Pith Number

pith:XBKAC62N

pith:2011:XBKAC62NQFPPT2UNUCPH2CE6UH

not attested not anchored not stored refs pending

On the Grothendieck-Lefschetz Theorem for a Family of Varieties

Marco Antei, Vikram Mehta

arxiv:1111.3003 v1 · 2011-11-13 · 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{XBKAC62NQFPPT2UNUCPH2CE6UH}

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	2026-05-18T03:45:23.172097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b854017b4d815ef9ea8da09e7d089ea1ddbb1dd6077ddf2c4f4ee9295906b4f0

Aliases

arxiv: 1111.3003 · arxiv_version: 1111.3003v1 · doi: 10.48550/arxiv.1111.3003 · pith_short_12: XBKAC62NQFPP · pith_short_16: XBKAC62NQFPPT2UN · pith_short_8: XBKAC62N

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/XBKAC62NQFPPT2UNUCPH2CE6UH \
  | 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: b854017b4d815ef9ea8da09e7d089ea1ddbb1dd6077ddf2c4f4ee9295906b4f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d23866eac7c90cd668e881d088df89bd892deb1d43244c50ad32315762f5830",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-11-13T12:08:00Z",
    "title_canon_sha256": "c4c83a3146581dedd63f05a8d19e64067cd5c976fa1b9262ba8a45499a427294"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.3003",
    "kind": "arxiv",
    "version": 1
  }
}