Pith Number

pith:CYUE34ZB

pith:2013:CYUE34ZBIRQLUYCEX4MUXVJAJ4

not attested not anchored not stored refs pending

Proofs of some conjectures on monotonicity of number-theoretic and combinatorial sequences

Bao-Xuan Zhu, Yi Wang

arxiv:1303.5595 v2 · 2013-03-22 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CYUE34ZBIRQLUYCEX4MUXVJAJ4}

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	2026-05-18T01:50:59.579839Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16284df3214460ba6044bf194bd5204f14f7759a46f630b76668051899d14245

Aliases

arxiv: 1303.5595 · arxiv_version: 1303.5595v2 · doi: 10.48550/arxiv.1303.5595 · pith_short_12: CYUE34ZBIRQL · pith_short_16: CYUE34ZBIRQLUYCE · pith_short_8: CYUE34ZB

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/CYUE34ZBIRQLUYCEX4MUXVJAJ4 \
  | 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: 16284df3214460ba6044bf194bd5204f14f7759a46f630b76668051899d14245

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e7a9776b6066d541b05263a4185eb60ab4f5b08149a5be766153e449bda9db1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-03-22T12:24:21Z",
    "title_canon_sha256": "cba8069d883c57b40fedaf9da40751b94daa7b139ff5c7866fb61683bd197c64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.5595",
    "kind": "arxiv",
    "version": 2
  }
}