Pith Number

pith:P7K3U7S7

pith:2013:P7K3U7S7ACMQM3LPK2UNGC2XCW

not attested not anchored not stored refs pending

Graham's Number is Less Than 2^^^6

John Mackey, Mikhail Lavrov, Mitchell Lee

arxiv:1304.6910 v2 · 2013-04-25 · 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{P7K3U7S7ACMQM3LPK2UNGC2XCW}

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	2026-05-18T03:15:05.905657Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fd5ba7e5f0099066d6f56a8d30b5715b15417e13f4cd6ee761c12aec1de15da

Aliases

arxiv: 1304.6910 · arxiv_version: 1304.6910v2 · doi: 10.48550/arxiv.1304.6910 · pith_short_12: P7K3U7S7ACMQ · pith_short_16: P7K3U7S7ACMQM3LP · pith_short_8: P7K3U7S7

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/P7K3U7S7ACMQM3LPK2UNGC2XCW \
  | 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: 7fd5ba7e5f0099066d6f56a8d30b5715b15417e13f4cd6ee761c12aec1de15da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e2240c8555b4f573b3332647cae99e9b4cdc0d7dc5de487427780a50193b72f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-04-25T13:50:35Z",
    "title_canon_sha256": "1e52cc9512379c9076b722627db79fbb5e852933fb103e13c8c2ccddf0f1aa02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.6910",
    "kind": "arxiv",
    "version": 2
  }
}