Pith Number

pith:Z6QVS5FT

pith:2011:Z6QVS5FTMVOQWTA4ZIEYOPDQMQ

not attested not anchored not stored refs pending

New estimates of Hilbert-Kunz multiplicities for local rings of fixed dimension

Florian Enescu, Ian M. Aberbach

arxiv:1101.5078 v4 · 2011-01-26 · 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{Z6QVS5FTMVOQWTA4ZIEYOPDQMQ}

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	2026-05-18T02:29:30.214642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfa15974b3655d0b4c1cca09873c7064199b223ca82a2922efbe353eb6be0830

Aliases

arxiv: 1101.5078 · arxiv_version: 1101.5078v4 · doi: 10.48550/arxiv.1101.5078 · pith_short_12: Z6QVS5FTMVOQ · pith_short_16: Z6QVS5FTMVOQWTA4 · pith_short_8: Z6QVS5FT

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/Z6QVS5FTMVOQWTA4ZIEYOPDQMQ \
  | 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: cfa15974b3655d0b4c1cca09873c7064199b223ca82a2922efbe353eb6be0830

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3914c25a4b6ff3d8c895393e24f20f9ad9379cabec85ab043af2daf53dbf1d4f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-01-26T14:58:23Z",
    "title_canon_sha256": "bbe4b7c3172bb2a80eb5ed73e21ebf6923d2b1159361022f81f264e8e3749b65"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.5078",
    "kind": "arxiv",
    "version": 4
  }
}