Pith Number

pith:4ENOZDEL

pith:2009:4ENOZDELGL2PAZHBMNBVZXKYH3

not attested not anchored not stored refs pending

Denjoy-Ahlfors Theorem for Harmonic Functions on Riemannian Manifolds and External Structure of Minimal Surfaces

Vladimir G. Tkachev, Vladimir M. Miklyukov

arxiv:0903.2326 v1 · 2009-03-13 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4ENOZDELGL2PAZHBMNBVZXKYH3}

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	2026-05-18T00:18:05.595667Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e11aec8c8b32f4f064e163435cdd583ee053cb3f0d9078f5f2af00bdc06b4a38

Aliases

arxiv: 0903.2326 · arxiv_version: 0903.2326v1 · doi: 10.48550/arxiv.0903.2326 · pith_short_12: 4ENOZDELGL2P · pith_short_16: 4ENOZDELGL2PAZHB · pith_short_8: 4ENOZDEL

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/4ENOZDELGL2PAZHBMNBVZXKYH3 \
  | 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: e11aec8c8b32f4f064e163435cdd583ee053cb3f0d9078f5f2af00bdc06b4a38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e3371b5022428a8e3d00696b28c5c52f39e7c07fc8a878b18725d8a07fa2465",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-03-13T07:36:39Z",
    "title_canon_sha256": "4eac793fe6284c1650bcc3cbac70e7dd2d2c7429df7eed92875b1f688aa6fbf7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.2326",
    "kind": "arxiv",
    "version": 1
  }
}