Pith Number

pith:QKFHQYIO

pith:2019:QKFHQYIOFSDJZ2EYKEC6IM2HLA

not attested not anchored not stored refs pending

Commutators, matrices and an identity of Copeland

Darij Grinberg

arxiv:1908.09179 v1 · 2019-08-24 · math.RA · 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{QKFHQYIOFSDJZ2EYKEC6IM2HLA}

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	2026-07-04T23:59:37.368570Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

828a78610e2c869ce8985105e433475831fb5c390c7450b657773aaad71c1dd5

Aliases

arxiv: 1908.09179 · arxiv_version: 1908.09179v1 · doi: 10.48550/arxiv.1908.09179 · pith_short_12: QKFHQYIOFSDJ · pith_short_16: QKFHQYIOFSDJZ2EY · pith_short_8: QKFHQYIO

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/QKFHQYIOFSDJZ2EYKEC6IM2HLA \
  | 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: 828a78610e2c869ce8985105e433475831fb5c390c7450b657773aaad71c1dd5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be223a6a31df3a0e80524b867476e2e05754a7c0e324eb82021dc6de5bfe7fb2",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2019-08-24T18:12:08Z",
    "title_canon_sha256": "67ba7807191d46badffb85a4eb6a919a7dbde809454a482a0d291ab73ae78ce0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.09179",
    "kind": "arxiv",
    "version": 1
  }
}