Pith Number

pith:PNVSM7VK

pith:2017:PNVSM7VKUVUVQLIWE7E5VLDGMT

not attested not anchored not stored refs pending

A general family of congruences for Bernoulli numbers

Julian Rosen

arxiv:1706.06618 v2 · 2017-06-20 · 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{PNVSM7VKUVUVQLIWE7E5VLDGMT}

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	2026-05-18T00:03:29.659482Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b6b267eaaa569582d1627c9daac6664d656458bd153b9053ed4fd5ee90b754a

Aliases

arxiv: 1706.06618 · arxiv_version: 1706.06618v2 · doi: 10.48550/arxiv.1706.06618 · pith_short_12: PNVSM7VKUVUV · pith_short_16: PNVSM7VKUVUVQLIW · pith_short_8: PNVSM7VK

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/PNVSM7VKUVUVQLIWE7E5VLDGMT \
  | 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: 7b6b267eaaa569582d1627c9daac6664d656458bd153b9053ed4fd5ee90b754a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8591986ce286229e7f2cd2d92bff3898e48aab1fec6e25a4d78f54f418dd0db",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-06-20T18:47:27Z",
    "title_canon_sha256": "65f2621354551300e5a2f6ead391b83aa41f3083495b62f3984af85bd5d3fb1b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.06618",
    "kind": "arxiv",
    "version": 2
  }
}