Pith Number

pith:J4VITNRG

pith:2010:J4VITNRGENXXVSIWXUKUNOBMF4

not attested not anchored not stored refs pending

Characterization and the pre-Schwarzian norm estimate for concave univalent functions

B. Bhowmik, K-J. Wirths, S. Ponnusamy

arxiv:1008.4861 v1 · 2010-08-28 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J4VITNRGENXXVSIWXUKUNOBMF4}

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	2026-05-18T04:41:43.534032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f2a89b626236f7ac916bd1546b82c2f38aedfa4829bc35465b3979654834744

Aliases

arxiv: 1008.4861 · arxiv_version: 1008.4861v1 · doi: 10.48550/arxiv.1008.4861 · pith_short_12: J4VITNRGENXX · pith_short_16: J4VITNRGENXXVSIW · pith_short_8: J4VITNRG

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/J4VITNRGENXXVSIWXUKUNOBMF4 \
  | 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: 4f2a89b626236f7ac916bd1546b82c2f38aedfa4829bc35465b3979654834744

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73e88f7d7ca55840ef85133589f4877a0e144be1a50976b2d7b3b55222e70e83",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2010-08-28T12:50:46Z",
    "title_canon_sha256": "56c37d6d04639cf0ced75b4ecfc9f17fc70a4e8d6de2733ab944e0f2dad85e30"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.4861",
    "kind": "arxiv",
    "version": 1
  }
}