Pith Number

pith:POU32ESS

pith:2010:POU32ESSD6V7PYETZTE7B5UAHM

not attested not anchored not stored refs pending

The symmetric and unimodal expansion of Eulerian polynomials via continued fractions

Heesung Shin, Jiang Zeng

arxiv:1005.4583 v3 · 2010-05-25 · 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{POU32ESSD6V7PYETZTE7B5UAHM}

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	2026-07-05T04:06:38.639048Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ba9bd12521fabf7e093ccc9f0f6803b38f6cfab8ffb8cf1b54fa56f77d941c9

Aliases

arxiv: 1005.4583 · arxiv_version: 1005.4583v3 · doi: 10.48550/arxiv.1005.4583 · pith_short_12: POU32ESSD6V7 · pith_short_16: POU32ESSD6V7PYET · pith_short_8: POU32ESS

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/POU32ESSD6V7PYETZTE7B5UAHM \
  | 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: 7ba9bd12521fabf7e093ccc9f0f6803b38f6cfab8ffb8cf1b54fa56f77d941c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e3bf3c29421e1ca5bb0f344ac2e82039d1621bc87aee713519758c76d85b1d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-05-25T14:15:32Z",
    "title_canon_sha256": "4ebbdc29b2df6077c2b308d8257b71fc67a082fd06d46721f23baf75a0c9d5ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.4583",
    "kind": "arxiv",
    "version": 3
  }
}