Pith Number

pith:WOJ7SAMB

pith:2014:WOJ7SAMBZSELH5NKJWVMFIKNIC

not attested not anchored not stored refs pending

Hilbert-Kunz functions of a Hirzebruch surface

V. Trivedi

arxiv:1407.6120 v3 · 2014-07-23 · 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{WOJ7SAMBZSELH5NKJWVMFIKNIC}

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	2026-05-18T01:32:19.016365Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b393f90181cc88b3f5aa4daac2a14d40a57b5f0228d78bbdd31ed8150ecb581d

Aliases

arxiv: 1407.6120 · arxiv_version: 1407.6120v3 · doi: 10.48550/arxiv.1407.6120 · pith_short_12: WOJ7SAMBZSEL · pith_short_16: WOJ7SAMBZSELH5NK · pith_short_8: WOJ7SAMB

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/WOJ7SAMBZSELH5NKJWVMFIKNIC \
  | 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: b393f90181cc88b3f5aa4daac2a14d40a57b5f0228d78bbdd31ed8150ecb581d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad7c352404b7f444f19aaca6f82377487cba20b843c9e64581a328cd05950e2b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2014-07-23T07:43:22Z",
    "title_canon_sha256": "a09d42748e470236213796c6a7f7e8deb54139cb95285bb043749f4da94f83a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.6120",
    "kind": "arxiv",
    "version": 3
  }
}