Pith Number

pith:4UBBZ47U

pith:2011:4UBBZ47UV6Q3EAEB277WCDPXWW

not attested not anchored not stored refs pending

Q-factorial Laurent rings

Antonella Grassi, Ugo Bruzzo

arxiv:1108.4116 v1 · 2011-08-20 · math.AG · math.AC · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4UBBZ47UV6Q3EAEB277WCDPXWW}

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	2026-05-18T04:04:33.253664Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5021cf3f4afa1b20081d7ff610df7b580a963a4285793f8cab9aab3a433180e

Aliases

arxiv: 1108.4116 · arxiv_version: 1108.4116v1 · doi: 10.48550/arxiv.1108.4116 · pith_short_12: 4UBBZ47UV6Q3 · pith_short_16: 4UBBZ47UV6Q3EAEB · pith_short_8: 4UBBZ47U

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/4UBBZ47UV6Q3EAEB277WCDPXWW \
  | 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: e5021cf3f4afa1b20081d7ff610df7b580a963a4285793f8cab9aab3a433180e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0cebf20e22f4a59645e2c0f95c75d699335661ff164c48f4c922bfcf8d524ea8",
    "cross_cats_sorted": [
      "math.AC",
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-08-20T13:41:51Z",
    "title_canon_sha256": "9024e9560225eabe22725b1f672715fd577fc252d111254a55c9c3c005c7adf0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4116",
    "kind": "arxiv",
    "version": 1
  }
}