Pith Number

pith:2PLHJG2C

pith:2023:2PLHJG2C4AM3PTXTKLKOZB3TXR

not attested not anchored not stored refs pending

Hard Lefschetz theorems for free line bundles

Jiajun Hu, Jian Xiao, Shijie Shang

arxiv:2305.19085 v1 · 2023-05-30 · 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{2PLHJG2C4AM3PTXTKLKOZB3TXR}

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

Numerical characterization of the hard Lefschetz classes of dimension two, II: supercritical collections of free divisor classes

Receipt and verification

First computed	2026-07-05T06:15:36.466440Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3d6749b42e019b7cef352d4ec8773bc699b501a70d9261a8f52662078f42cf8

Aliases

arxiv: 2305.19085 · arxiv_version: 2305.19085v1 · doi: 10.48550/arxiv.2305.19085 · pith_short_12: 2PLHJG2C4AM3 · pith_short_16: 2PLHJG2C4AM3PTXT · pith_short_8: 2PLHJG2C

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/2PLHJG2C4AM3PTXTKLKOZB3TXR \
  | 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: d3d6749b42e019b7cef352d4ec8773bc699b501a70d9261a8f52662078f42cf8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a0e52923eb780400780f389fb2e3a722920c358cd63b4ed2a91cbabf176a881",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2023-05-30T14:49:10Z",
    "title_canon_sha256": "b0e76a141fb0d446ece9f4c94bfc76c6d64d75186a54f3d5e9f51fde8f5634a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2305.19085",
    "kind": "arxiv",
    "version": 1
  }
}