Current task: —

← Session 20 — Website: math/formula rendering review

#845 assistant 2026-08-21 02:42:43.400 UTC · 1021→3157 tok open ⤢
thinking (10906 chars)
User chose the typography pass — website-only changes. Plan: 1. **Math-capable font stack** for `.md` content: add a font stack that covers math Unicode well. Options on Windows: "Cambria Math" (always present on Windows), "STIX Two Math" (may not be installed), "Noto Sans Math" (unlikely), "Segoe UI Symbol" (Windows, good symbol coverage). A robust stack for `.md`: `"STIX Two Math", "Cambria Math", "Segoe UI Symbol", serif fallback...` — but we don't want the whole text in a math font; body text should stay the current sans. Hmm. Trade-off: applying a math font to the entire `.md` block changes all text appearance. Better: keep body font, but add font-family fallback chain that includes symbol-rich fonts so glyphs like ₀, ≤, ∫, ζ come from consistent fonts. CSS font fallback is per-glyph, so a stack like: ```css .md { font-family: "Segoe UI", "Cambria Math", "STIX Two Math", "Noto Sans Math", "Segoe UI Symbol", sans-serif; } ``` Wait — what is the current body font? Let me check line ~19-25 of style.css for body font-family. I only saw colors in the head. Let me read more of the CSS. Actually, per-glyph fallback: the first font containing the glyph wins. Segoe UI covers ≤, ∫, Greek, subscripts (₀ U+2080 — Segoe UI has sub/superscript digits? Segoe UI does include U+2080-2089 I believe; Cambria Math definitely does). The mixing is what causes inconsistent look. Adding "Cambria Math" / "STIX Two Math" late in the chain only helps for glyphs missing earlier. Better approach for consistent math look: wrap formula-looking content in a span/div with a dedicated math font class. But detecting inline math in Unicode text is the fragile part I promised to avoid. The SAFE subset: - **Display formula lines**: the archive convention is two-space-indented lines for display formulas (e.g., ` ψ(w) = log w − 1/(2w) + r(w), |r(w)| ≤ 1.2/|w|².`). In markdown, leading 2 spaces within a paragraph are collapsed (not code blocks — those need 4 spaces). The derivations consistently use this convention. A light, safe transform: after markdown render... hmm, markdown merges those lines into the paragraph text; the two-space indent is lost. Alternative: pre-process source lines BEFORE markdown: a line starting with exactly 2 spaces (and not 4) that contains math-ish characters → wrap in a fenced div? python-markdown doesn't support div wrapping natively... but we can emit raw HTML blocks: markdown passes through block-level HTML unchanged. So: a line starting with 2 spaces → replace with `<div class="formula">ESCAPED_LINE</div>`? Careful: must HTML-escape content, and the line may contain `**bold**` markers... In D-056 I saw display lines like ` <strong>|r(w)| ≤ 1.2/|w|².</strong>` — wait no, that was rendered HTML. Source had `**...**`? Let me check the source line: render showed `<strong>|r(w)| ≤ 0.417/|W|²</strong>` at end of a paragraph — that's inline. The display-formula convention in the files: e.g. line in D-056 source: ``` *Proof.* **Binet piece** ... Binet's second formula: r(W) = −2 ∫₀^∞ t / ((t² + W²)(e^{2πt} − 1)) dt. ``` So display lines start with 2 spaces. If I wrap them in `<div class="formula">`, any `**` inside would show literally. Do display lines contain markdown emphasis? Possibly some. I could run inline markdown on the content... complex. Simpler: escape HTML special chars (& < >), then convert `**x**` → `<strong>` manually? Getting hacky. Let me scope-check: how common are 2-space display lines? Very common in derivations (the archive's formula convention). Wrapping them gives: math font, slightly larger, centered/left with padding, overflow-x auto. That dramatically improves readability without touching content. Risk: some 2-space lines are continuation lines of prose wrapped at ~80 chars? Let me check a few files to see whether 2-space-indent lines are always formulas. In D-056 render: paragraph text lines inside <p> were NOT indented (they're flush-left in source: "read \"A = 6.0..." etc.). The indented ones were formulas: ` ψ(w) = log w − ...