Pith Number

pith:4U2FXLPH

pith:2009:4U2FXLPHYGXCBFK2ZA64JVUQBI

not attested not anchored not stored refs pending

The lower semicontinuity of the Frobenius splitting numbers

Florian Enescu, Yongwei Yao

arxiv:0912.0216 v3 · 2009-12-01 · math.AC · 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{4U2FXLPHYGXCBFK2ZA64JVUQBI}

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	2026-05-18T04:42:01.920929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5345bade7c1ae20955ac83dc4d6900a2cee4bac07f788a3d35419b99e290c40

Aliases

arxiv: 0912.0216 · arxiv_version: 0912.0216v3 · doi: 10.48550/arxiv.0912.0216 · pith_short_12: 4U2FXLPHYGXC · pith_short_16: 4U2FXLPHYGXCBFK2 · pith_short_8: 4U2FXLPH

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/4U2FXLPHYGXCBFK2ZA64JVUQBI \
  | 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: e5345bade7c1ae20955ac83dc4d6900a2cee4bac07f788a3d35419b99e290c40

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "38d151160dd5edba1c7a20879b7877b3fe732d9bee356aec0ce46dc3cf42e46f",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2009-12-01T17:59:40Z",
    "title_canon_sha256": "98775e1aaa0b90f56c1d377f87da439638460b1a482e554747105d9dd1199ba3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.0216",
    "kind": "arxiv",
    "version": 3
  }
}