Pith Number

pith:GTZGPMHU

pith:2010:GTZGPMHUAUH3WSUAGN3HZESBXD

not attested not anchored not stored refs pending

The Hopf-Laplace equation: harmonicity and regularity

Jan Cristina, Jani Onninen, Leonid V. Kovalev, Tadeusz Iwaniec

arxiv:1011.5934 v2 · 2010-11-26 · math.CV · 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{GTZGPMHUAUH3WSUAGN3HZESBXD}

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	2026-05-18T03:39:06.538567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34f267b0f4050fbb4a8033767c9241b8dcf65b82c9733257e8d2bbb71e57b2bf

Aliases

arxiv: 1011.5934 · arxiv_version: 1011.5934v2 · doi: 10.48550/arxiv.1011.5934 · pith_short_12: GTZGPMHUAUH3 · pith_short_16: GTZGPMHUAUH3WSUA · pith_short_8: GTZGPMHU

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/GTZGPMHUAUH3WSUAGN3HZESBXD \
  | 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: 34f267b0f4050fbb4a8033767c9241b8dcf65b82c9733257e8d2bbb71e57b2bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9f04e54d9380a6112063d7c8764b5a454d302330aec9fffe88420adf9377075",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2010-11-26T22:53:43Z",
    "title_canon_sha256": "95a876bd58a50ca54cd032727080817685e6d9c8e867406b7c52936311f3030d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.5934",
    "kind": "arxiv",
    "version": 2
  }
}