Pith Number

pith:QOGFYICZ

pith:2013:QOGFYICZUCVZSXP6JBL656DWTU

not attested not anchored not stored refs pending

Small doubling in groups

Ben Green, Emmanuel Breuillard, Terence Tao

arxiv:1301.7718 v1 · 2013-01-31 · 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{QOGFYICZUCVZSXP6JBL656DWTU}

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	2026-05-18T03:34:48.838093Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

838c5c2059a0ab995dfe4857eef8769d0e80705b505ccc33e9d52e8435ac5afd

Aliases

arxiv: 1301.7718 · arxiv_version: 1301.7718v1 · doi: 10.48550/arxiv.1301.7718 · pith_short_12: QOGFYICZUCVZ · pith_short_16: QOGFYICZUCVZSXP6 · pith_short_8: QOGFYICZ

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/QOGFYICZUCVZSXP6JBL656DWTU \
  | 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: 838c5c2059a0ab995dfe4857eef8769d0e80705b505ccc33e9d52e8435ac5afd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fceb90e8596d1ddcc58715679e83ea9de93d426e5d4ba8746427c2518eced7a1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-01-31T19:08:30Z",
    "title_canon_sha256": "8f685bccb53c6a025aa835e41257ae77d91566595c67e6e0e9234e2f4665251f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.7718",
    "kind": "arxiv",
    "version": 1
  }
}