Pith Number

pith:52OIM25K

pith:2006:52OIM25KRA3RISB6HQ2ZDQZMOO

not attested not anchored not stored refs pending

Dimension, multiplicity, holonomic modules, and an analogue of the inequality of Bernstein for rings of differential operators in prime characteristic

V. V. Bavula

arxiv:math/0605073 v1 · 2006-05-02 · math.RA · 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{52OIM25KRA3RISB6HQ2ZDQZMOO}

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	2026-05-18T01:05:22.727213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee9c866baa883714483e3c3591c32c738719212e49731d8e2196bef92699732c

Aliases

arxiv: math/0605073 · arxiv_version: math/0605073v1 · doi: 10.48550/arxiv.math/0605073 · pith_short_12: 52OIM25KRA3R · pith_short_16: 52OIM25KRA3RISB6 · pith_short_8: 52OIM25K

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/52OIM25KRA3RISB6HQ2ZDQZMOO \
  | 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: ee9c866baa883714483e3c3591c32c738719212e49731d8e2196bef92699732c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a86ff1329537ec41bc92ebf1b98d43d9f2cf96fbf11fb75d6d0e050bf7582b3d",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.RA",
    "submitted_at": "2006-05-02T18:39:01Z",
    "title_canon_sha256": "6b3cb29642883680698d8e66ef63c9ee84a1d785a1320ab15c392c9200c1c5d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0605073",
    "kind": "arxiv",
    "version": 1
  }
}