Pith Number

pith:WKW26IMC

pith:2011:WKW26IMCS5YEZO7O3KWKG55B3B

not attested not anchored not stored refs pending

F-signature of pairs and the asymptotic behavior of Frobenius splittings

Karl Schwede, Kevin Tucker, Manuel Blickle

arxiv:1107.1082 v2 · 2011-07-06 · 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{WKW26IMCS5YEZO7O3KWKG55B3B}

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	2026-05-18T03:39:05.426144Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2adaf218297704cbbeedaaca377a1d854b90592aa87e30323fdb486470672a6

Aliases

arxiv: 1107.1082 · arxiv_version: 1107.1082v2 · doi: 10.48550/arxiv.1107.1082 · pith_short_12: WKW26IMCS5YE · pith_short_16: WKW26IMCS5YEZO7O · pith_short_8: WKW26IMC

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/WKW26IMCS5YEZO7O3KWKG55B3B \
  | 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: b2adaf218297704cbbeedaaca377a1d854b90592aa87e30323fdb486470672a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7518d8453b4d769f1d9e559879bd852d2db2414acb0e2b9d37c9ba5f36214f22",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-07-06T10:09:34Z",
    "title_canon_sha256": "ebe456fc8b2527f2f7ddb1a9a47f6fcf7805f50ab01f03948a415c3749effa64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.1082",
    "kind": "arxiv",
    "version": 2
  }
}