Pith Number

pith:GGDEIRX7

pith:2018:GGDEIRX7MF6TRND6FVRFHVGBE2

not attested not anchored not stored refs pending

The Betti side of the double shuffle theory. I. The harmonic coproducts

Benjamin Enriquez, Hidekazu Furusho

arxiv:1803.10151 v5 · 2018-03-27 · math.AG · math.NT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GGDEIRX7MF6TRND6FVRFHVGBE2}

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 Betti side of the double shuffle theory. III. Bitorsor structures

Receipt and verification

First computed	2026-07-05T02:25:58.436642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31864446ff617d38b47e2d6253d4c1268ce453eb76b4d3c9d563b1fac66287e3

Aliases

arxiv: 1803.10151 · arxiv_version: 1803.10151v5 · doi: 10.48550/arxiv.1803.10151 · pith_short_12: GGDEIRX7MF6T · pith_short_16: GGDEIRX7MF6TRND6 · pith_short_8: GGDEIRX7

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/GGDEIRX7MF6TRND6FVRFHVGBE2 \
  | 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: 31864446ff617d38b47e2d6253d4c1268ce453eb76b4d3c9d563b1fac66287e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bd473648c8933da16b2ddd9c5a319dce8887debc9c9c54185898e914f5457cf",
    "cross_cats_sorted": [
      "math.NT",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2018-03-27T15:51:18Z",
    "title_canon_sha256": "8945223efef9fa2fffc9ea60e5a78cf8cba97d11fcf7900d950002a7a86cc43d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.10151",
    "kind": "arxiv",
    "version": 5
  }
}