Pith Number

pith:PJA5OQKK

pith:2010:PJA5OQKKDYUUWHDQL7LJVXT4PY

not attested not anchored not stored refs pending

Bounds on three- and higher-distance sets

Hiroshi Nozaki, Oleg R. Musin

arxiv:1005.2639 v2 · 2010-05-14 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PJA5OQKKDYUUWHDQL7LJVXT4PY}

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	2026-05-18T04:14:55.198077Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a41d7414a1e294b1c705fd69ade7c7e17d58d7028bd54dceece172f5efb41b8

Aliases

arxiv: 1005.2639 · arxiv_version: 1005.2639v2 · doi: 10.48550/arxiv.1005.2639 · pith_short_12: PJA5OQKKDYUU · pith_short_16: PJA5OQKKDYUUWHDQ · pith_short_8: PJA5OQKK

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/PJA5OQKKDYUUWHDQL7LJVXT4PY \
  | 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: 7a41d7414a1e294b1c705fd69ade7c7e17d58d7028bd54dceece172f5efb41b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5dfe02fdb9beddd25474efe5182636e301946c1dd2e049670ff331933ea37a3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-05-14T23:12:57Z",
    "title_canon_sha256": "ba3f5a7e14348e9ebe94e68a63d8c35b100eab7e4f3a532928c4353cb17cc277"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.2639",
    "kind": "arxiv",
    "version": 2
  }
}