Pith Number

pith:VI56UDTQ

pith:2021:VI56UDTQCWC4J7HGS2H4DPOLED

not attested not anchored not stored refs pending

Product Expansions Redux

Karsten Henckell, Samuel Herman

arxiv:2110.11513 v1 · 2021-10-21 · math.GR · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VI56UDTQCWC4J7HGS2H4DPOLED}

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	2026-07-05T03:24:47.887140Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa3bea0e701585c4fce6968fc1bdcb20d55d20515d3d16c3db3526eb14ce2ef9

Aliases

arxiv: 2110.11513 · arxiv_version: 2110.11513v1 · doi: 10.48550/arxiv.2110.11513 · pith_short_12: VI56UDTQCWC4 · pith_short_16: VI56UDTQCWC4J7HG · pith_short_8: VI56UDTQ

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/VI56UDTQCWC4J7HGS2H4DPOLED \
  | 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: aa3bea0e701585c4fce6968fc1bdcb20d55d20515d3d16c3db3526eb14ce2ef9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16e446b74801774a708599c557b533cf0d6b5bc2cd98a29f9efd87edb546817f",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2021-10-21T23:00:39Z",
    "title_canon_sha256": "70101c03a2e90a0afc0602fffe567fcf13291f4ba26517a696e57f7e36254198"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.11513",
    "kind": "arxiv",
    "version": 1
  }
}