# Primary-source recovery: Erdős 1997, p. 532

This directory pins a public, official National Diet Library (Japan) record and
its public full-text-search snippets for:

> P. Erdős, “Some of my favourite unsolved problems,” *Mathematica Japonica*
> 46(3) (1997), 527–537.

Permanent issue identifier: **NDL PID 10996926**, DOI
[`10.11501/10996926`](https://doi.org/10.11501/10996926).

## Why snippets are used

The NDL metadata labels this scan `ooc`: its images are available at the NDL,
partner libraries, or through registered personal transmission. Anonymous image
viewing is therefore not authorized. The NDL API separately reports
`ooc/snippet = true`, and its public full-text endpoint returns short OCR
windows. No access restriction was bypassed.

`retrieve_primary_ocr.py` records:

1. the unmodified NDL item-metadata response;
2. an independent NDL Search SRU/DC-NDL record;
3. the NDL's explicit snippet permission response; and
4. 28 overlapping public OCR snippets from content index 85 of the digitized
   issue.

The capture is already pinned. Network access is **not** part of verification.
To audit it offline, run:

```bash
python3 check_answer/references/ndl_primary/audit_primary_ocr.py
```

The audit identifies the issue, volume/date/ISSN/DOI, article title and pages;
checks the article's start content and the target content UUID; selects each
snippet by exact OCR offset; and proves that their 943 characters overlap with
no conflict or gap.

## What the primary OCR establishes

The reconstructed passage itself says, in sequence:

- “Consider the triangular lattice … denote by `f(t)` …”;
- “Let … be any sequence of points” satisfying the separation condition;
- asks whether “the number of distances is less than or equal to `f(t)`,” with
  equality perhaps only for the triangular lattice;
- asks the “In particular” question; and
- immediately proposes the “stronger conjecture” using the set of distances
  occurring in the triangular lattice.

Thus the absolute-threshold/shell passage really occurs in Erdős's 1997
article. It is not a later catalog invention and is not the distinct 1987
Vesztergombi theorem about the multiplicities of the two smallest distances.

Mathematical glyph recognition in the NDL OCR is poor (`〓`, missing subscripts,
and errors such as `aquality` for “equality”). The audit therefore does **not**
claim that OCR alone recovers every displayed formula. The maintained catalog
transcription supplies those glyphs; the primary OCR authenticates the prose,
context, `f(t)` comparison, triangular equality question, particular clause,
and stronger shell formulation. The checker treats all surviving formula/count
normalizations separately rather than repairing an unread glyph silently.
