Pith Number

pith:WUZTRK3K

pith:2014:WUZTRK3KFWCOQ4GSYPMENOLKUN

not attested not anchored not stored refs pending

Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs

Caucher Birkar, De-Qi Zhang

arxiv:1410.0938 v2 · 2014-10-03 · 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{WUZTRK3KFWCOQ4GSYPMENOLKUN}

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	2026-05-18T00:05:14.965408Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b53338ab6a2d84e870d2c3d846b96aa37bb0b3ff9f494e4dc5d56ddc183b60c6

Aliases

arxiv: 1410.0938 · arxiv_version: 1410.0938v2 · doi: 10.48550/arxiv.1410.0938 · pith_short_12: WUZTRK3KFWCO · pith_short_16: WUZTRK3KFWCOQ4GS · pith_short_8: WUZTRK3K

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/WUZTRK3KFWCOQ4GSYPMENOLKUN \
  | 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: b53338ab6a2d84e870d2c3d846b96aa37bb0b3ff9f494e4dc5d56ddc183b60c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c329766a1d7d001c2ae411309c7e522cf28e2ae0b39591a691050f754bfc8ea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2014-10-03T18:46:45Z",
    "title_canon_sha256": "169e8b1e868a513d7253f5f1aaf8498bf8293dc3229069f7139a08f0dc1c161f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.0938",
    "kind": "arxiv",
    "version": 2
  }
}