Pith Number

pith:CPTEM6VU

pith:2015:CPTEM6VUQOS3DWZVEYEH7CVKIH

not attested not anchored not stored refs pending

Hilbert-Kunz density function and Hilbert-Kunz multiplicity

V. Trivedi

arxiv:1510.03294 v3 · 2015-10-12 · math.AC · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CPTEM6VUQOS3DWZVEYEH7CVKIH}

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	2026-05-18T00:40:52.858656Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13e6467ab483a5b1db3526087f8aaa41ebf07fe762d45f1df53a1d5fe3f713b1

Aliases

arxiv: 1510.03294 · arxiv_version: 1510.03294v3 · doi: 10.48550/arxiv.1510.03294 · pith_short_12: CPTEM6VUQOS3 · pith_short_16: CPTEM6VUQOS3DWZV · pith_short_8: CPTEM6VU

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/CPTEM6VUQOS3DWZVEYEH7CVKIH \
  | 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: 13e6467ab483a5b1db3526087f8aaa41ebf07fe762d45f1df53a1d5fe3f713b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bfeb72f493fb6417e375a76dcaf502bf9dea17ab5f7eef6395b7b1cd1f9cce0b",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-10-12T14:18:52Z",
    "title_canon_sha256": "61407da8c127e79e463f3b0cc4711702d8495f9e50e76e3c8b7d5f91bf2a3caa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.03294",
    "kind": "arxiv",
    "version": 3
  }
}