Pith Number

pith:5YZP4I2J

pith:2021:5YZP4I2JXY3XL25SIGNW75XLHS

not attested not anchored not stored refs pending

Boundedness and volume of generalised pairs

Caucher Birkar

arxiv:2103.14935 v2 · 2021-03-27 · 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{5YZP4I2JXY3XL25SIGNW75XLHS}

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

4 papers in Pith

Addendum: On generalized canonical bundle formula and boundedness of complements in complex analytic setting

On the DCC Property of Iitaka Volume with Real Coefficients and Generalised Pairs

Birational boundedness of stable families

Receipt and verification

First computed	2026-07-05T02:28:56.614282Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee32fe2349be3775ebb2419b6ff6eb3cb94b3bc8bb0e8d7a55d5be5439747d1f

Aliases

arxiv: 2103.14935 · arxiv_version: 2103.14935v2 · doi: 10.48550/arxiv.2103.14935 · pith_short_12: 5YZP4I2JXY3X · pith_short_16: 5YZP4I2JXY3XL25S · pith_short_8: 5YZP4I2J

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/5YZP4I2JXY3XL25SIGNW75XLHS \
  | 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: ee32fe2349be3775ebb2419b6ff6eb3cb94b3bc8bb0e8d7a55d5be5439747d1f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4b4b6b13cd39d62ba7b432a44c0e57ff4610148df7c3cd9d81a0a437c21c55e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2021-03-27T16:08:00Z",
    "title_canon_sha256": "ba1250034654dd70853fcabd98897b0390306117a8091f41f3881b13897c1fc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.14935",
    "kind": "arxiv",
    "version": 2
  }
}