Pith Number

pith:USC5NBZQ

pith:2018:USC5NBZQRHAPQ7UL2ZYRXA5JCE

not attested not anchored not stored refs pending

The cardinality of orthogonal exponentials of planar self-affine measures with three-element digit sets

Jing-Cheng Liu, Ming-Liang Chen

arxiv:1805.09941 v1 · 2018-05-25 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{USC5NBZQRHAPQ7UL2ZYRXA5JCE}

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	2026-05-18T00:14:58.737014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a485d6873089c0f87e8bd6711b83a9110c2a63c61549ecfda37d63d646d6e197

Aliases

arxiv: 1805.09941 · arxiv_version: 1805.09941v1 · doi: 10.48550/arxiv.1805.09941 · pith_short_12: USC5NBZQRHAP · pith_short_16: USC5NBZQRHAPQ7UL · pith_short_8: USC5NBZQ

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/USC5NBZQRHAPQ7UL2ZYRXA5JCE \
  | 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: a485d6873089c0f87e8bd6711b83a9110c2a63c61549ecfda37d63d646d6e197

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb0506f503bdca5ad312fcd33217745576cef13fdac3919e5592168a22a8fafb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-05-25T00:56:31Z",
    "title_canon_sha256": "e68bafd5b9034d298221dab2c36ccc309cf1892eb2b191c5aa3945867afb3591"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.09941",
    "kind": "arxiv",
    "version": 1
  }
}