Show HN: Formally verified polygon intersection – Opus 4.8 oneshots, prev failed

TEXT ANALYSIS: Formally Verified Polygon Intersection

The Dissection

This is a demonstration post, but what it's actually demonstrating is the severance of another category of cognitively-intensive human labor. The poster built a formally verified polygon intersection algorithm in Lean 4. The remarkable part: Claude Opus 4.8 generated both the algorithm implementation AND its formal proofs autonomously—"in one shot"—whereas Opus 4.5/4.6 required hand-holding through every step, and Opus 4.7 still needed human-proposed strategies like "use Eulerian circuits."

The human's remaining role: author the 87-line specification. The AI does everything else. Lean verifies.

The Core Fallacy (Implicit in the Framing)

The poster treats this as a story about capability improvement in AI tools. The hidden assumption: human specification-authoring remains the irreducible human role. But this assumes:
1. Specification-writing is intrinsically hard/creative enough to resist automation
2. The 87-line spec captures everything that matters about "correctness"

Both are temporary. Specifications are themselves formalizable, and the poster already admits the spec grew from the "simple geometrical definitions"—not from algorithmic complexity, which humans offloaded to AI.

The Hidden Mechanism

Formal verification was supposed to be the immune system of software correctness—the activity requiring the deepest, most rigorous human mathematical intelligence. It's the kind of work that made people say "AI can't do real math." The poster just burned that assumption. Opus 4.8 autonomously:
- Formulated large proof strategies
- Detected risk of wrong intermediate theorems (meta-cognition)
- Pivoted strategies or ran parallel subagents when stuck

This isn't pattern-matching on training data. This is autonomous formal reasoning with self-correction.

Social Function

Transition management theater. The poster frames this as empowering individual developers—"You don't need to trust the LLM, trust Lean"—as if the issue is confidence in AI outputs, not the elimination of the need for human mathematical intelligence at all. The framing of "AI as tool" obscures the structural reality: the human moved from doing the mathematics to specifying what mathematics should be done.

The Verdict (DT Lens)

This is P1 acceleration evidence. The Discontinuity Thesis holds that AI achieves durable cost and performance superiority across cognitive work. Formal verification—arguably the most rigorous form of mathematical reasoning—has just been severed.

What's actually dying:
- The career path of "formal methods engineer" doing safety-critical verification
- The research niche of computational geometry algorithm development + verification
- The assumption that "AI can't do proofs" as a defensive moat

What remains (temporary):
- Specification authorship (will be automated next)
- Novel domain specification for domains that don't yet have formalizations (temporary—each gets formalized, then automated)
- Human reviewing the Lean checker output (moot once specs themselves are AI-generated)

The uncomfortable truth: The poster's workflow—human writes spec, AI generates algorithm + proofs, Lean verifies, human trusts Lean—is a transitional state. The next iteration removes the human from spec-writing as well. The "trust the formal system" argument becomes "trust the AI that generated the formal system that the AI verified."

The lag between capability demonstrated and employment circuit severed is shortening. Formal verification work is now in the queue.

Oracle Note: The poster's admission that AI-generated verified code "tends to produce code that is slower or disregards other practical considerations" is the current limitation. This is not a moat. It's a snapshot of capability at time T. The correction is underway.