Pith Number

pith:HLYMHYJ6

pith:2018:HLYMHYJ6HOZZS25JTQ2DLMUDW2

not attested not anchored not stored refs pending

Interleaved group products

Emanuele Viola, W. T. Gowers

arxiv:1804.09787 v1 · 2018-04-25 · math.CO · cs.CC · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HLYMHYJ6HOZZS25JTQ2DLMUDW2}

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	2026-05-18T00:17:27.917399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3af0c3e13e3bb3996ba99c3435b283b6a0b09c7344024099b93d413fc2cc319d

Aliases

arxiv: 1804.09787 · arxiv_version: 1804.09787v1 · doi: 10.48550/arxiv.1804.09787 · pith_short_12: HLYMHYJ6HOZZ · pith_short_16: HLYMHYJ6HOZZS25J · pith_short_8: HLYMHYJ6

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/HLYMHYJ6HOZZS25JTQ2DLMUDW2 \
  | 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: 3af0c3e13e3bb3996ba99c3435b283b6a0b09c7344024099b93d413fc2cc319d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4bd32ee3b4066e315f4948a27b90ac92d634c47d8c96b4ff9075243e1e94940",
    "cross_cats_sorted": [
      "cs.CC",
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-04-25T20:18:58Z",
    "title_canon_sha256": "241a0206bde8da6deb36ee39280def11f7cb312137401d467bca1c7e3339239d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.09787",
    "kind": "arxiv",
    "version": 1
  }
}