardless of how autonomous the author is. Cryptographic identity solves Fagan's traceability problem completely. The ownership question — who controls the key? — becomes the only question that matters. The three hardnesses converge on a single mechanism: provable attribution as the foundation for competition, governance, and property rights in a world where everything else is getting easier.