---
id: F-027
title: Official NDL authentication of the Er97e threshold/shell passage
tier: gate
polarity: positive
depends_on: []
supersedes: []
verifier: cd verified_math/F-027_er97e-primary-source-authentication && ./verify.sh
date: 2026-07-12
---

## Statement

The official National Diet Library digitization PID `10996926` (DOI
`10.11501/10996926`) identifies *Mathematica Japonica* 46(3), November 1997,
and indexes P. Erdős, “Some of my favourite unsolved problems,” pp.527–537.
The digitized article's OCR content contains the #662 prose: a triangular-lattice
comparison function `f(t)`, an arbitrary separated point sequence, the question
whether its number of short distances is at most `f(t)` with equality perhaps
only for the triangular lattice, the particular clause, and the immediately
following stronger conjecture over the distance shells of the triangular
lattice.

More exactly, 28 pinned public NDL snippet responses from issue-content index
85 reconstruct OCR offsets 583 through 1525—943 consecutive characters—with
no missing offset and no conflicting overlap. Therefore the
absolute-threshold/shell passage is genuinely present in Erdős's 1997 primary
article. It is not a later catalog invention and is not the distinct
Vesztergombi 1987 theorem about multiplicities of the two smallest distance
values.

This gate fact authenticates source identity and prose/context. It does **not**
claim that the OCR recovers every displayed mathematical glyph: the NDL OCR
contains placeholders, missing subscripts, and obvious errors. No unique typo
repair or normalization is inferred here.

## Proof / verification

`verify.sh` first checks SHA-256 hashes of every capture and audit artifact,
then runs the offline semantic audit. The audit verifies:

1. item PID, DOI, title, volume, date, ISSN, collection, and `ooc` search
   permission;
2. the independent NDL Search SRU/DC-NDL title/page/date records;
3. the exact article index and content UUIDs (article start index 82, target
   index 85);
4. NDL's explicit anonymous snippet permission;
5. each of 28 responses, selected by target UUID and exact OCR offset;
6. agreement of every overlapping character, complete coverage of offsets
   583–1525, and byte-for-byte equality with the pinned reconstruction; and
7. the exact key phrases establishing the threshold comparison, equality
   question, particular clause, and stronger shell formulation.

No network request occurs during verification. `retrieve_primary_ocr.py` is
included only to document and reproduce the public API capture. The scan images
remain access-restricted; only the API-authorized snippets were used.

Artifacts:

- `artifacts/item_api.json`
- `artifacts/ndl_search_sru.xml`
- `artifacts/snippet_permission_api.json`
- `artifacts/snippet_api_capture.json`
- `artifacts/reconstructed_ocr.txt`
- `artifacts/audit_primary_ocr.py`
- `artifacts/retrieve_primary_ocr.py`
- `artifacts/README.md`
- `verify.sh`
