Pith Number

pith:P63AGDER

pith:2014:P63AGDERJ7LEYMVMOSFX447GMP

not attested not anchored not stored refs pending

The $p$-adic Order of Power Sums, the Erd\"os-Moser Equation, and Bernoulli Numbers

Emmanuel Tsukerman, Jonathan Sondow

arxiv:1401.0322 v1 · 2014-01-01 · 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{P63AGDERJ7LEYMVMOSFX447GMP}

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	2026-05-18T03:03:23.506029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fb6030c914fd64c32ac748b7e73e663d7a470b1cd3ae70093ff3c398a61ad83

Aliases

arxiv: 1401.0322 · arxiv_version: 1401.0322v1 · doi: 10.48550/arxiv.1401.0322 · pith_short_12: P63AGDERJ7LE · pith_short_16: P63AGDERJ7LEYMVM · pith_short_8: P63AGDER

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/P63AGDERJ7LEYMVMOSFX447GMP \
  | 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: 7fb6030c914fd64c32ac748b7e73e663d7a470b1cd3ae70093ff3c398a61ad83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4d06b6d8c2ae92954c9650280b7a087e58d8c27f59f3f7286badb63e2efa328",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-01-01T19:04:44Z",
    "title_canon_sha256": "0dd695ba416836c746d921da0e9a6c384fd040a47c06767cf1a421564ae4f8ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.0322",
    "kind": "arxiv",
    "version": 1
  }
}