Pith Number

pith:4UDPGC5M

pith:2011:4UDPGC5MURY3LXUI4UC6B4OEA4

not attested not anchored not stored refs pending

Superconvergence of the $Q_{k+1,k}$-$Q_{k,k+1}$ divergence-free finite element

Shangyou Zhang, Yunqing Huang

arxiv:1112.3705 v1 · 2011-12-16 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4UDPGC5MURY3LXUI4UC6B4OEA4}

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	2026-05-18T04:06:09.072884Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e506f30baca471b5de88e505e0f1c40700c083359b95e9c794de204fadef1a0e

Aliases

arxiv: 1112.3705 · arxiv_version: 1112.3705v1 · doi: 10.48550/arxiv.1112.3705 · pith_short_12: 4UDPGC5MURY3 · pith_short_16: 4UDPGC5MURY3LXUI · pith_short_8: 4UDPGC5M

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/4UDPGC5MURY3LXUI4UC6B4OEA4 \
  | 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: e506f30baca471b5de88e505e0f1c40700c083359b95e9c794de204fadef1a0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e781f3f3d9062f0d9c33560b2ca2df84bbb0bd8f502e3ca4773fb50612ba799",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2011-12-16T03:30:38Z",
    "title_canon_sha256": "95327bb073ef9af23baac90072283360ac91141b2e17089a858f827a67ba9d2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.3705",
    "kind": "arxiv",
    "version": 1
  }
}