Pith Number

pith:W5KX2HYZ

pith:2020:W5KX2HYZUBMFOCOSJDOFJJ4UBZ

not attested not anchored not stored refs pending

Pseudo-effectivity of the relative canonical divisor and uniruledness in positive characteristic

Zsolt Patakfalvi

arxiv:2009.07158 v2 · 2020-09-15 · 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{W5KX2HYZUBMFOCOSJDOFJJ4UBZ}

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	2026-05-20T14:03:15.368296Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7557d1f19a0585709d248dc54a7940e5d386feb6b21bca0577503f463bb7b52

Aliases

arxiv: 2009.07158 · arxiv_version: 2009.07158v2 · doi: 10.48550/arxiv.2009.07158 · pith_short_12: W5KX2HYZUBMF · pith_short_16: W5KX2HYZUBMFOCOS · pith_short_8: W5KX2HYZ

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/W5KX2HYZUBMFOCOSJDOFJJ4UBZ \
  | 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: b7557d1f19a0585709d248dc54a7940e5d386feb6b21bca0577503f463bb7b52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19d9811fac05680933b66c40a06407462bd4dcc4ef6f43a06750447a23707dbc",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2020-09-15T15:09:32Z",
    "title_canon_sha256": "f5f3d96c646db57db7d49ea0c87177917e19e50ed7bceb36bd4b5bb16656dba2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2009.07158",
    "kind": "arxiv",
    "version": 2
  }
}