Pith Number

pith:USEFG3HS

pith:2019:USEFG3HS5QRSNY4ZOUHVOOYOYJ

not attested not anchored not stored refs pending

Free group representations: duplicity on the boundary

M.Gabriella Kuhn, Tim Steger, Waldemar Hebisch

arxiv:1905.03011 v1 · 2019-05-08 · 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{USEFG3HS5QRSNY4ZOUHVOOYOYJ}

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	2026-05-17T23:46:43.170230Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a488536cf2ec2326e399750f573b0ec25eb8aeda17db741c3a60b9c9df454910

Aliases

arxiv: 1905.03011 · arxiv_version: 1905.03011v1 · doi: 10.48550/arxiv.1905.03011 · pith_short_12: USEFG3HS5QRS · pith_short_16: USEFG3HS5QRSNY4Z · pith_short_8: USEFG3HS

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/USEFG3HS5QRSNY4ZOUHVOOYOYJ \
  | 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: a488536cf2ec2326e399750f573b0ec25eb8aeda17db741c3a60b9c9df454910

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a557d32231f0eadf6062155a56dcf0cddbb9500b98931ca566eff42991120e6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-05-08T11:28:00Z",
    "title_canon_sha256": "046add678152fb6bf5dfe2561b91cbef5a3a9ac859836b681d1338f18b6951b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.03011",
    "kind": "arxiv",
    "version": 1
  }
}