Pith Number

pith:U4U5A7PU

pith:2010:U4U5A7PUFLSAAKYHO2HRSVKELE

not attested not anchored not stored refs pending

Reductive group schemes, the Greenberg functor, and associated algebraic groups

Alexander Stasinski

arxiv:1003.3598 v3 · 2010-03-18 · 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{U4U5A7PUFLSAAKYHO2HRSVKELE}

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	2026-05-18T02:56:58.707074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a729d07df42ae4002b07768f195544590fca9c5feb4dc42d78c0a1340fb5d697

Aliases

arxiv: 1003.3598 · arxiv_version: 1003.3598v3 · doi: 10.48550/arxiv.1003.3598 · pith_short_12: U4U5A7PUFLSA · pith_short_16: U4U5A7PUFLSAAKYH · pith_short_8: U4U5A7PU

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/U4U5A7PUFLSAAKYHO2HRSVKELE \
  | 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: a729d07df42ae4002b07768f195544590fca9c5feb4dc42d78c0a1340fb5d697

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4e372dc7c958bc6c1a2231655615f59199ef579c626aed749d642296ca37050",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-03-18T14:50:36Z",
    "title_canon_sha256": "1d9d16861c7836be03a942f1420af89e76f4ce4361bfecf58c8d1cb7a8d7a057"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.3598",
    "kind": "arxiv",
    "version": 3
  }
}