Pith Number

pith:45V2X2HB

pith:2004:45V2X2HB4YVNBPJLF6YMQVDIOM

not attested not anchored not stored refs pending

Finite flat commutative group schemes over complete discrete valuation fields: classification, structural results; application to reduction of Abelian varieties

M.V. Bondarko

arxiv:math/0412524 v3 · 2004-12-29 · math.NT · 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{45V2X2HB4YVNBPJLF6YMQVDIOM}

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	2026-05-18T02:49:39.211974Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e76babe8e1e62ad0bd2b2fb0c85468731ed886b1153235ee4bbe0dcf536abb93

Aliases

arxiv: math/0412524 · arxiv_version: math/0412524v3 · doi: 10.48550/arxiv.math/0412524 · pith_short_12: 45V2X2HB4YVN · pith_short_16: 45V2X2HB4YVNBPJL · pith_short_8: 45V2X2HB

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/45V2X2HB4YVNBPJLF6YMQVDIOM \
  | 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: e76babe8e1e62ad0bd2b2fb0c85468731ed886b1153235ee4bbe0dcf536abb93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c57bb482eebb0880783bdac09bfc56c93056a2835cf1d4b1a377250420937da3",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2004-12-29T10:07:15Z",
    "title_canon_sha256": "5767b8f036b0dd5f4dc0ea58b237ba8971449252bfdef49f9b50ed0162e0261a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412524",
    "kind": "arxiv",
    "version": 3
  }
}