Pith Number

pith:JDPQGETD

pith:2018:JDPQGETDQMC52N2QPRHSZXHQH4

not attested not anchored not stored refs pending

Bank-Laine functions, the Liouville transformation and the Eremenko-Lyubich class

J.K. Langley

arxiv:1804.04388 v4 · 2018-04-12 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JDPQGETDQMC52N2QPRHSZXHQH4}

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	2026-05-17T23:57:46.934538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48df0312638305dd37507c4f2cdcf03f36ccb52b83999780e1d3037ff7ac3588

Aliases

arxiv: 1804.04388 · arxiv_version: 1804.04388v4 · doi: 10.48550/arxiv.1804.04388 · pith_short_12: JDPQGETDQMC5 · pith_short_16: JDPQGETDQMC52N2Q · pith_short_8: JDPQGETD

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/JDPQGETDQMC52N2QPRHSZXHQH4 \
  | 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: 48df0312638305dd37507c4f2cdcf03f36ccb52b83999780e1d3037ff7ac3588

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9fe691836844f67ad3982be6f554c88ce0e6a471afb91fcf8c289db3554fa05",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2018-04-12T09:26:01Z",
    "title_canon_sha256": "43034bc290fa8aeb3dda79d3adb414eafb99666133ff93aa856e9b7e18006146"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.04388",
    "kind": "arxiv",
    "version": 4
  }
}