Pith Number

pith:VXIDDEDK

pith:2012:VXIDDEDKNMCOHOEY4YNYZYNJSO

not attested not anchored not stored refs pending

Positivity criteria for log canonical divisors and hyperbolicity

De-Qi Zhang, Steven S. Y. Lu

arxiv:1207.7346 v4 · 2012-07-31 · math.AG · math.CV · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VXIDDEDKNMCOHOEY4YNYZYNJSO}

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	2026-05-18T00:05:15.022851Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

add031906a6b04e3b898e61b8ce1a9939e58f3306778edda528a18150aac65c6

Aliases

arxiv: 1207.7346 · arxiv_version: 1207.7346v4 · doi: 10.48550/arxiv.1207.7346 · pith_short_12: VXIDDEDKNMCO · pith_short_16: VXIDDEDKNMCOHOEY · pith_short_8: VXIDDEDK

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/VXIDDEDKNMCOHOEY4YNYZYNJSO \
  | 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: add031906a6b04e3b898e61b8ce1a9939e58f3306778edda528a18150aac65c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "630961af259349d3707180f92596f26fbfe50f7b93f92b8b9ff52ee1eef7f150",
    "cross_cats_sorted": [
      "math.CV",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-07-31T19:15:48Z",
    "title_canon_sha256": "1a79257258330c4200e6b7ec2c46e4c599d41845b4d81b31ec2af5fdf8a3ac30"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.7346",
    "kind": "arxiv",
    "version": 4
  }
}