Pith Number

pith:TTCO33PE

pith:2019:TTCO33PENWJA67THZGQRANKWXJ

not attested not anchored not stored refs pending

Sharp Bounds for the Arc Lemniscate Sine Function

Horst Alzer, Man Kam Kwong

arxiv:1903.03897 v1 · 2019-03-10 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TTCO33PENWJA67THZGQRANKWXJ}

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	2026-05-17T23:51:40.672369Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cc4edede46d920f7e67c9a1103556ba5424aac8ec376d803fe353e4cf56d684

Aliases

arxiv: 1903.03897 · arxiv_version: 1903.03897v1 · doi: 10.48550/arxiv.1903.03897 · pith_short_12: TTCO33PENWJA · pith_short_16: TTCO33PENWJA67TH · pith_short_8: TTCO33PE

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/TTCO33PENWJA67THZGQRANKWXJ \
  | 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: 9cc4edede46d920f7e67c9a1103556ba5424aac8ec376d803fe353e4cf56d684

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fba0c990b890dd5ad581b2c512cb5d4a163b21e512b53e55b0568b7b75c4fe7f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-03-10T01:17:20Z",
    "title_canon_sha256": "60ade0bddef3464d7588b16f236c624177411b30f3d3da852e9cb90a0ab2b07a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.03897",
    "kind": "arxiv",
    "version": 1
  }
}