Pith Number

pith:OXDOZY6Z

pith:2012:OXDOZY6ZNNWDLZUPIRYHJTRNNC

not attested not anchored not stored refs pending

Umbral calculus and Frobenius-Euler polynomials

Dae San Kim, Taekyun Kim

arxiv:1211.6802 v1 · 2012-11-29 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OXDOZY6ZNNWDLZUPIRYHJTRNNC}

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	2026-05-18T03:39:42.975172Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

75c6ece3d96b6c35e68f447074ce2d6880652bd27ed80476216c0460396fca2b

Aliases

arxiv: 1211.6802 · arxiv_version: 1211.6802v1 · doi: 10.48550/arxiv.1211.6802 · pith_short_12: OXDOZY6ZNNWD · pith_short_16: OXDOZY6ZNNWDLZUP · pith_short_8: OXDOZY6Z

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/OXDOZY6ZNNWDLZUPIRYHJTRNNC \
  | 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: 75c6ece3d96b6c35e68f447074ce2d6880652bd27ed80476216c0460396fca2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b240aec6b250b74e96f10ce2b61f56dd5055e01f55ab009787e9984e32f7039",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-11-29T03:00:16Z",
    "title_canon_sha256": "e375c3c2b5e0e7523c59ffb758db75fb866794b832920a6cd9b8df8170d81012"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6802",
    "kind": "arxiv",
    "version": 1
  }
}