AGI impossibility claims

Definition here: the genre of papers and press claiming a mathematical proof that LLM or foundation-model technology rules AGI out outright. Verdict from the September 2026 deep-research run recorded in outputs/llm-degradation-toward-the-mean.md: the run found no accepted proof, and the genre has a fixed anatomy.

The anatomy, four steps

1. Prove something true about an idealized object: one forward pass, fixed depth and precision, a worst-case task family, a closed-loop density-matching dynamical system, or a stipulated definition.
2. Omit the idealization in the summary layer.
3. Supply the AGI verdict in prose, or let coverage supply it. “AGI” is the decisive word, and it is never a formal object in the proof.
4. Blogs harden “conditional theorem” into “impossible.”

The specimens, ranked by honesty

• sikka-2025-hallucination-stations: a real arithmetic bound (O(N²·d) per token, measured to the FLOP) plus a time-hierarchy appeal that does not license the theorem’s wording. The paper never mentions AGI (grep-verified) and concedes composite systems exceed single-model bounds. Press supplied the epitaph.
• guerzhoy-2024-barriers: not a claim but the instrument. The intractability proofs of the iris-van-rooij program turn on (i) an unjustified worst-case input-distribution assumption and (ii) an undefined “human-like.” Both failures recur across the genre.
• zenil-2026-self-improvement-limits: the strongest genuine content (proven entropy decay and variance amplification as external grounding vanishes) and the loudest inflation (April 2026 blogs: “self-improvement mathematically impossible”). The v2 full-text read (2026-10-04) found the quarantine four times (abstract, section 4.6, section 5, conclusion), plus the paper’s own Theorem 5 proving convergence under persistent grounding, and a second hedge the blogs also dropped: the symbolic escape holds only “provided that the underlying reality remains algorithmically simple.” Step 2 of the anatomy is doing all the work here.
• Panigrahy & Sharan, “Limitations on Accurate, Trusted, Human-Level Reasoning” (FORC 2026, LIPIcs vol 368, paper 11, DOI 10.4230/LIPIcs.FORC.2026.11; arXiv:2509.21654; honorable-mention best paper per the program page): the only fully refereed item in this set. A real theorem that no system can be accurate, trusted, and human-level by construction, with the content living in the stipulated definitions; the authors frame it as interpreting Gödel and Turing.

What is genuinely proven in the neighborhood (and silent about AGI)

• Fixed-depth log-precision transformers sit in non-uniform TC^0 (Merrill & Sabharwal, arXiv:2207.00729); chain-of-thought-as-depth, retrieval, and tools are the acknowledged escapes.
• A single transformer layer cannot compose functions on large domains (Peng, Narayanan & Papadimitriou, arXiv:2402.08164; communication complexity, conditional on standard conjectures; ACL status unverified this run).
• No computable predictor learns every computable ground truth, so a general problem solver hallucinates sometimes (Xu, Jain & Kankanhalli, arXiv:2401.11817). Same bound applies to any computable brain; it is about computability, not LLMs.
• A formal agent (decision, execution, memory modules) is Turing-complete for any target machine even where a fixed single transformer is not (Qiao, Yu, Qiu & Gao, arXiv:2609.20335; abstract-level). The per-model bound does not transfer to the agent.
• Catalogue for adjudicating new claims: Brcić & Yampolskiy, “Impossibility Results in AI: A Survey,” ACM Computing Surveys 2024 (arXiv:2109.00484).

The recurring category errors

1. Worst-case existence bounds do not describe average-case agency with tools, memory, and iteration.
2. A bound that condemns LLMs also condemns unaided humans (nobody brute-forces 10^17 TSP routes), so it is not tracking general intelligence.
3. Self-improvement ceilings that don’t require an external signal describe one mechanism, not all improvement. Verification changes the fixed point (see model-collapse).
4. Press framing reaches the AGI verdict the math does not. WIRED’s own closing line called agentic AI “both impossible and inevitable.”

Related discourse map: doomer-taxonomy (these claims are cited by doomer and accelerationist camps alike); over-trust in confident formalism is a species of ai-psychosis at the audience layer; citation hygiene is phantom-citations.

Sources

• Full evidence tables: outputs/llm-degradation-toward-the-mean.provenance.md; impossibility worker note under .pi-subagents/artifacts/outputs/22bbe52f-7ffe-46a9-80fd-4e911e9fa29f/notes/.
• Inline IDs and DOIs above, each verified at the tier stated in the provenance sidecar.