Pith Number

pith:AJG5TEGF

pith:2014:AJG5TEGF2Z7I5PNSUW6VHWJALU

not attested not anchored not stored refs pending

Approximate subgroups

Frank Olaf Wagner (ICJ), Jean-Cyrille Massicot

arxiv:1406.6007 v3 · 2014-06-23 · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AJG5TEGF2Z7I5PNSUW6VHWJALU}

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	2026-05-18T02:25:26.453790Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

024dd990c5d67e8ebdb2a5bd53d9205d09e2f2ada27a66fe26e235407db1cf54

Aliases

arxiv: 1406.6007 · arxiv_version: 1406.6007v3 · doi: 10.48550/arxiv.1406.6007 · pith_short_12: AJG5TEGF2Z7I · pith_short_16: AJG5TEGF2Z7I5PNS · pith_short_8: AJG5TEGF

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/AJG5TEGF2Z7I5PNSUW6VHWJALU \
  | 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: 024dd990c5d67e8ebdb2a5bd53d9205d09e2f2ada27a66fe26e235407db1cf54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20375a66d98ec72dd4f28a778b0b0265ed8f9e40114ba0bc8afa026d934b0d7e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2014-06-23T17:50:07Z",
    "title_canon_sha256": "78a761b8bb0dd950c99126fa3bef9a7afb4bd9c2113ec31d07f880a93f229157"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.6007",
    "kind": "arxiv",
    "version": 3
  }
}