Pith Number

pith:KHU45LS6

pith:2010:KHU45LS6L5ZOXBPCGLDG2UCZ6G

not attested not anchored not stored refs pending

Sweeping Preconditioner for the Helmholtz Equation: Hierarchical Matrix Representation

Bj\"orn Engquist, Lexing Ying

arxiv:1007.4290 v2 · 2010-07-25 · 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{KHU45LS6L5ZOXBPCGLDG2UCZ6G}

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	2026-05-18T04:42:43.120872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51e9ceae5e5f72eb85e232c66d5059f1a98a048ec9bd654dde97c5c8633044a9

Aliases

arxiv: 1007.4290 · arxiv_version: 1007.4290v2 · doi: 10.48550/arxiv.1007.4290 · pith_short_12: KHU45LS6L5ZO · pith_short_16: KHU45LS6L5ZOXBPC · pith_short_8: KHU45LS6

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/KHU45LS6L5ZOXBPCGLDG2UCZ6G \
  | 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: 51e9ceae5e5f72eb85e232c66d5059f1a98a048ec9bd654dde97c5c8633044a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dee1b230acd540007eed3ef4ca2ffbb9f78a54e31013305875cb646f1d845462",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2010-07-25T00:40:14Z",
    "title_canon_sha256": "7be072c8a6b8b2c058fb02abce3172ca5c8cae478d9301141c8f3091f22e894e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.4290",
    "kind": "arxiv",
    "version": 2
  }
}