Pith Number

pith:OZT3G6LC

pith:2019:OZT3G6LC4HL54W6MC5IWIH5BBO

not attested not anchored not stored refs pending

The Minimal Model Program for threefolds in characteristic five

Christopher Hacon, Jakub Witaszek

arxiv:1911.12895 v1 · 2019-11-28 · 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{OZT3G6LC4HL54W6MC5IWIH5BBO}

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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

Abundance for threefolds in positive characteristic when $\nu=2$

Receipt and verification

First computed	2026-07-05T00:22:50.059402Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7667b37962e1d7de5bcc1751641fa10bb3bf76815f21a08e710ebc4416d49a77

Aliases

arxiv: 1911.12895 · arxiv_version: 1911.12895v1 · doi: 10.48550/arxiv.1911.12895 · pith_short_12: OZT3G6LC4HL5 · pith_short_16: OZT3G6LC4HL54W6M · pith_short_8: OZT3G6LC

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/OZT3G6LC4HL54W6MC5IWIH5BBO \
  | 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: 7667b37962e1d7de5bcc1751641fa10bb3bf76815f21a08e710ebc4416d49a77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87bb1c4211e431f6a70009b5f1af98791a0553b1ac104125285a98552e69f72b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-11-28T23:06:56Z",
    "title_canon_sha256": "25ee7596c6aeeeb48a9f17aa838b719467a897aacd5c8894cc01a3d9dcbd5d6d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1911.12895",
    "kind": "arxiv",
    "version": 1
  }
}