Pith Number

pith:VGUUJCW2

pith:2013:VGUUJCW2ULSRQ2JKTOQOZNVGF3

not attested not anchored not stored refs pending

Upper bound of multiplicity of F-rational rings and F-pure rings

Craig Huneke, Kei-ichi Watanabe

arxiv:1310.0584 v1 · 2013-10-02 · 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{VGUUJCW2ULSRQ2JKTOQOZNVGF3}

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	2026-05-18T03:11:34.777651Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9a9448adaa2e518692a9ba0ecb6a62ecf332e3cd9a5d5e8d36e7bf4bf260468

Aliases

arxiv: 1310.0584 · arxiv_version: 1310.0584v1 · doi: 10.48550/arxiv.1310.0584 · pith_short_12: VGUUJCW2ULSR · pith_short_16: VGUUJCW2ULSRQ2JK · pith_short_8: VGUUJCW2

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/VGUUJCW2ULSRQ2JKTOQOZNVGF3 \
  | 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: a9a9448adaa2e518692a9ba0ecb6a62ecf332e3cd9a5d5e8d36e7bf4bf260468

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d299c5d481651d4d272f04af0d059a400c7dd16664401f47f1ffb6e037289c80",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-10-02T06:28:08Z",
    "title_canon_sha256": "b2af05957b5ad679e549cf86871318f66dc14f3caaacc1444ac4d2cd73a6baa0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.0584",
    "kind": "arxiv",
    "version": 1
  }
}