Pith Number

pith:TBME2OI5

pith:2015:TBME2OI5RHYYQCYPCJEBRJUMHI

not attested not anchored not stored refs pending

Hilbert-Kunz multiplicity of products of ideals

Javid Validashti, Neil Epstein

arxiv:1601.00014 v2 · 2015-12-31 · 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{TBME2OI5RHYYQCYPCJEBRJUMHI}

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	2026-05-18T01:19:57.037146Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98584d391d89f1880b0f124818a68c3a10136eee41a183f1fe941b80c25b07b0

Aliases

arxiv: 1601.00014 · arxiv_version: 1601.00014v2 · doi: 10.48550/arxiv.1601.00014 · pith_short_12: TBME2OI5RHYY · pith_short_16: TBME2OI5RHYYQCYP · pith_short_8: TBME2OI5

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/TBME2OI5RHYYQCYPCJEBRJUMHI \
  | 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: 98584d391d89f1880b0f124818a68c3a10136eee41a183f1fe941b80c25b07b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ddd388027e016d6bd7a72e386907c424f1f1d5c2ec8f700b8119b783066c3084",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-12-31T21:37:24Z",
    "title_canon_sha256": "5cb36dbdf8141cad29ad4aa205cf62f8b22753ac21bd236a46ddd719e80b6ba7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.00014",
    "kind": "arxiv",
    "version": 2
  }
}