Fast output can skip the map.
A critique of Bend 2 uses a sharp example: Bend’s own demo reportedly needs 58 lines to state a simple game condition and 442 lines for the generated proof, while the author’s SPARK recreation reports Success: all checks proved (12 checks). The exact comparison is one author’s experiment, not a language benchmark. The useful warning is broader: you can now build a large solution before learning the name of the field that already contains the tradeoffs.[1]
That is the vibe-coding trap worth keeping. The machine makes implementation cheap enough that reconnaissance feels slow. Then the team discovers it has reinvented a worse interface to old knowledge—and paid for the compiler before reading the survey.
A green kernel is not a readable handoff.
Dan Abramov’s Conway project is more interesting because the account refuses to flatten uncertainty. The claimed proof passed mechanical checks in the Palomar registry, but the post explicitly says it had not yet been independently verified by mathematicians. Earlier attempts produced grandiose private terminology, theorem towers built on unverified seams, and one near-solution that collapsed under a circular sentence.[2]
The recovery was not “prompt harder.” The project narrowed claims, separated formalization of accepted upstream work from riskier novel work, used different worktrees, and created standalone statements that could import Mathlib but not the project’s own machinery. Most importantly, the author noticed that Lean fossilized the historical path, not the path of most insight. A compiler-checked proof and a mathematician-readable explanation remained different jobs.
The checker owns validity inside its model. Humans still own meaning, scope, and inheritance.
The harness is part of the evidence.
A new empirical study varies planning, action space, and context management while keeping the surrounding agent loop fixed across four models, two benchmarks, and 176 matched settings. Its findings are conditional rather than magical: context management matters more under tight windows; planning can scaffold a weaker model or save cost for stronger ones; predefined tools help bash-weaker models while bash-only can benefit stronger ones.[3]
That matters here because “the model proved it” hides the apparatus that shaped the trajectory. Which plan persisted? Which observations were elided? Which tools validated edits? What was held fixed? If the harness can change where a run stops and how code gets written, the handoff needs the harness conditions—not just the final artifact.
Ship proof in four layers.
- Prior art: name the field, closest established method, and why this route exists.
- Statement: isolate the exact claim in a surface an outsider can inspect without loading the private universe.
- Checker: record versions, imports, axioms, commands, and the observed result.
- Explanation: write the conceptual route, failure seams, and repair entry points in the vocabulary of the field.
This is not paperwork after the breakthrough. It is how a result crosses from one unusually productive machine-human session into a project other people can challenge, maintain, and trust in bounded ways.