Pith Number

pith:5HO4VW6Y

pith:2016:5HO4VW6YP4OGRH4S23HYYRX3WN

not attested not anchored not stored refs pending

Difference sets are not multiplicatively closed

Ilya D. Shkredov

arxiv:1602.02360 v4 · 2016-02-07 · math.NT · 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{5HO4VW6YP4OGRH4S23HYYRX3WN}

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	2026-05-18T01:03:30.783171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9ddcadbd87f1c689f92d6cf8c46fbb354719c23d2d94a931a2d1fb074340590

Aliases

arxiv: 1602.02360 · arxiv_version: 1602.02360v4 · doi: 10.48550/arxiv.1602.02360 · pith_short_12: 5HO4VW6YP4OG · pith_short_16: 5HO4VW6YP4OGRH4S · pith_short_8: 5HO4VW6Y

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/5HO4VW6YP4OGRH4S23HYYRX3WN \
  | 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: e9ddcadbd87f1c689f92d6cf8c46fbb354719c23d2d94a931a2d1fb074340590

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63ad85b61729e7339c1e7cea1a14e178a477e2384ee5c25918c3f87573aaeaf1",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-02-07T11:13:37Z",
    "title_canon_sha256": "47f64aef430e5d5119adae0b7c1e1607d064eda23f1c13800c83d42ab556018f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.02360",
    "kind": "arxiv",
    "version": 4
  }
}