Pith Number

pith:QVMPB2FA

pith:2006:QVMPB2FANYLOK6D2TKCKNAQPYN

not attested not anchored not stored refs pending

Small bound for birational automorphism groups of algebraic varieties (with an Appendix by Yujiro Kawamata)

De-Qi Zhang

arxiv:math/0609083 v1 · 2006-09-04 · 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{QVMPB2FANYLOK6D2TKCKNAQPYN}

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	2026-05-18T00:05:09.996649Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8558f0e8a06e16e5787a9a84a6820fc3688808af33d8489397bb179db814f258

Aliases

arxiv: math/0609083 · arxiv_version: math/0609083v1 · doi: 10.48550/arxiv.math/0609083 · pith_short_12: QVMPB2FANYLO · pith_short_16: QVMPB2FANYLOK6D2 · pith_short_8: QVMPB2FA

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/QVMPB2FANYLOK6D2TKCKNAQPYN \
  | 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: 8558f0e8a06e16e5787a9a84a6820fc3688808af33d8489397bb179db814f258

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3fc42d99695d7758a21a2099e0eeb1e40e1ec1426e1ec348dd367450e6a97b28",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2006-09-04T02:42:22Z",
    "title_canon_sha256": "206253db23cecddf496a5998f8bfac20d87006647dd2859803dc4933f7b6f51f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609083",
    "kind": "arxiv",
    "version": 1
  }
}