Brief — Part IV "Computational Methodology" (file manuscript/sections/part04_methodology.tex; bib manuscript/references_part04.bib)
Target 35–50 pages (≈ 15,000–22,000 words) with real mathematics. Document EXACTLY what the code does — read these files before writing: RESEARCH_PLAN.md §3–§7, protocol/PROTOCOL.md, ingestion/link_sources.py, systematic_review/define_corpus.py, taxonomy/classify.py + taxonomy/ontology.yaml (assignment_rule) + taxonomy/VALIDATION.md, bibliometrics/01–03, knowledge_graph/01–03, econometrics/structural_change.py + run_structural_change.py, embeddings/embed_corpus.py + semantic_atlas.py, experiments/emerging_detection.py. Where the code and the plan differ, describe the code and flag the difference in your report. Sections:
- Notation and the corpus as a measurable object (works w, dates, categories C(w) ⊆ 𝒦, periods B/P, month-precision filter).
- Record linkage and deduplication (deterministic DOI/arXiv keys, normalised-title blocking, precision estimation design).
- Multi-label classification: score s_k(w) = Σ_signal min(1, Σ weights), threshold, primary rule, validation metrics (precision/recall/F1, Cohen's κ, Jaccard), and the known failure modes.
- Bibliometric indicators with definitions and estimators: counts, shares, CAGR, fixed-window citations c12/c36, field-normalised NCS, FWCI (OpenAlex definition, cite the documentation), Gini, HHI, fractional counting, international collaboration share, Rao–Stirling and Leinster–Cobbold diversity (define with formulas), citation-age bias and why fixed windows.
- Networks: citation graph internal/external, category flow matrices F_t, modularity Q (Newman–Girvan formula as implemented in knowledge_graph/02), cross-area share; co-authorship/country networks.
- Semantic mapping: SPECTER2/SciNCL/MiniLM embeddings, cosine geometry, UMAP + HDBSCAN (state assumptions), stability by split-half ARI, category centroid drift, novelty definition.
- Structural change: ITS model with seasonality and HAC errors (write the regression), placebo distribution and its p-value, Bai–Perron DP with BIC/LWZ (state the SSR criterion and minimum segment h), PELT penalty, BOCPD with Normal–Inverse-Gamma conjugacy (give the predictive and the run-length recursion), alternative event dates, right-truncation handling.
- Emerging-topic detection: features, label definition at horizon h, train/test cutoffs, metrics, look-ahead safeguards, the preregistered known-emergence set.
- Knowledge-graph extraction: schema, provenance span, machine verification, confidence; what is and is not evidence.
- Uncertainty and reproducibility: bootstrap/HAC intervals, seeds, ledgers, hashes. Cite method sources (Waltman 2016, Bai–Perron, Killick, Adams–MacKay, McInnes UMAP/HDBSCAN, Cohan SPECTER, Stirling, Newman…) — verify each.