Pith Number

pith:5TTBOCHO

pith:2016:5TTBOCHOQBQ5KRVHMV7C4R3P45

not attested not anchored not stored refs pending

MultiGrid Preconditioners for Mixed Finite Element Methods of Vector Laplacian

Jie Zhou, Lin Zhong, Long Chen, Yongke Wu

arxiv:1601.04095 v1 · 2016-01-15 · 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{5TTBOCHOQBQ5KRVHMV7C4R3P45}

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	2026-05-18T01:22:45.900737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ece61708ee8061d546a7657e2e476fe74379f6d11dca4d1f5e1e42835aa1769e

Aliases

arxiv: 1601.04095 · arxiv_version: 1601.04095v1 · doi: 10.48550/arxiv.1601.04095 · pith_short_12: 5TTBOCHOQBQ5 · pith_short_16: 5TTBOCHOQBQ5KRVH · pith_short_8: 5TTBOCHO

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/5TTBOCHOQBQ5KRVHMV7C4R3P45 \
  | 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: ece61708ee8061d546a7657e2e476fe74379f6d11dca4d1f5e1e42835aa1769e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bda9752aa483b150ab3d7f1e22123a6b4ba4d908bbbc386bfddfbcf8269b0119",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2016-01-15T22:58:01Z",
    "title_canon_sha256": "644aef324fe4fa88462001529f33c125dac86203a307bfea7db3ec7ec334be76"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.04095",
    "kind": "arxiv",
    "version": 1
  }
}