Pith Number

pith:GDPY4MKT

pith:2011:GDPY4MKTESFPYUKV6WYNVAA2VT

not attested not anchored not stored refs pending

A Direct Limit for Limit Hilbert-Kunz Multiplicity for Smooth Projective Curves

Claudia Miller, Holger Brenner, Jinjia Li

arxiv:1104.2662 v2 · 2011-04-14 · 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{GDPY4MKTESFPYUKV6WYNVAA2VT}

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	2026-05-18T03:43:18.889820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30df8e3153248afc5155f5b0da801aacdc45612c6e8836762625c0e99cd787dd

Aliases

arxiv: 1104.2662 · arxiv_version: 1104.2662v2 · doi: 10.48550/arxiv.1104.2662 · pith_short_12: GDPY4MKTESFP · pith_short_16: GDPY4MKTESFPYUKV · pith_short_8: GDPY4MKT

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/GDPY4MKTESFPYUKV6WYNVAA2VT \
  | 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: 30df8e3153248afc5155f5b0da801aacdc45612c6e8836762625c0e99cd787dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56576ef69c89fd8c915acbff01162e6b76610a2c06b3c79fbe657f263764d185",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-04-14T03:59:08Z",
    "title_canon_sha256": "853bb3f1e00c8276d07f425f21c32b56859f7f8f235fbbca6fde858e5c67b42f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.2662",
    "kind": "arxiv",
    "version": 2
  }
}