What went wrong, and
what was done about it.

Every report carries the same six columns. Identifier · Page · Conf. · LaTeX source · Rendered · Scan image — the equation's id, the page it sits on, MathPix's confidence in its own reading, that reading as LaTeX, the LaTeX rendered, and the crop the reading came from. The coloured square is the confidence: ■ ≥0.9, ■ 0.5–0.9, ■ <0.5, and — for no value.

Seventeen carry a second reading. An inkdrill residual measured between the rendered LaTeX and the scan, knowing nothing about the confidence value, printed as a coloured bullet with a selectable code: • C component, • W weak, • S stable, • U unrendered, • N noise, • K clean. The Residual column above is that distribution per report, and report.ink.json carries the measurements machine-readably. The two instruments disagree usefully — neither predicts the other.

Four do not, and the reason is the point of the column. A residual is only worth printing if each one is attached to the right equation, and rows pair to identifiers by position. Where that pairing cannot be shown to hold, no residual is published rather than a plausible one.

• BradleyGastaldiTerilla2023 — not measured. The lattice finds 16 rows for 8 equations on a single page. A count taken after pairing would truncate to 8 and look correct while every row was 2:1 mispaired; the check that catches it compares raw detected rows against identifiers, before truncation.
• 0902.0431 — withdrawn, having previously been published here. The lattice detects 55 rows for 57 identifiers: two equations, on report pages 13 and 19, are not detected at all. The cause is enclosure, not size — the lattice builds rows from background enclosed inside the table region, and content spanning from rule to rule leaves none, so the row does not exist as far as it is concerned. Page 13 yields 8 holes, all in the header band, against page 12’s 27; row coverage 0.015 against a corpus median of 0.986. Height only correlates, because a tall row is likelier to span. A row missing mid-sequence does not truncate, it shifts — so from page 13 on, each residual was attached to the following equation. Confirmed by recovering identifiers page by page from the published PDF: exact through page 12, then exactly one displacement per page, always forward, ten of them with no exception. That report has since been rebuilt without the residual apparatus, so the PDF above carries no bullets at all rather than wrong ones; its Conf. column, LaTeX, renders and crops were never affected. If you downloaded its report.ink.json before 2026-08-24, discard it.
• penev_B — no ink pass yet. It was drilled after the residual pipeline stalled on two open lattice defects, so nothing has been measured against its scans. Not a refusal and not a withdrawal: simply not done. The Conf. column is complete.

One carries a second reading of a different kind. The Penev scan was OCR’d once in 2023 and again in 2026. The 2023 pass was merged into a single LaTeX document and hand-corrected until it compiled; that reconstruction is attached to the 2026 model as a competing tex provenance and scored against it, which is what the compare link opens: one row per equation, both readings rendered side by side, with the scan crop between them.

• penev_B — 59 of 62 have both. 25 agree exactly, 15 score 0.90–0.99, 5 score 0.70–0.89, and 14 fall below 0.70. Mean 0.874.

This is not a gold column. The author’s LaTeX for this thesis does not exist here — the source is a 1998 print, scanned four pages to a sheet. What the tex column holds is one reader’s corrected transcription, so a disagreement means the two passes differ, not that the OCR is wrong. That is the useful shape: the rows below 0.70 are where a human once decided the machine had misread something, and they are the first place to look.

Equations counts what is in the report, not what is in the document. 0902.0431 is filtered to --max-conf 0.5 --types equation, so its 57 rows are the 57 display equations MathPix doubted out of 1,219. The other seven are unfiltered: every display equation in the document, at whatever confidence.

Sources are linked where they resolve. Crops are excerpts of the papers named above, reproduced for verification of the extraction.