Pith Number

pith:4O5A5CEK

pith:2019:4O5A5CEKB63MSWIOK3KGQ3RCOI

not attested not anchored not stored refs pending

Large, lengthy graphs look locally like lines

Itai Benjamini, Tom Hutchcroft

arxiv:1905.00316 v3 · 2019-05-01 · math.MG · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4O5A5CEKB63MSWIOK3KGQ3RCOI}

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	2026-07-05T01:55:41.627047Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3ba0e888a0fb6c9590e56d4686e227202f36660fcd7e3536e61442d1ec310b2

Aliases

arxiv: 1905.00316 · arxiv_version: 1905.00316v3 · doi: 10.48550/arxiv.1905.00316 · pith_short_12: 4O5A5CEKB63M · pith_short_16: 4O5A5CEKB63MSWIO · pith_short_8: 4O5A5CEK

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/4O5A5CEKB63MSWIOK3KGQ3RCOI \
  | 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: e3ba0e888a0fb6c9590e56d4686e227202f36660fcd7e3536e61442d1ec310b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5f1cb3cedf4c1761e0a1aade4839f2361aba7a522af7e133694fc0435385c20",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2019-05-01T13:54:45Z",
    "title_canon_sha256": "213cd01bf7def487fddd1687d07079a6cb1009b6e7f61b11f81d8dd2e80c0304"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.00316",
    "kind": "arxiv",
    "version": 3
  }
}