Pith Number

pith:4N43WI2J

pith:2013:4N43WI2JN7RBWKSL7QHBWYEP5C

not attested not anchored not stored refs pending

Gaussian Beam Methods for the Helmholtz Equation

Hailiang Liu, James Ralston, Nicolay M. Tanushev, Olof Runborg

arxiv:1304.1291 v1 · 2013-04-04 · 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{4N43WI2JN7RBWKSL7QHBWYEP5C}

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	2026-05-18T03:29:04.097170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e379bb23496fe21b2a4bfc0e1b608fe89ea39340aa2752c36350959911e45d9b

Aliases

arxiv: 1304.1291 · arxiv_version: 1304.1291v1 · doi: 10.48550/arxiv.1304.1291 · pith_short_12: 4N43WI2JN7RB · pith_short_16: 4N43WI2JN7RBWKSL · pith_short_8: 4N43WI2J

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/4N43WI2JN7RBWKSL7QHBWYEP5C \
  | 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: e379bb23496fe21b2a4bfc0e1b608fe89ea39340aa2752c36350959911e45d9b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebd10550b1bce0b3d51f320b9d5d4c65361e8d40117a5b9d685b05f99e43b4fe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2013-04-04T09:46:03Z",
    "title_canon_sha256": "19bf43a891e1da46b0cd625630b35ec5e53a43c25dcbd2cc3dd01621d995be08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.1291",
    "kind": "arxiv",
    "version": 1
  }
}