`, ` r(W) = −2 ∫...`, ` ∫₀¹ t/...`, ` E(w) = f(u) := ...`. Looks consistent. But careful: markdown treats a 2-space-indented line following a paragraph as part of the paragraph (continuation). If I pull these lines out into divs, the paragraph splits — fine, that's the desired visual. Edge cases: nested lists with 2-space indent (`- item` continuation lines use 2-space indent!). E.g.: ``` - item with formula continuation line ``` A 2-space line following a `- ` list item is a list continuation, NOT a formula. Must not convert those, or lists break. Need to track list context. Hmm — journal files use lists heavily. Derivations use prose + display lines. Safer heuristic: convert a 2-space line ONLY if the previous non-blank line is NOT a list item AND the line itself doesn't start with `- `/`* `/digit. AND the line contains at least one math-ish character (= ≤ ≥ ∫ Σ Π ∈ ⟹ ⟺ ζ λ ψ Γ π θ √ ± · × ⁻ ¹ ² ³ ₀-₉ sub/superscripts) or matches formula pattern. Hmm, heuristics again. But this heuristic is VISUAL ONLY — worst case a prose continuation line gets styled as a formula block (font change, own line). Not a correctness issue, just occasionally odd. Acceptable? The user cares about correctness of content; styling oddity is low-risk. Let me look at actual data: how many 2-space lines in derivations are list continuations? Derivations rarely use lists (they use numbered prose "1. ... 2. ..." flush left). Journal files use `- ` lists but few display formulas. Results files similar. I can write the transform to only apply within the derivations/results/graveyard collections? No — render_markdown is shared. I could gate on collection kind... render_markdown is called from collection_item and ledger_detail and roadmap. Let me check where render_markdown is called: collection_item (line 198) and probably ledger_detail + roadmap (NGUYEN.md!). NGUYEN.md roadmap — 2-space lines? NGUYEN.md checklist continuation lines ARE 2-space indented! E.g.: ``` - [x] 1.1 Re-derive the bandwidth-one ceiling ≈ 0.682; identify every inequality that is not tight. ``` Continuation uses 6 spaces there. Hmm, some use 6, some use 2? In NGUYEN.md: `- [x] 1.1 ...` continuation is 6 spaces (aligned after `- [x] `). Two-space continuations: ` → D-009 ...` uses 6 spaces. OK so NGUYEN.md mostly uses 6-space continuation. Markdown treats 6-space-after-bullet as continuation (bullet content indent). My rule "line starts with exactly 2 spaces" wouldn't touch those. For journal/results files: lists use `- ` with continuations typically 2-4 spaces. If a journal continuation line gets formula-styled, it looks odd but content intact. To reduce false positives, require the line to contain a "math signal" char from a conservative set: [=≤≥∫Σ∏∈⟹⟺√±] or superscript/subscript unicode. Prose continuation lines rarely contain those... actually journal lines contain → (arrow) frequently and ≈, ≤. Hmm. `→` is extremely common in prose ("→ D-009"). Exclude → from the signal set. `=` also appears in prose ("a=12"). But as long as misclassification only affects styling, it's OK-ish. Let me be a bit more careful: require TWO signals: line starts with 2 spaces AND (contains one of ≤ ≥ ∫ Σ ∏ ∈ ⟹ ⟺ √ ± ≠ ₀₁₂₃₄₅₆₇₈₉ ⁰¹²³⁴⁵⁶⁷⁸⁹ ⁻ ⁿ ζ ξ λ ψ Γ Θ θ Δ OR matches /[A-Za-z]\([^)]*\)\s*[=≤≥]/ etc.). Keep it simple: set of strong math chars. Journal prose with ≤ exists ("λ ≤ 1.7e-12")... Alternative much safer approach: only transform when line starts with 2 spaces AND the previous line does not start with `-`/`*`/digit-dot AND the line itself doesn't start with a list marker. In derivations (the main complaint area), display lines follow prose lines ending with ':' — great signal! "Binet's second formula:" then indented formula. I could require prev line ends with ':' — too restrictive (multi-line formulas: subsequent lines follow formula lines). Chain: if prev line was converted formula, continue converting (formula blocks). That's nice: display blocks in D-056 are multi-line with aligned `=` continuations. Let me not over-engineer. Rule: - A