Pith Number

pith:YVOPAE2P

pith:2020:YVOPAE2P65P53ASWPQYOQ2DPNP

not attested not anchored not stored refs pending

Globally +-regular varieties and the minimal model program for threefolds in mixed characteristic

Bhargav Bhatt, Jakub Witaszek, Joe Waldron, Karl Schwede, Kevin Tucker, Linquan Ma, Zsolt Patakfalvi

arxiv:2012.15801 v3 · 2020-12-31 · math.AG · math.AC · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YVOPAE2P65P53ASWPQYOQ2DPNP}

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	2026-07-05T05:22:26.081081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c55cf0134ff75fdd82567c30e8686f6bf792c544823df9d4b18a8ba0b4536656

Aliases

arxiv: 2012.15801 · arxiv_version: 2012.15801v3 · doi: 10.48550/arxiv.2012.15801 · pith_short_12: YVOPAE2P65P5 · pith_short_16: YVOPAE2P65P53ASW · pith_short_8: YVOPAE2P

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/YVOPAE2P65P53ASWPQYOQ2DPNP \
  | 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: c55cf0134ff75fdd82567c30e8686f6bf792c544823df9d4b18a8ba0b4536656

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74c62ac09a3b7a728e4daf287c9dbac4f7189972f1a3af9dc10c4b836a5d4cbb",
    "cross_cats_sorted": [
      "math.AC",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2020-12-31T18:22:48Z",
    "title_canon_sha256": "203173afbf9d79ed75be88639d8da3c09ca8a443be08d7b548872d8f7eaea2fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.15801",
    "kind": "arxiv",
    "version": 3
  }
}