Pith Number

pith:PO5D2AX6

pith:2012:PO5D2AX6N7HJGZ7PUNCKIOD5L6

not attested not anchored not stored refs pending

Numerical Study of Geometric Multigrid Methods on CPU--GPU Heterogeneous Computers

Chen-Song Zhang, Chunsheng Feng, Jinchao Xu, Shi Shu

arxiv:1208.4247 v2 · 2012-08-21 · math.NA · cs.NA · physics.comp-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PO5D2AX6N7HJGZ7PUNCKIOD5L6}

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	2026-05-18T03:36:46.333603Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bba3d02fe6fce9367efa344a4387d5f8b044c6d836813b3b85506b0ed864d3a

Aliases

arxiv: 1208.4247 · arxiv_version: 1208.4247v2 · doi: 10.48550/arxiv.1208.4247 · pith_short_12: PO5D2AX6N7HJ · pith_short_16: PO5D2AX6N7HJGZ7P · pith_short_8: PO5D2AX6

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/PO5D2AX6N7HJGZ7PUNCKIOD5L6 \
  | 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: 7bba3d02fe6fce9367efa344a4387d5f8b044c6d836813b3b85506b0ed864d3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c52a8c081692959bbffc576b148f5761931a41de4afb65641d05098f92d74254",
    "cross_cats_sorted": [
      "cs.NA",
      "physics.comp-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2012-08-21T12:24:17Z",
    "title_canon_sha256": "a3d98cac81b1205f0c487100f44700181b41320c39a3e26b73dc9bc4b684a623"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4247",
    "kind": "arxiv",
    "version": 2
  }
}