Pith Number

pith:F2EURGHK

pith:2018:F2EURGHKZ4KTW2HKXAYWYNSEVZ

not attested not anchored not stored refs pending

The Betti side of the double shuffle theory. II. Double shuffle relations for associators

Benjamin Enriquez, Hidekazu Furusho

arxiv:1807.07786 v5 · 2018-07-20 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F2EURGHKZ4KTW2HKXAYWYNSEVZ}

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	2026-07-05T04:00:10.082796Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e894898eacf153b68eab8316c3644ae7fcef30cb570b3ca7a5a3f9cb366d0d6

Aliases

arxiv: 1807.07786 · arxiv_version: 1807.07786v5 · doi: 10.48550/arxiv.1807.07786 · pith_short_12: F2EURGHKZ4KT · pith_short_16: F2EURGHKZ4KTW2HK · pith_short_8: F2EURGHK

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/F2EURGHKZ4KTW2HKXAYWYNSEVZ \
  | 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: 2e894898eacf153b68eab8316c3644ae7fcef30cb570b3ca7a5a3f9cb366d0d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23e83b8188257df25acfc1643f4e5a06006cb61374c1e0dac03bd19b6cf6f52f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2018-07-20T10:52:16Z",
    "title_canon_sha256": "d1b782141fb6fff1b8fbc80bc50307853d1e2e05e1d899f92eb5e15bb45fd70a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.07786",
    "kind": "arxiv",
    "version": 5
  }
}