Pith Number

pith:KJDK45CE

pith:2011:KJDK45CEWRTUSQMSCPPHDBFV2S

not attested not anchored not stored refs pending

A Groupoid Structure on a Vector Space

Gheorghe Ivan, Vasile Poputa

arxiv:1101.1405 v1 · 2011-01-07 · 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{KJDK45CEWRTUSQMSCPPHDBFV2S}

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	2026-05-18T04:31:59.589680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5246ae7444b46749419213de7184b5d4b0ce6d7e730ce1b4a7cd39fc3ce5d69f

Aliases

arxiv: 1101.1405 · arxiv_version: 1101.1405v1 · doi: 10.48550/arxiv.1101.1405 · pith_short_12: KJDK45CEWRTU · pith_short_16: KJDK45CEWRTUSQMS · pith_short_8: KJDK45CE

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/KJDK45CEWRTUSQMSCPPHDBFV2S \
  | 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: 5246ae7444b46749419213de7184b5d4b0ce6d7e730ce1b4a7cd39fc3ce5d69f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dae96677f08124360bfafa67acac5f6028e519f0b4eb6d6f7130ee7306fde383",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-01-07T11:21:36Z",
    "title_canon_sha256": "c6180d1edf14c6728c5a99853e09b60d818f8e35aa625ba63192e351a88c4e57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.1405",
    "kind": "arxiv",
    "version": 1
  }
}