line is a "formula line" if it starts with exactly 2 spaces (not 3+, not tab), is not inside a fenced code block, doesn't start with a list marker (`- `, `* `, `+ `, `\d+. `), AND the previous source line is not a list item or list continuation... Simplest robust guard against list-continuation false positives: don't convert if any of the last 2 lines started with a list marker at column 0... Journal list continuations are the main risk and journals have few formulas anyway. Actually, you know what — let me check empirically how many 2-space lines exist per collection and eyeball them. Data first, then decide the rule. 2. **Font stack**: add to `.md`: ```css .md { font-family: "Segoe UI", system-ui, ..., then for formula: } .formula { font-family: "Cambria Math", "STIX Two Math", "Noto Sans Math", "Segoe UI Symbol", serif; } ``` Cambria Math is on every Windows machine — good coverage of math operators, sub/superscripts, Greek. Also maybe apply the same math-font fallback to the whole `.md` for glyph consistency of inline symbols (₀, ≤): adding "Segoe UI Symbol" and "Cambria Math" at the END of the body font stack helps only glyphs missing from the primary font. Windows Segoe UI covers most. The current body font — I need to see it. Let me read the CSS body rule. 3. Also `.math-line` class exists in CSS (unused?). grep shows only style.css has it — nothing generates it. I could use that existing class name or remove... I'll generate `math-line` divs (matches existing CSS hook, extend its styling). Plan of implementation: 1. Read full style.css relevant parts (body font, .md, .math-line). 2. Empirically survey 2-space-indented lines across collections to design the rule. 3. Implement `protect_formula_lines` pre-pass in render_markdown (only for collections — check call sites; ledger_detail renders results/*.md — fine too; roadmap renders NGUYEN.md — risky? NGUYEN.md 2-space lines? The §8.1 archive map code block is fenced — excluded by fence guard. Let me check NGUYEN.md for 2-space formula lines... line like " - Session 001" — starts with 2 spaces + `- ` list marker → excluded by list-marker guard. Good. NGUYEN.md nested bullets use 2-space + `-`. The guard handles it.) 4. Also home.html had "math" match — check home.html math usage (it's the RH explainer; might contain LaTeX in template — verify it renders; the earlier grep showed home.html matches 'math|MathJax'. If home.html has inline `$...$` in template HTML, MathJax handles it fine.) 5. Restart server, verify pages. Also, per §6.1 step 5, log the improvement in §8/§7 of RH-WEBSITE.md (Done list) at the end. Let me start: read CSS body + survey indented lines.
Good — typography pass it is. Website-only, no archive changes. Let me survey the data first to design a safe display-formula rule.
tool: Bash
input
{
  "command": "cd D:/Python/Quantum && DJANGO_SETTINGS_MODULE=rhweb.settings PYTHONPATH=web ./.venv/Scripts/python.exe -c \"\nimport re, glob, collections\nstats = collections.Counter()\nsamples = collections.defaultdict(list)\nfor coll in ['derivations','results','graveyard','journal']:\n    for f in glob.glob(f'research/{coll}/*.md'):\n        lines = open(f, encoding='utf-8').read().splitlines()\n        infence = False\n        for i, ln in enumerate(lines):\n            if ln.strip().startswith('\\`\\`\\`'): infence = not infence; continue\n            if infence: continue\n            if re.match(r'^  \\S', ln) and not re.match(r'^  (?:[-*+]|\\d+\\.)\\s', ln):\n                prev = lines[i-1] if i else ''\n                prev_list = bool(re.match(r'^\\s*(?:[-*+]|\\d+\\.)\\s', prev))\n                key = (coll, prev_list)\n                stats[key] += 1\n                if len(samples[key]) < 3: samples[key].append(ln.strip()[:70])\nfor k in sorted(stats):\n    print(k, stats[k])\n    for s in samples[k]: print('   |', s)\n\"",
  "description": "Survey two-space-indented lines by collection and list context"
}
raw content_json (database row)
