Pith Number

pith:4UVJBDQ6

pith:2009:4UVJBDQ6D6D7NSWZGAU7A2MSGP

not attested not anchored not stored refs pending

KZ equation on the moduli space ${\mathcal M}_{0,5}$ and the harmonic product of multiple polylogarithms

Kimio Ueno, Shu Oi

arxiv:0910.0718 v3 · 2009-10-05 · math.QA · math.CA · 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{4UVJBDQ6D6D7NSWZGAU7A2MSGP}

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	2026-05-18T03:35:54.677029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e52a908e1e1f87f6cad93029f0699233f060bafacfb9fe3b79d817a1eed477f7

Aliases

arxiv: 0910.0718 · arxiv_version: 0910.0718v3 · doi: 10.48550/arxiv.0910.0718 · pith_short_12: 4UVJBDQ6D6D7 · pith_short_16: 4UVJBDQ6D6D7NSWZ · pith_short_8: 4UVJBDQ6

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/4UVJBDQ6D6D7NSWZGAU7A2MSGP \
  | 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: e52a908e1e1f87f6cad93029f0699233f060bafacfb9fe3b79d817a1eed477f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8a31c4333ead33c1cc9d76cd3a5fda4fa57367281942c603ebc7df45e31decd",
    "cross_cats_sorted": [
      "math.CA",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2009-10-05T10:42:53Z",
    "title_canon_sha256": "1b69aa4305fb377239420845fdbd5a603f79536bb7a28a654cbf47abe31fd0df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.0718",
    "kind": "arxiv",
    "version": 3
  }
}