Standardize reproduction number notation to $\mathcal{R}(t)$

[Copilot]

Standardizes all mathematical notation for the time-varying reproduction number to $\mathcal{R}(t)$. This disambiguates the reproduction number from the recovered compartment (R) in SIR-family models and emphasizes the time-dependent function over subscript notation.

Changes

Before:

$R_t$ or $R(t)$

After:

$\mathcal{R}(t)$, $\mathcal{R}_k(t)$, $\mathcal{R}_{\text{baseline}}(t)$

Files Updated

• README.md: Core equation and description
• pyrenew/latent/infections.py: Docstring equations
• docs/tutorials/building_multisignal_models.qmd: 9 instances
• docs/tutorials/latent_hierarchical_infections.qmd: 6 instances including hierarchical forms
• equations.md: Mermaid diagram labels

All changes are documentation-only (docstrings, markdown, Quarto tutorials).

Original prompt

---

This section details on the original issue you should resolve

<issue_title>Standardize on \mathcal{R}(t) for the time-varying reproduction number in the docs</issue_title>
<issue_description>- Propose $\mathcal{R}$ over $R$ to disambiguate the reproduction number from the recovered compartment in SIR-family models.

• Propose $\mathcal{R}(t)$ over $\mathcal{R}_t$ to reflect that the reproduction number is a function of time is a latent quantity, not a datapoint.

I think this should wait for #650 to land. After that, it might be a good task for a coding agent.</issue_description>

<agent_instructions>Please standardize all docstrings and documentation so that the time-varying reproduction number R(t) is rendered in TeX-style math as $\mathcal{R}(t)$ rather than $R(t)$, $R_t$, or $\mathcal{R}_t$.</agent_instructions>

Comments on the Issue (you are @copilot in this section)

@dylanhmorris Note that GH renders `$\mathcal{R}$` in markdown identically to `$R$` (at least for me), but they render differently in our docs (which use [katex](https://katex.org/)).

• Fixes Standardize on \mathcal{R}(t) for the time-varying reproduction number in the docs #676

---

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.58%. Comparing base (265b2bf) to head (2b1be52).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #681   +/-   ##
=======================================
  Coverage   97.58%   97.58%           
=======================================
  Files          55       55           
  Lines        1697     1697           
=======================================
  Hits         1656     1656           
  Misses         41       41           

Flag	Coverage Δ
unittests	97.58% <ø> (ø)

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[github-actions]

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[dylanhmorris]

LGTM. Diffs look correct and so do the rendered docs.