Pith Number

pith:GGDBYSUI

pith:2015:GGDBYSUIH3AQLOLUV5GZG5K3VJ

not attested not anchored not stored refs pending

Critical surface of the 1-2 model

Geoffrey R. Grimmett, Zhongyang Li

arxiv:1506.08406 v3 · 2015-06-28 · math.PR · math-ph · math.CO · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GGDBYSUIH3AQLOLUV5GZG5K3VJ}

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	2026-05-18T00:49:00.202259Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31861c4a883ec105b974af4d93755baa464cb32361192eb7ccbb2c8bf868bdbc

Aliases

arxiv: 1506.08406 · arxiv_version: 1506.08406v3 · doi: 10.48550/arxiv.1506.08406 · pith_short_12: GGDBYSUIH3AQ · pith_short_16: GGDBYSUIH3AQLOLU · pith_short_8: GGDBYSUI

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/GGDBYSUIH3AQLOLUV5GZG5K3VJ \
  | 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: 31861c4a883ec105b974af4d93755baa464cb32361192eb7ccbb2c8bf868bdbc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "026c359755921844a3c783b95f3f5368ed1a9653afe5d5ced01e2e5fdc89188f",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-06-28T14:31:01Z",
    "title_canon_sha256": "396a09b1c0573a26b6e6040d3dd04545badacfc6a82505285327fe2e20724168"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.08406",
    "kind": "arxiv",
    "version": 3
  }
}