Pith Number

pith:WGN2M6PW

pith:2015:WGN2M6PW6CP27GEJGTDZBG5WOM

not attested not anchored not stored refs pending

Generalized Hilbert-Kunz function in graded dimension two

Alessio Caminata, Holger Brenner

arxiv:1508.05771 v2 · 2015-08-24 · 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{WGN2M6PW6CP27GEJGTDZBG5WOM}

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	2026-05-18T00:01:15.602463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b19ba679f6f09faf988934c7909bb6733197759b70c0156ec1f8ae13e7abd470

Aliases

arxiv: 1508.05771 · arxiv_version: 1508.05771v2 · doi: 10.48550/arxiv.1508.05771 · pith_short_12: WGN2M6PW6CP2 · pith_short_16: WGN2M6PW6CP27GEJ · pith_short_8: WGN2M6PW

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/WGN2M6PW6CP27GEJGTDZBG5WOM \
  | 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: b19ba679f6f09faf988934c7909bb6733197759b70c0156ec1f8ae13e7abd470

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7d2838d0cce6a26fbe2f9596de70bfc013f511bcab734b91e8924b3ede87d30",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-08-24T12:08:55Z",
    "title_canon_sha256": "5331983d01361f731b7c581882f9819e669736e63495c3536e958feeb1f54cde"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05771",
    "kind": "arxiv",
    "version": 2
  }
}