Pith Number

pith:5Z2QAKKJ

pith:2019:5Z2QAKKJSR2EPJ2Q3NVP43CGNE

not attested not anchored not stored refs pending

General superpositions of Gaussian beams and propagation errors

Hailiang Liu, James Ralston, Peimeng Yin

arxiv:1905.09090 v1 · 2019-05-22 · 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{5Z2QAKKJSR2EPJ2Q3NVP43CGNE}

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	2026-05-17T23:45:22.008021Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee75002949947447a750db6afe6c46693cf7c0020d27b3c1c4b947c10959c51d

Aliases

arxiv: 1905.09090 · arxiv_version: 1905.09090v1 · doi: 10.48550/arxiv.1905.09090 · pith_short_12: 5Z2QAKKJSR2E · pith_short_16: 5Z2QAKKJSR2EPJ2Q · pith_short_8: 5Z2QAKKJ

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/5Z2QAKKJSR2EPJ2Q3NVP43CGNE \
  | 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: ee75002949947447a750db6afe6c46693cf7c0020d27b3c1c4b947c10959c51d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7564f6600d79e43eb8783df316394b15122e8543647e3f05b0a5f6407d39150c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2019-05-22T12:01:46Z",
    "title_canon_sha256": "e9094bf5cfed377edac3a8e409ed9db212548b8bdb8d9435e3667b12d22b5ac9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.09090",
    "kind": "arxiv",
    "version": 1
  }
}