Pith Number

pith:PJTHMSOQ

pith:2013:PJTHMSOQH7YRX5X24SJQVIVQZP

not attested not anchored not stored refs pending

On generalized Hilbert-Kunz function and multiplicity

Hailong Dao, Ilya Smirnov

arxiv:1305.1833 v5 · 2013-05-08 · 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{PJTHMSOQH7YRX5X24SJQVIVQZP}

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	2026-05-17T23:43:33.658914Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a667649d03ff11bf6fae4930aa2b0cbc184473b9016ccb9e600179aba29d1c5

Aliases

arxiv: 1305.1833 · arxiv_version: 1305.1833v5 · doi: 10.48550/arxiv.1305.1833 · pith_short_12: PJTHMSOQH7YR · pith_short_16: PJTHMSOQH7YRX5X2 · pith_short_8: PJTHMSOQ

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/PJTHMSOQH7YRX5X24SJQVIVQZP \
  | 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: 7a667649d03ff11bf6fae4930aa2b0cbc184473b9016ccb9e600179aba29d1c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b2d21ab2ad9cb5fabe32f0390b3b8aee95371b92ae9d9ce5f8d83259e072a6c",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-05-08T14:40:14Z",
    "title_canon_sha256": "2e91a795c6f88e338e6e69f2a739cfa48cf529569f8e5b5a2aaead63d4cb37d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.1833",
    "kind": "arxiv",
    "version": 5
  }
}