Pith Number

pith:4ZMEG3KO

pith:2017:4ZMEG3KOEENSL2OOPMRM5N7SO5

not attested not anchored not stored refs pending

On the few products, many sums problem

Brendan Murphy, Ilya D. Shkredov, Misha Rudnev, Yurii N. Shteinikov

arxiv:1712.00410 v1 · 2017-12-01 · 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{4ZMEG3KOEENSL2OOPMRM5N7SO5}

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	2026-05-18T00:29:06.293024Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e658436d4e211b25e9ce7b22ceb7f2777435ff1546b420ff7683f10a5fbd9e86

Aliases

arxiv: 1712.00410 · arxiv_version: 1712.00410v1 · doi: 10.48550/arxiv.1712.00410 · pith_short_12: 4ZMEG3KOEENS · pith_short_16: 4ZMEG3KOEENSL2OO · pith_short_8: 4ZMEG3KO

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/4ZMEG3KOEENSL2OOPMRM5N7SO5 \
  | 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: e658436d4e211b25e9ce7b22ceb7f2777435ff1546b420ff7683f10a5fbd9e86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f879a4e011e8aa4dd817ba454cf6beccdf84654607dd5e801d1f858db7a1b8e3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-12-01T17:13:15Z",
    "title_canon_sha256": "bb8a2579d2d796e2854b160438a98fce2425de405c23e43b99bf64a113a370ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.00410",
    "kind": "arxiv",
    "version": 1
  }
}