Pith Number

pith:BHQOHL3A

pith:2001:BHQOHL3AOZ4PJCAVSN6EEBNZV4

not attested not anchored not stored refs pending

Commensurability of graph products

Jacek Swiatkowski, Tadeusz Januszkiewicz

arxiv:math/0111239 v1 · 2001-11-21 · 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{BHQOHL3AOZ4PJCAVSN6EEBNZV4}

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	2026-05-18T02:41:33.174628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09e0e3af607678f48815937c4205b9af0fa795dcb58f7e3015a750eebc2c0d25

Aliases

arxiv: math/0111239 · arxiv_version: math/0111239v1 · doi: 10.48550/arxiv.math/0111239 · pith_short_12: BHQOHL3AOZ4P · pith_short_16: BHQOHL3AOZ4PJCAV · pith_short_8: BHQOHL3A

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/BHQOHL3AOZ4PJCAVSN6EEBNZV4 \
  | 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: 09e0e3af607678f48815937c4205b9af0fa795dcb58f7e3015a750eebc2c0d25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f5e894fcd05046a4c96d46db4490f6fff8f9508a819f9a6c6d44264bb8e771b",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2001-11-21T19:47:18Z",
    "title_canon_sha256": "e9f20bad5f9b7c69979738a3ec5fc762e96a30ccec487c10ee46a9d1c680fc5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0111239",
    "kind": "arxiv",
    "version": 1
  }
}