google-deepmind / google-deepmind/formal-conjectures

Paper/Homogenous: `countablyMonolithicSpace_exists_nhds_generated_countable`: ω-monolithic, not monolithic

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ai-audit ai-audit-c90271f0fa misformalization
Dominant language
Lean
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Description

`Homogeneous.countablyMonolithicSpace_exists_nhds_generated_countable` assumes only `CountablyMonolithicSpace X`, that closures of countable subsets are metrizable, whereas Problem 17 in the source asks about monolithic compact spaces, where the closure of every subset of infinite cardinality κ has weight at most κ, so the Lean statement asks a stronger question under a weaker hypothesis.

https://tadamcz.com/fc-review-results/c90271f0fa/#/f/Paper/Homogenous

- 1 misformalization
- 1 minor
- 1 equivalent reformulation
- trivial proof: bailed out
- fix compiles

Found by a language-model audit of the repository at c90271f0fa. Not reviewed by a human. This issue's title and description were written by a language model as well.

Contributor guide

Open the contributing guide

Research direction

Locate `Homogeneous.countablyMonolithicSpace_exists_nhds_generated_countable` in the Paper/Homogenous formalization and compare its hypotheses and conclusion with Problem 17 in the linked source. Confirm the corrected statement expresses monolithic compact spaces as intended, then run the relevant Lean checks to ensure the formalization compiles.

Written by the indexing model from the issue text.

Assessment

Domain
content
Issue type
Bug
Difficulty
3/5
Estimated time
1-2 days
Activity status
Active
Clarity
Mostly clear
Newbie friendliness
68/100

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