Pith Number

pith:YCOW77PV

pith:2012:YCOW77PVX2AXN5BHY6QHDJ7SSM

not attested not anchored not stored refs pending

On the moduli part of the Kawamata-Kodaira canonical bundle formula

Caucher Birkar, Yifei Chen

arxiv:1207.4070 v1 · 2012-07-17 · math.AG · 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{YCOW77PVX2AXN5BHY6QHDJ7SSM}

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	2026-05-18T03:50:49.095765Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c09d6ffdf5be8176f427c7a071a7f2930d7fd95d66b9dfbf62db3cfa21c061f9

Aliases

arxiv: 1207.4070 · arxiv_version: 1207.4070v1 · doi: 10.48550/arxiv.1207.4070 · pith_short_12: YCOW77PVX2AX · pith_short_16: YCOW77PVX2AXN5BH · pith_short_8: YCOW77PV

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/YCOW77PVX2AXN5BHY6QHDJ7SSM \
  | 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: c09d6ffdf5be8176f427c7a071a7f2930d7fd95d66b9dfbf62db3cfa21c061f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93164aec7a46df10a0daa82e06a42b791de923abbbc2be96c17b87d022df1609",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-07-17T17:28:57Z",
    "title_canon_sha256": "a2417869afaf10069b4086fe8249968041c92562160022ea6422e9c8cf961770"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4070",
    "kind": "arxiv",
    "version": 1
  }
}