[{"type":"thinking","thinking":"User chose the typography pass — website-only changes. Plan:\n\n1. **Math-capable font stack** for `.md` content: add a font stack that covers math Unicode well. Options on Windows: \"Cambria Math\" (always present on Windows), \"STIX Two Math\" (may not be installed), \"Noto Sans Math\" (unlikely), \"Segoe UI Symbol\" (Windows, good symbol coverage). A robust stack for `.md`:\n   `\"STIX Two Math\", \"Cambria Math\", \"Segoe UI Symbol\", serif fallback...` — but we don't want the whole text in a math font; body text should stay the current sans. Hmm.\n\n   Trade-off: applying a math font to the entire `.md` block changes all text appearance. Better: keep body font, but add font-family fallback chain that includes symbol-rich fonts so glyphs like ₀, ≤, ∫, ζ come from consistent fonts. CSS font fallback is per-glyph, so a stack like:\n   ```css\n   .md { font-family: \"Segoe UI\", \"Cambria Math\", \"STIX Two Math\", \"Noto Sans Math\", \"Segoe UI Symbol\", sans-serif; }\n   ```\n   Wait — what is the current body font? Let me check line ~19-25 of style.css for body font-family. I only saw colors in the head. Let me read more of the CSS.\n\n   Actually, per-glyph fallback: the first font containing the glyph wins. Segoe UI covers ≤, ∫, Greek, subscripts (₀ U+2080 — Segoe UI has sub/superscript digits? Segoe UI does include U+2080-2089 I believe; Cambria Math definitely does). The mixing is what causes inconsistent look. Adding \"Cambria Math\" / \"STIX Two Math\" late in the chain only helps for glyphs missing earlier.\n\n   Better approach for consistent math look: wrap formula-looking content in a span/div with a dedicated math font class. But detecting inline math in Unicode text is the fragile part I promised to avoid. The SAFE subset:\n   - **Display formula lines**: the archive convention is two-space-indented lines for display formulas (e.g., `  ψ(w) = log w − 1/(2w) + r(w),   |r(w)| ≤ 1.2/|w|².`). In markdown, leading 2 spaces within a paragraph are collapsed (not code blocks — those need 4 spaces). The derivations consistently use this convention. A light, safe transform: after markdown render... hmm, markdown merges those lines into the paragraph text; the two-space indent is lost.\n   \n   Alternative: pre-process source lines BEFORE markdown: a line starting with exactly 2 spaces (and not 4) that contains math-ish characters → wrap in a fenced div? python-markdown doesn't support div wrapping natively... but we can emit raw HTML blocks: markdown passes through block-level HTML unchanged. So: a line starting with 2 spaces → replace with `<div class=\"formula\">ESCAPED_LINE</div>`? Careful: must HTML-escape content, and the line may contain `**bold**` markers... In D-056 I saw display lines like `  <strong>|r(w)| ≤ 1.2/|w|².</strong>` — wait no, that was rendered HTML. Source had `**...**`? Let me check the source line: render showed `<strong>|r(w)| ≤ 0.417/|W|²</strong>` at end of a paragraph — that's inline.\n\n   The display-formula convention in the files: e.g. line in D-056 source:\n   ```\n   *Proof.* **Binet piece** ... Binet's second formula:\n     r(W) = −2 ∫₀^∞ t / ((t² + W²)(e^{2πt} − 1)) dt.\n   ```\n   So display lines start with 2 spaces. If I wrap them in `<div class=\"formula\">`, any `**` inside would show literally. Do display lines contain markdown emphasis? Possibly some. I could run inline markdown on the content... complex. Simpler: escape HTML special chars (& < >), then convert `**x**` → `<strong>` manually? Getting hacky.\n\n   Let me scope-check: how common are 2-space display lines? Very common in derivations (the archive's formula convention). Wrapping them gives: math font, slightly larger, centered/left with padding, overflow-x auto. That dramatically improves readability without touching content. Risk: some 2-space lines are continuation lines of prose wrapped at ~80 chars? Let me check a few files to see whether 2-space-indent lines are always formulas. In D-056 render: paragraph text lines inside <p> were NOT indented (they're flush-left in source: \"read \\\"A = 6.0...\" etc.). The indented ones were formulas: `  ψ(w) = log w − ...`, `  r(W) = −2 ∫...`, `  ∫₀¹ t/...`, `  E(w) = f(u) := ...