Pith Number

pith:65URATFJ

pith:2024:65URATFJK76HMBELJT4XRFCWZ6

not attested not anchored not stored refs pending

Optimal error bounds on an exponential wave integrator Fourier spectral method for the logarithmic Schr\"odinger equation

Chushan Wang, Weizhu Bao, Ying Ma

arxiv:2412.16902 v3 · 2024-12-22 · math.NA · cs.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{65URATFJK76HMBELJT4XRFCWZ6}

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	2026-07-05T12:01:20.289117Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f769104ca957fc76048b4cf9789456cf946ca0a4a25efe4edab594b10c7c4d80

Aliases

arxiv: 2412.16902 · arxiv_version: 2412.16902v3 · doi: 10.48550/arxiv.2412.16902 · pith_short_12: 65URATFJK76H · pith_short_16: 65URATFJK76HMBEL · pith_short_8: 65URATFJ

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/65URATFJK76HMBELJT4XRFCWZ6 \
  | 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: f769104ca957fc76048b4cf9789456cf946ca0a4a25efe4edab594b10c7c4d80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4f69a2f1edb970ca937bb96369c17ab21ab1b0af3458154ae230a0feca3b361",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2024-12-22T07:24:24Z",
    "title_canon_sha256": "ae680f978be5453b749ccdbecd52ba8fd0b94adf2d459a3d16e6d0246a41473f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.16902",
    "kind": "arxiv",
    "version": 3
  }
}