Pith Number

pith:R2VKNF4X

pith:2019:R2VKNF4XI45NUSBSVEC5ZE6T54

not attested not anchored not stored refs pending

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

Benjamin Enriquez, Hidekazu Furusho

arxiv:1908.00444 v5 · 2019-08-01 · 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{R2VKNF4XI45NUSBSVEC5ZE6T54}

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	2026-07-05T04:00:10.502059Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8eaaa69797473ada4832a905dc93d3ef104ffc68af4e9a3fd05c9072bc32ebf3

Aliases

arxiv: 1908.00444 · arxiv_version: 1908.00444v5 · doi: 10.48550/arxiv.1908.00444 · pith_short_12: R2VKNF4XI45N · pith_short_16: R2VKNF4XI45NUSBS · pith_short_8: R2VKNF4X

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/R2VKNF4XI45NUSBSVEC5ZE6T54 \
  | 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: 8eaaa69797473ada4832a905dc93d3ef104ffc68af4e9a3fd05c9072bc32ebf3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24e8dfb32bb1034d646a2c0756f4f182980e2340f9cacf1a937ca8d7fc8f782e",
    "cross_cats_sorted": [
      "math.NT",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-08-01T14:55:59Z",
    "title_canon_sha256": "927cd81e72cfe55dfc243456d299bf1f52f3ff9d1f26f950a8d548a8decf52b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.00444",
    "kind": "arxiv",
    "version": 5
  }
}