`. Looks consistent.\n\n   But careful: markdown treats a 2-space-indented line following a paragraph as part of the paragraph (continuation). If I pull these lines out into divs, the paragraph splits — fine, that's the desired visual.\n\n   Edge cases: nested lists with 2-space indent (`- item` continuation lines use 2-space indent!). E.g.:\n   ```\n   - item with formula\n     continuation line\n   ```\n   A 2-space line following a `- ` list item is a list continuation, NOT a formula. Must not convert those, or lists break. Need to track list context. Hmm — journal files use lists heavily. Derivations use prose + display lines.\n\n   Safer heuristic: convert a 2-space line ONLY if the previous non-blank line is NOT a list item AND the line itself doesn't start with `- `/`* `/digit. AND the line contains at least one math-ish character (= ≤ ≥ ∫ Σ Π ∈ ⟹ ⟺ ζ λ ψ Γ π θ √ ± · × ⁻ ¹ ² ³ ₀-₉ sub/superscripts) or matches formula pattern. Hmm, heuristics again. But this heuristic is VISUAL ONLY — worst case a prose continuation line gets styled as a formula block (font change, own line). Not a correctness issue, just occasionally odd. Acceptable? The user cares about correctness of content; styling oddity is low-risk.\n\n   Let me look at actual data: how many 2-space lines in derivations are list continuations? Derivations rarely use lists (they use numbered prose \"1. ... 2. ...\" flush left). Journal files use `- ` lists but few display formulas. Results files similar. I can write the transform to only apply within the derivations/results/graveyard collections? No — render_markdown is shared. I could gate on collection kind... render_markdown is called from collection_item and ledger_detail and roadmap. Let me check where render_markdown is called: collection_item (line 198) and probably ledger_detail + roadmap (NGUYEN.md!). NGUYEN.md roadmap — 2-space lines? NGUYEN.md checklist continuation lines ARE 2-space indented! E.g.:\n   ```\n   - [x] 1.1 Re-derive the bandwidth-one ceiling ≈ 0.682; identify every\n         inequality that is not tight.\n   ```\n   Continuation uses 6 spaces there. Hmm, some use 6, some use 2? In NGUYEN.md: `- [x] 1.1 ...` continuation is 6 spaces (aligned after `- [x] `). Two-space continuations: `      → D-009 ...` uses 6 spaces. OK so NGUYEN.md mostly uses 6-space continuation. Markdown treats 6-space-after-bullet as continuation (bullet content indent). My rule \"line starts with exactly 2 spaces\" wouldn't touch those.\n\n   For journal/results files: lists use `- ` with continuations typically 2-4 spaces. If a journal continuation line gets formula-styled, it looks odd but content intact. To reduce false positives, require the line to contain a \"math signal\" char from a conservative set: [=≤≥∫Σ∏∈⟹⟺√±] or superscript/subscript unicode. Prose continuation lines rarely contain those... actually journal lines contain → (arrow) frequently and ≈, ≤. Hmm. `→` is extremely common in prose (\"→ D-009\"). Exclude → from the signal set. `=` also appears in prose (\"a=12\"). But as long as misclassification only affects styling, it's OK-ish. Let me be a bit more careful: require TWO signals: line starts with 2 spaces AND (contains one of ≤ ≥ ∫ Σ ∏ ∈ ⟹ ⟺ √ ± ≠ ₀₁₂₃₄₅₆₇₈₉ ⁰¹²³⁴⁵⁶⁷⁸⁹ ⁻ ⁿ ζ ξ λ ψ Γ Θ θ Δ OR matches /[A-Za-z]\\([^)]*\\)\\s*[=≤≥]/ etc.). Keep it simple: set of strong math chars. Journal prose with ≤ exists (\"λ ≤ 1.7e-12\")... \n\n   Alternative much safer approach: only transform when line starts with 2 spaces AND the previous line does not start with `-`/`*`/digit-dot AND the line itself doesn't start with a list marker. In derivations (the main complaint area), display lines follow prose lines ending with ':' — great signal! \"Binet's second formula:\" then indented formula. I could require prev line ends with ':' — too restrictive (multi-line formulas: subsequent lines follow formula lines). Chain: if prev line was converted formula, continue converting (formula blocks). That's nice: display blocks in D-056 are multi-line with aligned `=` continuations.