Pith Number

pith:5J2L2ND2

pith:2011:5J2L2ND2NDR2GSPNABOHA3UTYN

not attested not anchored not stored refs pending

On divisibility of sums of Apery polynomials

Hao Pan

arxiv:1108.1546 v1 · 2011-08-07 · math.NT · 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{5J2L2ND2NDR2GSPNABOHA3UTYN}

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	2026-05-18T04:16:00.756968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea74bd347a68e3a349ed005c706e93c354a567e633a2f3d4bb8922c6d23d2be7

Aliases

arxiv: 1108.1546 · arxiv_version: 1108.1546v1 · doi: 10.48550/arxiv.1108.1546 · pith_short_12: 5J2L2ND2NDR2 · pith_short_16: 5J2L2ND2NDR2GSPN · pith_short_8: 5J2L2ND2

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/5J2L2ND2NDR2GSPNABOHA3UTYN \
  | 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: ea74bd347a68e3a349ed005c706e93c354a567e633a2f3d4bb8922c6d23d2be7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "688d8ab526902fc0c3a1f3919fa99a0287b40c95583bd3739341d2e43fd3d756",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-08-07T14:57:51Z",
    "title_canon_sha256": "14764e129d3d6b0cf9c2c074c719a3993b0466c1044e5a45985e402761501e61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1546",
    "kind": "arxiv",
    "version": 1
  }
}