Pith Number

pith:GX4JLTGP

pith:2004:GX4JLTGPBVOHGEG5N5TTQAZJSE

not attested not anchored not stored refs pending

Expansion around half-integer values, binomial sums and inverse binomial sums

Stefan Weinzierl

arxiv:hep-ph/0402131 v1 · 2004-02-12 · hep-ph · 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{GX4JLTGPBVOHGEG5N5TTQAZJSE}

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.

Cited by

1 paper in Pith

The $\mu$-extension of iterated integrals and nested sums

Receipt and verification

First computed	2026-07-04T16:48:06.805172Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35f895cccf0d5c7310dd6f67380329913e42b999efa77d72503cf3398db4b9ba

Aliases

arxiv: hep-ph/0402131 · arxiv_version: hep-ph/0402131v1 · doi: 10.48550/arxiv.hep-ph/0402131 · pith_short_12: GX4JLTGPBVOH · pith_short_16: GX4JLTGPBVOHGEG5 · pith_short_8: GX4JLTGP

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/GX4JLTGPBVOHGEG5N5TTQAZJSE \
  | 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: 35f895cccf0d5c7310dd6f67380329913e42b999efa77d72503cf3398db4b9ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dbf879dcf708875796794866a51c490443b425b53c5386fabf709db1c05237a",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2004-02-12T10:52:12Z",
    "title_canon_sha256": "0e1132b6b68cab3e1f65e59b6612874ee4301a1dbc1440dd653e27b4ac427064"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0402131",
    "kind": "arxiv",
    "version": 1
  }
}