Pith Number

pith:VZKZL7RR

pith:2009:VZKZL7RRT37RFNSC62EJ6PACFI

not attested not anchored not stored refs pending

A categorical invariant for cubic threefolds

Emanuele Macri, Marcello Bernardara, Paolo Stellari, Sukhendu Mehrotra

arxiv:0903.4414 v2 · 2009-03-25 · 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{VZKZL7RRT37RFNSC62EJ6PACFI}

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	2026-05-18T04:10:48.480140Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae5595fe319eff12b642f6889f3c022a3d79a524eaf71e78f00e14fd5ab99419

Aliases

arxiv: 0903.4414 · arxiv_version: 0903.4414v2 · doi: 10.48550/arxiv.0903.4414 · pith_short_12: VZKZL7RRT37R · pith_short_16: VZKZL7RRT37RFNSC · pith_short_8: VZKZL7RR

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/VZKZL7RRT37RFNSC62EJ6PACFI \
  | 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: ae5595fe319eff12b642f6889f3c022a3d79a524eaf71e78f00e14fd5ab99419

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "718441758dd9cf7e4ffdbce2fe2b20df6d854645bfb9e0a6c2c2e71165f7bc52",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-03-25T18:16:59Z",
    "title_canon_sha256": "7c1f48022ded501aec51a60ff6ec9f380c061a70e84a29e594675e58cca98983"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.4414",
    "kind": "arxiv",
    "version": 2
  }
}