Pith Number

pith:NJAXLU2T

pith:2012:NJAXLU2T4K5FLT5G4SCIG4OP3X

not attested not anchored not stored refs pending

Lectures on birational geometry

Caucher Birkar

arxiv:1210.2670 v1 · 2012-10-09 · 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{NJAXLU2T4K5FLT5G4SCIG4OP3X}

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	2026-05-18T03:43:40.981169Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a4175d353e2ba55cfa6e4848371cfddc0c4759f5945affa466dac9c82c7e109

Aliases

arxiv: 1210.2670 · arxiv_version: 1210.2670v1 · doi: 10.48550/arxiv.1210.2670 · pith_short_12: NJAXLU2T4K5F · pith_short_16: NJAXLU2T4K5FLT5G · pith_short_8: NJAXLU2T

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/NJAXLU2T4K5FLT5G4SCIG4OP3X \
  | 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: 6a4175d353e2ba55cfa6e4848371cfddc0c4759f5945affa466dac9c82c7e109

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c8ed0cf7e725f54f5988f1ed4c8abf19f079d0fa00e3862b231ab16b1d16ae4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-10-09T17:22:53Z",
    "title_canon_sha256": "b4bf67315ccb5f000ed62077698b78c7d5cbee2b873a0f622065791c709bbfd5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2670",
    "kind": "arxiv",
    "version": 1
  }
}