Pith Number

pith:54SNQIYJ

pith:2022:54SNQIYJ2F462TO55UO3L72MDN

not attested not anchored not stored refs pending

On the equivalence of classical Helmholtz equation and fractional Helmholtz equation with arbitrary order

Dong Li, Wen Yang, Xinyu Cheng

arxiv:2203.12419 v2 · 2022-03-23 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{54SNQIYJ2F462TO55UO3L72MDN}

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	2026-07-05T05:04:12.561997Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef24d82309d179ed4ddded1db5ff4c1b5ca5a15736ff9aa80466b0bbca789cbb

Aliases

arxiv: 2203.12419 · arxiv_version: 2203.12419v2 · doi: 10.48550/arxiv.2203.12419 · pith_short_12: 54SNQIYJ2F46 · pith_short_16: 54SNQIYJ2F462TO5 · pith_short_8: 54SNQIYJ

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/54SNQIYJ2F462TO55UO3L72MDN \
  | 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: ef24d82309d179ed4ddded1db5ff4c1b5ca5a15736ff9aa80466b0bbca789cbb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32085bdbea963432ce9987e2b01b36bd1eb869a3e379cce2c05644ec7d34c71f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2022-03-23T13:56:29Z",
    "title_canon_sha256": "cf71cb724badad2a7db00a74eba5646120d6175f31f56e47c7b550b857acbd80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2203.12419",
    "kind": "arxiv",
    "version": 2
  }
}