Pith Number

pith:YERPSGOY

pith:2020:YERPSGOYMDMEKELB44XD3BAU3Y

not attested not anchored not stored refs pending

Generalised pairs in birational geometry

Caucher Birkar

arxiv:2008.01008 v2 · 2020-08-03 · 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{YERPSGOYMDMEKELB44XD3BAU3Y}

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.

Cited by

1 paper in Pith

Discreteness of volumes of divisors on Calabi-Yau type varieties

Receipt and verification

First computed	2026-07-05T01:25:27.198690Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c122f919d860d8451161e72e3d8414de37f2d4ac2c610781173d4cb5976218d7

Aliases

arxiv: 2008.01008 · arxiv_version: 2008.01008v2 · doi: 10.48550/arxiv.2008.01008 · pith_short_12: YERPSGOYMDME · pith_short_16: YERPSGOYMDMEKELB · pith_short_8: YERPSGOY

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/YERPSGOYMDMEKELB44XD3BAU3Y \
  | 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: c122f919d860d8451161e72e3d8414de37f2d4ac2c610781173d4cb5976218d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a5cf64ae07f561c33c0cb8416714314d57f3c3d35f4cee27ca9f0cbf7fb9c55",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2020-08-03T16:45:26Z",
    "title_canon_sha256": "48ac2f699b07d7bbb8a30099e0d149452a150ba633f6a17feafa4a6cfbcc5ce7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2008.01008",
    "kind": "arxiv",
    "version": 2
  }
}