Title every definition and result callout (base for #872 diagram)

[d-morrison]

Base PR of a two-PR stack addressing #872.

What this PR does

Adds a concise #### Title to every previously-untitled def/thm/lem/cor/prp callout, so each one:

• renders as "Definition N (Title)" / "Theorem N (Title)" instead of an anonymous "Definition N", and
• is easy to refer to by name.

This covers point 3 of #872 ("make sure all definitions and results are in divs, and each div has a concise title"). It titles 89 previously-untitled callouts across 38 files, leaving 0 untitled of the 434 result callouts in the notes. The titles are content-derived noun phrases following the existing house convention (a #### heading as the div's first inner line).

Why split it out

The stacked PR (#873) builds the relationship diagram and descendants table for #872. Those node/table labels come straight from these titles, so getting every result into self-describing div form first keeps that PR focused on the graph code and keeps this large-but-mechanical titling diff reviewable on its own.

Checks

• quarto render ✅ — all 11 affected parent chapters render clean
  (basic-statistical-methods, probability, algebra, poisson, negbinom, parametric-survival-models, logistic-regression, proportional-hazards-models, intro-to-survival-analysis, intro-MLEs, Linear-models-overview)
• lintr ✅ — no new findings (7 pre-existing findings remain in R chunks not touched here)
• spelling::spell_check_package() ✅ — clean

Stacked PR for the diagram + table: to follow, based on this branch.

🤖 Generated with Claude Code

[claude]

Claude finished @d-morrison's task in 5m 13s —— View job

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Code Review — PR #875

• Gather context and understand PR scope
• Review git diff for title correctness and convention compliance
• Spot-check a sample of changed files for content accuracy
• Check for any formatting or structural issues
• Post review findings

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Summary

This is a well-executed mechanical PR. All 89 new titles are accurate noun-phrase descriptions of their callouts' mathematical content, and an automated search confirms the PR's claim: 0 untitled def/thm/lem/cor callouts remain across chapters/ and _subfiles/. The changes are mostly additive (135 insertions, 4 deletions), and the deletions are minor whitespace fixes.

Below are a few issues worth addressing before merging, ordered by severity.

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Issues

1. Inline LaTeX in titles will break diagram node labels (PR #873) — medium priority

Two titles contain inline LaTeX:

• chapters/basic-statistical-methods.qmd, #def-r-squared: "Coefficient of determination ($R^2$)"
• chapters/algebra.qmd:64, #thm-negative-one: "Negation is multiplication by $-1$"

Since PR #873 derives node and table labels directly from these #### headings, the raw LaTeX strings $R^2$ and $-1$ will appear literally in graph source (e.g., DOT/Mermaid) unless the diagram code explicitly strips or renders math. Consider using plain-text equivalents: "Coefficient of determination (R²)" and "Negation is multiplication by negative one" (or keep $R^2$ and handle it in the diagram code, but the safer choice is plain text here). Fix this →

2. #thm-mult-ineq theorem body has a logical error (pre-existing, now visible via title) — low priority

chapters/algebra.qmd:55–59:

:::{#thm-mult-ineq}
#### Multiplying both sides of an inequality by a nonnegative number
If $a < b$ and $c \geq 0$, then $ca < cb$.

When c = 0, ca = 0 = cb, so the strict inequality ca < cb fails. The condition should be c > 0 (positive, not nonnegative). This bug is pre-existing; the new title faithfully mirrors the stated condition. But now that the theorem is named, the inconsistency (≥ 0 in the body, "nonnegative" in the title) is more visible — worth fixing the theorem body to say c > 0 and updating the title to "…by a positive number." Fix this →

3. One title describes the proof method, not the mathematical result — low priority

_subfiles/logistic-regression/_sec_logistic_score_fn.qmd:27, #lem-logistic-score-comp:

"Chain rule applied to the score component"

All other new titles describe the mathematical relationship (e.g., "Derivative of log-odds with respect to coefficients", "Score function decomposes over observations"). This one names the proof technique. A result-oriented title like "Score component as a chain rule expansion" or "Chain-rule expansion of the score component" would be more consistent. Fix this →

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Minor observations (no action needed)

• Blank line after title is inconsistent: Several new #### lines are immediately followed by content with no blank line (e.g., _sec_expit.qmd #thm-expit-prob-logodds, chapters/probability.qmd #thm-prob-subset). This doesn't affect rendering, but differs from callouts where a blank line already existed. Not worth fixing separately.

• Incidental trailing whitespace removal: Three diffs (_thm-d_pi_d_beta.qmd, _sec-understand-coxph.qmd, chapters/poisson.qmd) also strip trailing spaces from adjacent lines. Harmless, slightly beyond scope.

• Pre-existing ID/title mismatch: #lem-deriv-invodds has an ID suggesting "inverse-odds" but both the content and the new title ("Derivative of odds w.r.t. log-odds") describe the derivative of odds. Pre-existing and not introduced by this PR.

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Overall this is clean and mergeable once the LaTeX-in-title issue is resolved (item 1), since that's the only change that could cause a concrete downstream problem in PR #873.

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_{2026-06-03 18:21 UTC}