Pith Number

pith:UBBXZYD2

pith:2000:UBBXZYD2VIYULWRSMT2R7KSZH3

not attested not anchored not stored refs pending

Groupes p-divisibles, groupes finis et modules filtr\'es

Christophe Breuil

arxiv:math/0009252 v1 · 2000-09-01 · 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{UBBXZYD2VIYULWRSMT2R7KSZH3}

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	2026-05-18T01:05:38.241930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a0437ce07aaa3145da3264f51faa593ed2302aadb4e3e35d8816cd80b8fe6667

Aliases

arxiv: math/0009252 · arxiv_version: math/0009252v1 · doi: 10.48550/arxiv.math/0009252 · pith_short_12: UBBXZYD2VIYU · pith_short_16: UBBXZYD2VIYULWRS · pith_short_8: UBBXZYD2

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/UBBXZYD2VIYULWRSMT2R7KSZH3 \
  | 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: a0437ce07aaa3145da3264f51faa593ed2302aadb4e3e35d8816cd80b8fe6667

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9a1dfb1071be4546d5ac608abf38d620e5a03a84d73a39c32d9d8a7ba01bc4d",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2000-09-01T00:00:00Z",
    "title_canon_sha256": "dc6f75a327444453f5804fc5976b5a5cd934754a4f28c26bca7b0f604c3e4387"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0009252",
    "kind": "arxiv",
    "version": 1
  }
}