feat: heuristic LaTeX recovery for formula regions (0.7.5)

[abimaelmartell]

Summary

Adds extractFormulasInRegionsAsLatex (NAPI) and extract_formulas_in_regions_as_latex (Rust) — converts the linearized text from formula bboxes into LaTeX using positioned text data, with a calibrated confidence score so callers can gate on quality.

Builds on top of extractFormulasInRegions from #40. Bumps NAPI package to 0.7.5.

Pipeline (per formula bbox)

1. Pull positioned text items inside the bbox via the existing positioned-text extractor
2. Apply Unicode → LaTeX char mapping (160+ symbols: Greek, operators, relations) via a dedicated unicode_map module
3. Detect simple structure from item geometry — sub/superscripts via font-size + y-baseline, basic two-row fractions
4. Score the result with positive points for clean conversion, plus penalties for failure modes that produce broken output

Calibrated confidence

The calibration uses additive penalties (clamped to [0, 1]) that fire on the failure modes manual inspection surfaced:

Penalty	Trigger	Value
MANY_ITEMS	item_count > 15	-0.20
VERY_MANY_ITEMS	item_count > 25 (additional)	-0.10
MULTI_BAND	3+ distinct y-clusters	-0.30
FRAC_MISMATCH (width)	fraction fired AND denominator x-range > 1.5× numerator	-0.30
FRAC_LEFT_SHIFT	fraction fired AND denominator starts > 0.5× numer-width to the left	-0.30
HUGE_OPERATOR	item with font_size > 1.3× median AND char in {∫ ∑ ∏ √ ∮ ∯ ∰}	-0.30
FONT_SIZE_VARIANCE	items in same y-band have > 2 distinct font sizes	-0.15

FormulaResult.confidence_breakdown: Vec<String> lists which penalties fired for each formula — useful for inspection and tuning.

Validation

Tested against PP-DocLayoutV3's actual formula bboxes from a formula-heavy academic test PDF (74 formulas).

Confidence band	Phase 1 (positive points only)	After calibration
HIGH (> 0.85)	60 (81%)	28 (37.8%)
MID (0.5 - 0.85)	16 (22%)	12 (16.2%)
LOW (< 0.5)	~24	34 (45.9%)
Mean confidence	~0.82	0.536

Manual inspection of the recalibrated bands:

• HIGH — all spot-checked entries produce structurally-correct LaTeX. Example: dW1\ndω → \frac{dW1}{d\omega}, region z ≪ 1. → region z \ll 1.
• MID — Greek/operator mapping correct, structural reconstruction uncertain. Caller-dependent: a strict orchestrator can fall back to OCR; a permissive one can use the LaTeX as-is.
• LOW — multi-row display equations where linearization fails. Should fall back to OCR. Examples include 8-band mega-formulas where even raw text is jumbled.

Quality note

This is intended as a Phase 1 baseline. The current heuristic does not handle:

• Matrices (\begin{matrix}...\end{matrix})
• Multi-line \begin{align} equations
• Bounded operators (\int_a^b, \sum_{i=0}^n)
• Nested fractions
• Delimiter pairs (\left( ... \right))

These are deliberately Phase 2 territory. They produce low-confidence output today so callers can route them to OCR.

API surface

pub fn extract_formulas_in_regions_as_latex(
    buffer: &[u8],
    page_regions: &[(u32, Vec<[f32; 4]>)],
) -> Result<Vec<PageFormulaResult>, PdfError>;

pub struct FormulaResult {
    pub latex: String,
    pub raw_text: String,
    pub confidence: f32,
    pub needs_ocr: bool,
    pub confidence_breakdown: Vec<String>,
}

NAPI mirror: extractFormulasInRegionsAsLatex(buffer, pageRegions): PageFormulaLatexResults[].

Test plan

• All previously-passing tests still pass — 393 lib + 104 integration + 2 doc
• 33 new unit tests — 8 penalty tests + 15 reconstruction tests + 10 unicode-map tests
• cargo clippy --lib --bin detect-pdf --bin pdf2md --bin dump_ops --bin probe-formulas --bin probe-formulas-latex -- -D warnings clean
• probe-formulas-latex binary added for manual quality inspection (compares raw-text vs LaTeX side-by-side with penalty breakdown per formula)