Pith Number

pith:3B7RFHNW

pith:2023:3B7RFHNW3JZCRMIVI5L7X6MSSZ

not attested not anchored not stored refs pending

Hopf algebras for the shuffle algebra and fractions from multiple zeta values

Bin Zhang, Hongyu Xiang, Li Guo, Wenchuan Hu

arxiv:2401.01372 v3 · 2023-12-29 · math.NT · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3B7RFHNW3JZCRMIVI5L7X6MSSZ}

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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

Extended Shuffle Product for Multiple Zeta Values

Receipt and verification

First computed	2026-07-05T11:15:16.571947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d87f129db6da7228b1154757fbf992966b58489c0fc523319d3f87e9018d23df

Aliases

arxiv: 2401.01372 · arxiv_version: 2401.01372v3 · doi: 10.48550/arxiv.2401.01372 · pith_short_12: 3B7RFHNW3JZC · pith_short_16: 3B7RFHNW3JZCRMIV · pith_short_8: 3B7RFHNW

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/3B7RFHNW3JZCRMIVI5L7X6MSSZ \
  | 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: d87f129db6da7228b1154757fbf992966b58489c0fc523319d3f87e9018d23df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fcfb39734bca88d845ecadec3e15a40f505c4ddc483a2e18a9b7d11ee88914a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2023-12-29T13:07:25Z",
    "title_canon_sha256": "0a803c8f0d22bd36771689d5df4d47857f8c70807e9531563ecdc796c88c2a3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2401.01372",
    "kind": "arxiv",
    "version": 3
  }
}