Pith Number

pith:VYEA5LCP

pith:2002:VYEA5LCPJT6QXLX73BFCF25UI6

not attested not anchored not stored refs pending

On the existence of F-crystals

M. Rapoport, R. Kottwitz

arxiv:math/0202229 v1 · 2002-02-22 · 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{VYEA5LCPJT6QXLX73BFCF25UI6}

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	2026-05-18T01:05:29.755131Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae080eac4f4cfd0baeffd84a22ebb44783ee3f270c177002452eebf3ae4324ad

Aliases

arxiv: math/0202229 · arxiv_version: math/0202229v1 · doi: 10.48550/arxiv.math/0202229 · pith_short_12: VYEA5LCPJT6Q · pith_short_16: VYEA5LCPJT6QXLX7 · pith_short_8: VYEA5LCP

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/VYEA5LCPJT6QXLX73BFCF25UI6 \
  | 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: ae080eac4f4cfd0baeffd84a22ebb44783ee3f270c177002452eebf3ae4324ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9dcf1ca048b9a0588d903a0b76fd9a3d5997f28ef2b72a1b759daa2ec169c88f",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2002-02-22T13:56:00Z",
    "title_canon_sha256": "4393a3684a6796403014424bd74cd122894acdc8b69260bd8c257bb6e344753a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0202229",
    "kind": "arxiv",
    "version": 1
  }
}