Pith Number

pith:PWOBA3WH

pith:2011:PWOBA3WHVAG4F2NEWVR7XJMD7H

not attested not anchored not stored refs pending

Lean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear Solver (Journal Version)

Achi Brandt, Oren E. Livne

arxiv:1108.1310 v2 · 2011-08-05 · 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{PWOBA3WHVAG4F2NEWVR7XJMD7H}

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	2026-05-18T03:54:04.415144Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d9c106ec7a80dc2e9a4b563fba583f9d8f161d2b3c981484a516dfdb7bf851f

Aliases

arxiv: 1108.1310 · arxiv_version: 1108.1310v2 · doi: 10.48550/arxiv.1108.1310 · pith_short_12: PWOBA3WHVAG4 · pith_short_16: PWOBA3WHVAG4F2NE · pith_short_8: PWOBA3WH

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/PWOBA3WHVAG4F2NEWVR7XJMD7H \
  | 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: 7d9c106ec7a80dc2e9a4b563fba583f9d8f161d2b3c981484a516dfdb7bf851f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "619d1e8fca404776c05c27b09eb7af251ab8c61ce005a376d445f7d53bca9fcc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2011-08-05T12:04:00Z",
    "title_canon_sha256": "2a89d9ca044bed5b8f839121443c3393e9e7e9d669de0f0b418627c4579e2e44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1310",
    "kind": "arxiv",
    "version": 2
  }
}