Pith Number

pith:UNLL3VCG

pith:2004:UNLL3VCG2U542JU65HZA62U2XY

not attested not anchored not stored refs pending

Bernoulli Number Identities from Quantum Field Theory and Topological String Theory

Christian Schubert (UTPA), Gerald V. Dunne (Univ. of Connecticut)

arxiv:math/0406610 v2 · 2004-06-29 · math.NT · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UNLL3VCG2U542JU65HZA62U2XY}

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	2026-05-18T02:57:24.543803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a356bdd446d53bcd269ee9f20f6a9abe0c5251cc6cdf967edec205d7888bc8aa

Aliases

arxiv: math/0406610 · arxiv_version: math/0406610v2 · doi: 10.48550/arxiv.math/0406610 · pith_short_12: UNLL3VCG2U54 · pith_short_16: UNLL3VCG2U542JU6 · pith_short_8: UNLL3VCG

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/UNLL3VCG2U542JU65HZA62U2XY \
  | 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: a356bdd446d53bcd269ee9f20f6a9abe0c5251cc6cdf967edec205d7888bc8aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5bb3a4797cd2bff78156ec811317427b7013924fe4de8a46aea62c407b3bf0b4",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2004-06-29T20:13:56Z",
    "title_canon_sha256": "5be9c4be9831ed9b672e676ec20f23fad327bb35d6510f649996b10a057f0631"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0406610",
    "kind": "arxiv",
    "version": 2
  }
}