Pith Number

pith:BQGQANQT

pith:2021:BQGQANQTSWX67PCEUKRO4Z6BLN

not attested not anchored not stored refs pending

Borel subgroups of the plane Cremona group

Isac Hed\'en, Jean-Philippe Furter

arxiv:2107.14353 v3 · 2021-07-29 · 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{BQGQANQTSWX67PCEUKRO4Z6BLN}

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	2026-07-05T04:59:57.350136Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c0d00361395afefbc44a2a2ee67c15b50052ffca327b98d84a48a5923fcdc70

Aliases

arxiv: 2107.14353 · arxiv_version: 2107.14353v3 · doi: 10.48550/arxiv.2107.14353 · pith_short_12: BQGQANQTSWX6 · pith_short_16: BQGQANQTSWX67PCE · pith_short_8: BQGQANQT

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/BQGQANQTSWX67PCEUKRO4Z6BLN \
  | 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: 0c0d00361395afefbc44a2a2ee67c15b50052ffca327b98d84a48a5923fcdc70

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3cca1730a02da11f70184dfe467656ef19d2dcb9b3661ec2419bb8d08a4b7a9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2021-07-29T22:22:16Z",
    "title_canon_sha256": "9ddcafaaefe1cbc8727edb27201769e60d1837d2e86c9cd1048b345256793604"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.14353",
    "kind": "arxiv",
    "version": 3
  }
}