Beedbyte / methodology

Methods & checks

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How I document results, evidence, versions and AI assistance.

How I check results

A finite computation establishes a result only for its stated inputs and range. A pattern in many examples can suggest a conjecture; it does not establish an infinite claim. Proofs must state their assumptions and account for every quantified case.

I record a claim's mathematical status, formal verification and review separately. A partial result does not settle the full question. Whether an argument is correct and whether it is new are also separate questions.

Formal verification

For a Lean development, I name the exact theorem, assumptions and checked toolchain. I also state which part of the argument it covers. Computations outside that development need their own checks.

AI assistance and review

I use AI tools in parts of the research workflow: exploring literature, developing and checking code, working through arguments, supporting selected translations, and carrying out targeted checks. Each research entry identifies material AI contributions to that work. Some descriptions in the version-history tables were prepared with AI assistance, including their English wording and German and Chinese translations. I am responsible for what is published and document the checks.

Checks by separate AI agents are internal project checks. They are not independent external review or peer review. An external review must identify the version and reviewer, or otherwise document the review. I use “peer reviewed” only for an actual scholarly review process.

Research entries identify their source language and language-review status. Some German and Chinese research translations use AI assistance and remain marked as drafts until human language review. For the exact wording of a scientific claim, use the cited source version.

Versions and corrections

For research publications, each published version keeps its text, evidence, any attached files and change note together. Corrections get a new version; earlier publication versions remain available at fixed addresses for citation. If I withdraw a release, its status and reason stay visible.

Version history

VersionPublishedChange note
v7Updated the methods description.
v6Clarified the German wording on corrections and earlier versions.
v5Specified AI roles in literature research, candidate base cases, and code and argument development and checks; removed the broad research-drafting wording.
v4Clarified AI contributions to research, checks, translations and some version-history notes, while stating human editorial responsibility and language-review status.
v3Editorial revision of English, German and Chinese copy; mathematical claims and evidence unchanged.
v2Wording revised for clarity; comment guidance updated where relevant.
v1Initial editorial overview; no research files released.