Pith Number

pith:RMPE6K4B

pith:2021:RMPE6K4BVCUL4IMCMR4R72VQ7A

not attested not anchored not stored refs pending

Faulhaber's Formula, Odd Bernoulli Numbers, and the Method of Partial Sums

Ryan Zielinski

arxiv:2106.14607 v4 · 2021-05-25 · math.GM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RMPE6K4BVCUL4IMCMR4R72VQ7A}

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	2026-07-05T04:46:11.467608Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b1e4f2b81a8a8be218264791feab0f81225de2885312c8979197e9d8c38abca

Aliases

arxiv: 2106.14607 · arxiv_version: 2106.14607v4 · doi: 10.48550/arxiv.2106.14607 · pith_short_12: RMPE6K4BVCUL · pith_short_16: RMPE6K4BVCUL4IMC · pith_short_8: RMPE6K4B

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/RMPE6K4BVCUL4IMCMR4R72VQ7A \
  | 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: 8b1e4f2b81a8a8be218264791feab0f81225de2885312c8979197e9d8c38abca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "396776255faf08d87444bf396b07c7cd824e9d2996ff1ff993019928820cf542",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2021-05-25T16:38:27Z",
    "title_canon_sha256": "ec4c16ac59fe087dc9cd2b655fec56a08d084946f08431b41696195e9263de76"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.14607",
    "kind": "arxiv",
    "version": 4
  }
}