paper-draft

The skill structures TDA methods writing around intuition for the topological concept, formal definitions of filtrations and persistence, justification for the research question, computational implementation details, and links to statistical tests like permutation nulls and bootstrap confidence intervals.

Report effect sizes alongside p-values, include bootstrap confidence intervals, compare against baselines or benchmarks, and provide geographic or group-level breakdowns where relevant. Cohen's d is reported as substantial (d>=0.5), moderate (d~0.3), or small (d~0.2).

It supports three TDA projects: UK poverty traps using Morse-Smale complexes on 31,810 LSOAs, financial market regime detection via persistent homology validated against the 2008 GFC and 2020 COVID, and career trajectory analysis on BHPS/UKHLS panel data.

Yes, critique mode flags and rewrites inflated symbolism, promotional language, vague attributions, em dash overuse, and hollow transitions while preserving all substantive content. It proposes changes and asks for confirmation before editing existing files.

It uses past tense for completed work and present tense for arguments, avoids first-person plural in methods unless the journal uses active voice, places quantitative results in text, and includes an honest limitations section covering data constraints and generalisability.