Pith Number

pith:4ZN3VE4M

pith:2013:4ZN3VE4MCN7RXK27SU46EB4OCZ

not attested not anchored not stored refs pending

The augmented base locus of real divisors over arbitrary fields

Caucher Birkar

arxiv:1312.0239 v1 · 2013-12-01 · 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{4ZN3VE4MCN7RXK27SU46EB4OCZ}

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	2026-05-18T03:05:46.304228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e65bba938c137f1bab5f9539e2078e1640fc127f543d1ba1169d7c8bf27cf3c6

Aliases

arxiv: 1312.0239 · arxiv_version: 1312.0239v1 · doi: 10.48550/arxiv.1312.0239 · pith_short_12: 4ZN3VE4MCN7R · pith_short_16: 4ZN3VE4MCN7RXK27 · pith_short_8: 4ZN3VE4M

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/4ZN3VE4MCN7RXK27SU46EB4OCZ \
  | 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: e65bba938c137f1bab5f9539e2078e1640fc127f543d1ba1169d7c8bf27cf3c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67a04ac3fa88837d24453ffce7e03f0657d98519e2d252a513ab8a6897c53bf4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-12-01T15:51:16Z",
    "title_canon_sha256": "f3e358e27253b7de2d606b46266e3c7883205c628a7a33b59217abd286389d69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.0239",
    "kind": "arxiv",
    "version": 1
  }
}