Pith Number

pith:5BEGQ4NQ

pith:2015:5BEGQ4NQIDJEKAN3NJ7UVVIJTU

not attested not anchored not stored refs pending

Free Pluriharmonic Functions on Noncommutative Polyballs

Gelu Popescu

arxiv:1511.08852 v2 · 2015-11-27 · math.OA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5BEGQ4NQIDJEKAN3NJ7UVVIJTU}

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	2026-05-18T01:17:11.475136Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8486871b040d24501bb6a7f4ad5099d090b871e0d08862a52ae26032c91d039

Aliases

arxiv: 1511.08852 · arxiv_version: 1511.08852v2 · doi: 10.48550/arxiv.1511.08852 · pith_short_12: 5BEGQ4NQIDJE · pith_short_16: 5BEGQ4NQIDJEKAN3 · pith_short_8: 5BEGQ4NQ

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/5BEGQ4NQIDJEKAN3NJ7UVVIJTU \
  | 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: e8486871b040d24501bb6a7f4ad5099d090b871e0d08862a52ae26032c91d039

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6a4b076838f4b24f92b937fb345fa19ba25b6565f64acf1ae88cee865e14701",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-11-27T23:40:43Z",
    "title_canon_sha256": "b10d14fed62a4ef3d876b5b797265629775ee02b05200cdea709d2b5d7889bbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.08852",
    "kind": "arxiv",
    "version": 2
  }
}