Pith Number

pith:F22WZU4C

pith:2015:F22WZU4CCZMZFILJSWXEBTP3TQ

not attested not anchored not stored refs pending

On the behavior of singularities at the $F$-pure threshold

Alessandro De Stefani, Daniel Hern\'andez, Emily Witt, Eric Canton, George Whelan, Jack Jeffries, Karl Schwede, Robert Walker, Zhibek Kadyrsizova

arxiv:1508.05427 v3 · 2015-08-21 · 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{F22WZU4CCZMZFILJSWXEBTP3TQ}

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	2026-05-17T23:42:43.865093Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2eb56cd382165992a16995ae40cdfb9c1787747e427a7965b10f06f0ee76379f

Aliases

arxiv: 1508.05427 · arxiv_version: 1508.05427v3 · doi: 10.48550/arxiv.1508.05427 · pith_short_12: F22WZU4CCZMZ · pith_short_16: F22WZU4CCZMZFILJ · pith_short_8: F22WZU4C

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/F22WZU4CCZMZFILJSWXEBTP3TQ \
  | 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: 2eb56cd382165992a16995ae40cdfb9c1787747e427a7965b10f06f0ee76379f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1edafad354e0b6c99dda88489b04a9c9c4d302bfe14002f01df5b19ddfb1424",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-08-21T22:14:00Z",
    "title_canon_sha256": "2fcaa023a26e1d585d2b95ea3fec8f1173e8e7205b23cff7de4f351cf8ced4de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05427",
    "kind": "arxiv",
    "version": 3
  }
}