Pith Number

pith:MQEUBRIO

pith:2010:MQEUBRIOI3RYQMYE57PDZ4JJR7

not attested not anchored not stored refs pending

Square-free values of $n^2+1$

D. R. Heath-Brown

arxiv:1010.6217 v3 · 2010-10-29 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MQEUBRIOI3RYQMYE57PDZ4JJR7}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:56:08.685987Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

640940c50e46e3883304efde3cf1298fe5f619d8d3f9db89318d20d519fb4da0

Aliases

arxiv: 1010.6217 · arxiv_version: 1010.6217v3 · doi: 10.48550/arxiv.1010.6217 · pith_short_12: MQEUBRIOI3RY · pith_short_16: MQEUBRIOI3RYQMYE · pith_short_8: MQEUBRIO

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MQEUBRIOI3RYQMYE57PDZ4JJR7 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 640940c50e46e3883304efde3cf1298fe5f619d8d3f9db89318d20d519fb4da0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d06749e58439bde84f69ce34d542d58bd602cb49110022f1ba9b35832d0348c4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-10-29T14:19:50Z",
    "title_canon_sha256": "4f90877ea915734293979c6ce7c1b8c4b993b0363568036af42c70e96d2251aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.6217",
    "kind": "arxiv",
    "version": 3
  }
}