Pith Number

pith:BDXOEVJX

pith:2011:BDXOEVJX5MNIVILMOCI4MP6NUA

not attested not anchored not stored refs pending

Subharmonicity of the modulus of quasiregular harmonic mappings

David Kalaj, Vesna Manojlovi\'c

arxiv:1103.1032 v1 · 2011-03-05 · 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{BDXOEVJX5MNIVILMOCI4MP6NUA}

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	2026-05-18T04:27:17.238381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08eee25537eb1a8aa16c7091c63fcda02f009c69d0547ebe875f320f54718135

Aliases

arxiv: 1103.1032 · arxiv_version: 1103.1032v1 · doi: 10.48550/arxiv.1103.1032 · pith_short_12: BDXOEVJX5MNI · pith_short_16: BDXOEVJX5MNIVILM · pith_short_8: BDXOEVJX

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/BDXOEVJX5MNIVILMOCI4MP6NUA \
  | 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: 08eee25537eb1a8aa16c7091c63fcda02f009c69d0547ebe875f320f54718135

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a896910f9401db25e39fcf58a5709f225f0562fea018b44b89b1cb35580b4c97",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-03-05T09:38:17Z",
    "title_canon_sha256": "61f187e6c86ea0af955ff9c02248c86474338ca8ad69c3e4484b19e61042b356"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1032",
    "kind": "arxiv",
    "version": 1
  }
}