Pith Number

pith:XSIDE4GM

pith:2009:XSIDE4GMWBXTSMU4QYPLDUMG4I

not attested not anchored not stored refs pending

Purity results for $p$-divisible groups and abelian schemes over regular bases of mixed characteristic

Adrian vasiu, Thomas Zink

arxiv:0909.0969 v3 · 2009-09-04 · math.AG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XSIDE4GMWBXTSMU4QYPLDUMG4I}

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	2026-05-18T03:50:22.234458Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc903270ccb06f39329c861eb1d186e2207f2fea7500e12b913d57355da9ef2c

Aliases

arxiv: 0909.0969 · arxiv_version: 0909.0969v3 · doi: 10.48550/arxiv.0909.0969 · pith_short_12: XSIDE4GMWBXT · pith_short_16: XSIDE4GMWBXTSMU4 · pith_short_8: XSIDE4GM

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/XSIDE4GMWBXTSMU4QYPLDUMG4I \
  | 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: bc903270ccb06f39329c861eb1d186e2207f2fea7500e12b913d57355da9ef2c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb11d1a1001f0c52fdc226a5b1a095f0f41db3b3df4a858108a185290c2974d1",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-09-04T21:50:02Z",
    "title_canon_sha256": "4c2794606a74e71a45a3fc39dae92593ebcdf90ee9f12c264538fd0a2090ebfc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.0969",
    "kind": "arxiv",
    "version": 3
  }
}