Pith Number

pith:VDI5JJDV

pith:2010:VDI5JJDVKAVX5Z37NQGZGOGCBD

not attested not anchored not stored refs pending

Hyperplane sections and the subtlety of the Lefschetz properties

David Cook II, Uwe Nagel

arxiv:1012.2601 v1 · 2010-12-12 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VDI5JJDVKAVX5Z37NQGZGOGCBD}

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	2026-05-18T04:04:17.142846Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8d1d4a475502b7ee77f6c0d9338c208dca79ed99b89f3166585f24dcf0ca6d1

Aliases

arxiv: 1012.2601 · arxiv_version: 1012.2601v1 · doi: 10.48550/arxiv.1012.2601 · pith_short_12: VDI5JJDVKAVX · pith_short_16: VDI5JJDVKAVX5Z37 · pith_short_8: VDI5JJDV

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/VDI5JJDVKAVX5Z37NQGZGOGCBD \
  | 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: a8d1d4a475502b7ee77f6c0d9338c208dca79ed99b89f3166585f24dcf0ca6d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f8f52e9ed6243a1a5c1be21633a313b8a17dde6a740f47aed8f283b1478967f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-12-12T23:09:08Z",
    "title_canon_sha256": "27e19d3df70ed77485e12756d94b9bd395d69fdf64d302a364e61dfdbf3bc3bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2601",
    "kind": "arxiv",
    "version": 1
  }
}