Pith Number

pith:2ZHHRAKW

pith:2011:2ZHHRAKWKNMXJSKRBJ4XS2JAPV

not attested not anchored not stored refs pending

Some nonlinear functions of Bernoulli and Euler umbrae

C. Vignat

arxiv:1101.0770 v1 · 2011-01-04 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2ZHHRAKWKNMXJSKRBJ4XS2JAPV}

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	2026-05-18T04:32:02.139297Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d64e788156535974c9510a797969207d4aae02e73d84715651c2de706a3023d3

Aliases

arxiv: 1101.0770 · arxiv_version: 1101.0770v1 · doi: 10.48550/arxiv.1101.0770 · pith_short_12: 2ZHHRAKWKNMX · pith_short_16: 2ZHHRAKWKNMXJSKR · pith_short_8: 2ZHHRAKW

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/2ZHHRAKWKNMXJSKRBJ4XS2JAPV \
  | 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: d64e788156535974c9510a797969207d4aae02e73d84715651c2de706a3023d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51a7c0d9aaeee02a1f054a47db6fdba4df5f2c8f4b1f22582166e383b1f0a97e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-01-04T17:20:30Z",
    "title_canon_sha256": "ae83fad06af6d2469646bd12d5c0b41ba72ea3e0de77b5ea1177ce96cd8ae0d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0770",
    "kind": "arxiv",
    "version": 1
  }
}