Pith Number

pith:ZNMHIHLJ

pith:2018:ZNMHIHLJ5GYFVOMX2A4CJKPV6E

not attested not anchored not stored refs pending

A note on the set $\boldsymbol{A(A+A)}$

Fran\c{c}ois Hennecart, Ilya Shkredov, Pierre-Yves Bienvenu

arxiv:1811.08869 v2 · 2018-11-21 · 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{ZNMHIHLJ5GYFVOMX2A4CJKPV6E}

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	2026-05-17T23:44:58.475129Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb58741d69e9b05ab997d03824a9f5f101542a976251a78b8da5605553a38829

Aliases

arxiv: 1811.08869 · arxiv_version: 1811.08869v2 · doi: 10.48550/arxiv.1811.08869 · pith_short_12: ZNMHIHLJ5GYF · pith_short_16: ZNMHIHLJ5GYFVOMX · pith_short_8: ZNMHIHLJ

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/ZNMHIHLJ5GYFVOMX2A4CJKPV6E \
  | 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: cb58741d69e9b05ab997d03824a9f5f101542a976251a78b8da5605553a38829

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b758fd2c71fc39ce701bd54d77dd82540ffddd10d7a23352fc8607bfcd30f8c6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-11-21T18:28:14Z",
    "title_canon_sha256": "0054a14a581addfa51249279692ce9b9016ee35f034979704d1a61eb8851a7e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.08869",
    "kind": "arxiv",
    "version": 2
  }
}