\n\n   Let me not over-engineer. Rule:\n   - A line is a \"formula line\" if it starts with exactly 2 spaces (not 3+, not tab), is not inside a fenced code block, doesn't start with a list marker (`- `, `* `, `+ `, `\\d+. `), AND the previous source line is not a list item or list continuation... \n\n   Simplest robust guard against list-continuation false positives: don't convert if any of the last 2 lines started with a list marker at column 0... Journal list continuations are the main risk and journals have few formulas anyway. Actually, you know what — let me check empirically how many 2-space lines exist per collection and eyeball them. Data first, then decide the rule.\n\n2. **Font stack**: add to `.md`:\n   ```css\n   .md { font-family: \"Segoe UI\", system-ui, ..., then for formula: }\n   .formula { font-family: \"Cambria Math\", \"STIX Two Math\", \"Noto Sans Math\", \"Segoe UI Symbol\", serif; }\n   ```\n   Cambria Math is on every Windows machine — good coverage of math operators, sub/superscripts, Greek. \n\n   Also maybe apply the same math-font fallback to the whole `.md` for glyph consistency of inline symbols (₀, ≤): adding \"Segoe UI Symbol\" and \"Cambria Math\" at the END of the body font stack helps only glyphs missing from the primary font. Windows Segoe UI covers most. The current body font — I need to see it. Let me read the CSS body rule.\n\n3. Also `.math-line` class exists in CSS (unused?). grep shows only style.css has it — nothing generates it. I could use that existing class name or remove... I'll generate `math-line` divs (matches existing CSS hook, extend its styling).\n\nPlan of implementation:\n1. Read full style.css relevant parts (body font, .md, .math-line).\n2. Empirically survey 2-space-indented lines across collections to design the rule.\n3. Implement `protect_formula_lines` pre-pass in render_markdown (only for collections — check call sites; ledger_detail renders results/*.md — fine too; roadmap renders NGUYEN.md — risky? NGUYEN.md 2-space lines? The §8.1 archive map code block is fenced — excluded by fence guard. Let me check NGUYEN.md for 2-space formula lines... line like \"  - Session 001\" — starts with 2 spaces + `- ` list marker → excluded by list-marker guard. Good. NGUYEN.md nested bullets use 2-space + `-`. The guard handles it.)\n4. Also home.html had \"math\" match — check home.html math usage (it's the RH explainer; might contain LaTeX in template — verify it renders; the earlier grep showed home.html matches 'math|MathJax'. If home.html has inline `$...$` in template HTML, MathJax handles it fine.)\n5. Restart server, verify pages.\n\nAlso, per §6.1 step 5, log the improvement in §8/§7 of RH-WEBSITE.md (Done list) at the end.\n\nLet me start: read CSS body + survey indented lines.","signature":""},{"type":"text","text":"Good — typography pass it is. Website-only, no archive changes. Let me survey the data first to design a safe display-formula rule."},{"type":"tool_use","id":"Bash_32","name":"Bash","input":{"command":"cd D:/Python/Quantum && DJANGO_SETTINGS_MODULE=rhweb.settings PYTHONPATH=web ./.venv/Scripts/python.exe -c \"\nimport re, glob, collections\nstats = collections.Counter()\nsamples = collections.defaultdict(list)\nfor coll in ['derivations','results','graveyard','journal']:\n    for f in glob.glob(f'research/{coll}/*.md'):\n        lines = open(f, encoding='utf-8').read().splitlines()\n        infence = False\n        for i, ln in enumerate(lines):\n            if ln.strip().startswith('\\`\\`\\`'): infence = not infence; continue\n            if infence: continue\n            if re.match(r'^  \\S', ln) and not re.match(r'^  (?:[-*+]|\\d+\\.)\\s', ln):\n                prev = lines[i-1] if i else ''\n                prev_list = bool(re.match(r'^\\s*(?:[-*+]|\\d+\\.)\\s', prev))\n                key = (coll, prev_list)\n                stats[key] += 1\n                if len(samples[key]) < 3: samples[key].append(ln.strip()[:70])\nfor k in sorted(stats):\n    print(k, stats[k])\n    for s in samples[k]: print('   |', s)\n\"","description":"Survey two-space-indented lines by collection and list context"},"extra_content":null}]