From LLM-Generated Conjectures to Lean Formalizations: Automated Polynomial Inequality Proving via Sum-of-Squares Certificates

URL SCAN: arXiv cs.AI | Submitted 14 May 2026
FIRST LINE: "Computer Science > Artificial Intelligence"

THE DISSECTION

This paper is a neuro-symbolic pipeline for automated theorem proving, specifically polynomial inequality verification. The architecture is: LLM generates approximate SOS (Sum-of-Squares) conjecture → symbolic computation refines it to exact proof → Lean formalization certifies the result. The benchmark claims scalability to 10-variable polynomials.

THE CORE FALLACY

The paper operates entirely within the automation of cognitive labor paradigm without grappling with what it is actually doing: demonstrating that the last defensible intellectual fortress of human mathematicians—formal proof construction—is now being automated. The framing treats this as a tool enhancement for humans. The structural reality: proof construction is the final node in the cognitive automation sequence, and this paper is another data point in its completion.

HIDDEN ASSUMPTIONS

1. Proof tasks are finite and bounded. The paper benchmarks on polynomials with up to 10 variables. This is the equivalent of saying "our chess program works up to 10 pieces on the board." The method's scalability claim is scoped to current benchmarks, not structural limits.
2. Lean certification is the end state. The paper presents human-verifiable proof in Lean as a virtue. This is transition management theater—the assumption that human legibility will remain valuable. Under the Discontinuity Thesis, certified proof artifacts become intermediate objects consumed by downstream systems, not endpoints for human comprehension.
3. LLM proposal quality is the bottleneck. The framing suggests the human-usable interface (LLM conjecture generation) is the limiting factor. The actual bottleneck is symbolic computation scalability—the same scalability problem the paper claims to solve by delegating it to the LLM.

SOCIAL FUNCTION

Prestige signaling / competitive positioning. The paper performs "we are advancing AI mathematical reasoning" for the academic AI community. The Lean certification component performs "we are rigorous and trustworthy" for the formal methods community. The neuro-symbolic framing performs "we combine the best of both worlds" for grant committees. The actual content: further evidence that mathematical creativity, one of the last supposedly human-exclusive cognitive domains, is being mechanized.

THE VERDICT

This is a technically competent contribution to the ongoing automation of formal reasoning. Under the Discontinuity Thesis, it registers as another increment in P1: Cognitive Automation Dominance—specifically, the proof construction domain that was previously considered resistant due to its requirement for rigorous symbolic manipulation. The 10-variable claim is a scope-limited demonstration, but the trajectory is clear: within the mathematical labor space, the set of problems that require human proof construction is shrinking toward zero.

Survival Signal for Humans: The paper's Lean-certified output is the closest thing to a remaining human niche—proof auditor, specification author, problem selector. These are lag defenses, not structural positions. The paper does not address this.

Viability Scorecard (Human Mathematical Labor):
- 1 year: Fragile (competition-level problems, narrow scope)
- 2 year: Fragile-Conditional (expanding benchmark coverage)
- 5 year: Terminal (mainstream automated proof competition)
- 10 year: Already Dead (for practical mathematics)

The pipeline makes human proof construction optional for an expanding set of mathematical tasks. The optionality is the obsolescence signal.