Pith Number

pith:DCXNUQMN

pith:2011:DCXNUQMNR73QOEL7JNN4D4WIWD

not attested not anchored not stored refs pending

The Hilbert-Kunz function for Binomial Hypersurfaces

Shyamashree Upadhyay

arxiv:1101.5936 v2 · 2011-01-31 · math.CO · 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{DCXNUQMNR73QOEL7JNN4D4WIWD}

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	2026-05-18T03:48:59.265110Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

18aeda418d8ff707117f4b5bc1f2c8b0f7a59d1ba1e146ab4c5ca2091a0f3342

Aliases

arxiv: 1101.5936 · arxiv_version: 1101.5936v2 · doi: 10.48550/arxiv.1101.5936 · pith_short_12: DCXNUQMNR73Q · pith_short_16: DCXNUQMNR73QOEL7 · pith_short_8: DCXNUQMN

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/DCXNUQMNR73QOEL7JNN4D4WIWD \
  | 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: 18aeda418d8ff707117f4b5bc1f2c8b0f7a59d1ba1e146ab4c5ca2091a0f3342

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9eb467c4195e6f822348a0e73ca417e9bb54f90b4f3354f5e6b05633339241cd",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-01-31T12:30:57Z",
    "title_canon_sha256": "50a986647623615e0516e4aa75bf1a333995c180682821cfabab4e97f347fd41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.5936",
    "kind": "arxiv",
    "version": 2
  }
}