Pith Number

pith:HW7GTVQU

pith:2018:HW7GTVQUVXXXNP6EB6NMXDWVQA

not attested not anchored not stored refs pending

Global Frobenius Betti numbers and F-splitting ratio

Alessandro De Stefani, Thomas Polstra, Yongwei Yao

arxiv:1811.11022 v1 · 2018-11-27 · math.AC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HW7GTVQUVXXXNP6EB6NMXDWVQA}

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	2026-05-17T23:59:45.456306Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3dbe69d614adef76bfc40f9acb8ed5803b443202dc305c77a600cfaf9e361e5a

Aliases

arxiv: 1811.11022 · arxiv_version: 1811.11022v1 · doi: 10.48550/arxiv.1811.11022 · pith_short_12: HW7GTVQUVXXX · pith_short_16: HW7GTVQUVXXXNP6E · pith_short_8: HW7GTVQU

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/HW7GTVQUVXXXNP6EB6NMXDWVQA \
  | 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: 3dbe69d614adef76bfc40f9acb8ed5803b443202dc305c77a600cfaf9e361e5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd7f35415fb498d2345beae66f8db767d6848a5d55d78f2a511782825b0d653c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2018-11-27T14:29:28Z",
    "title_canon_sha256": "ceabc5ba3105d79c3bad4e00fd86aa2fb7ef201a0cc750bdb0cfbb3ce01c9276"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.11022",
    "kind": "arxiv",
    "version": 1
  }
}