agentic research

A dated log of research on open problems, led by the author with AI assistance.

Over the last year I have watched AI systems go from fumbling textbook exercises to closing real gaps in research mathematics. The question I keep coming back to is how much of that carries into the problems I actually work on — quantum information, complexity, quantum many-body physics. The only honest way to find out is to run the experiment.

The manuscripts stay here as a public research log. Selected manuscripts are also archived on Zenodo so that a reader can retrieve and cite the exact version behind a claim. The archive provides a stable research record; external proof review and literature novelty remain separate questions.

Human and AI contributions. The author set the research directions, designed the harness that coordinated model tasks, tools, memory, and checking, supplied physical and mathematical intuitions and proof skeletons, and guided the development and revision of the research ideas. AI models developed detailed candidate arguments and derivations, searched the literature, wrote and ran computational checks, and drafted and revised the manuscripts under this supervision.

Most attempts do not close the problem. From 24 September 2026, new research entries are published only when they cover the complete original question and pass the project’s internal verification. Partial results and exploratory bounds stay in the local research log. Earlier entries retain their stated scope. Each public note records what was established and which checks, source questions, or external reviews remain outstanding.

What “verified” means here. Each entry states its checks. Some have exact rational-arithmetic certificates; analytic proof candidates state whether their audit was sequential or independent, and describe the checks performed. Neither label means external refereeing or formal proof-assistant verification. Read each entry as a claim with its working attached. A proof candidate remains open to correction, and literature novelty is a separate question. The label “solved (negative)” records this research log's conclusion that an explicit counterexample refutes the stated claim. It does not mean QIQCOP has accepted the result, that an external expert has approved it, or that publication priority has been established.

The twenty-one archived manuscripts are collected in Agentic Proofs for QIQC: Collected Manuscripts, version 1.3 (16 October 2026). The archive index identifies each paper and its date; the website articles link to the corresponding QIQC reports. Version 1.3 adds the two-pass Chernoff counterexample, which refutes the universal measured-exponent equality while leaving the optimal unrestricted LOCC and SEP exponents unresolved. The twenty earlier manuscript PDFs and their source archive are unchanged. Each archived paper’s entry below links to its Zenodo record.

The 22 October 2026 release adds ten internally reviewed manuscripts on Gibbs preparation and mixing, shallow-circuit sampling, Gaussian entanglement, cooling, reflected entropy and an accepted-instance attack bound. Each has a full PDF and a source package with proof and checking records. These ten website papers are separate from the twenty-one archived manuscripts above.

The 26 October 2026 release adds M26 on large-order QAOA energy bounds and G02 on near-critical weak-field Ising Gibbs preparation. Both have complete candidate manuscripts, PDFs and source packages. Their current audit is sequential; independent review of the complete manuscripts and their novelty remains outstanding.

Log

If you think one of these is wrong, I would like to know — that is rather the point of putting them somewhere public instead of on arXiv. Write to zhangyx@comp.nus.edu.sg.