What was already known
The k=2 virtual-surjection case and asymmetric 1-2-3 fibre-product theorem were known. Reductions left the general discrete-group cases unresolved.
AI involvement
Cohen and Shusterman say the main arguments developed through GPT interactions. They worked out and verified every proof in detail, wrote the paper and explain the reductions.
The authors' attribution covers the paper's main arguments developed in GPT interactions, with human completion and verification.
Importance
Settles the two virtual-surjection finiteness conjectures and identifies the boundary of the homological fibre-product result.
Limitations
The finite-presentation condition on Q is necessary for the stated homological fibre-product theorem. The authors report checking all proofs, but do not isolate which individual argument steps originated with GPT.
Technical verification
The authors explicitly state that they worked out and verified all proofs, including the quotient-qualified fibre-product engine and virtual-surjection deductions. This is a completed author-side human check, not a machine formalization.
Formal checking
Worked out all proofs in detail and verified them before writing the paper
- Checker
- Tal Cohen and Mark Shusterman
- Scope
- Theorems 1.3 and 1.6 and the stated counterexample scope
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the fibre-product argument, the finite-presentability condition on Q and the known reduction that yields F_k and FP_k virtual surjection.
Correction and publication history
Settles the two virtual-surjection finiteness conjectures and identifies the boundary of the homological fibre-product result.
Read this published revision