Pith Number

pith:7BREYV3X

pith:2012:7BREYV3XP5SK2QN5HIEGJPNHAS

not attested not anchored not stored refs pending

Kottwitz-Rapoport and p-rank strata in the reduction of Shimura varieties of PEL type

Philipp Hartwig

arxiv:1210.1559 v1 · 2012-10-04 · 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{7BREYV3XP5SK2QN5HIEGJPNHAS}

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	2026-05-18T03:44:03.147922Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8624c57777f64ad41bd3a0864bda70480b605b513ac14dbaa65ffbb9ae12454

Aliases

arxiv: 1210.1559 · arxiv_version: 1210.1559v1 · doi: 10.48550/arxiv.1210.1559 · pith_short_12: 7BREYV3XP5SK · pith_short_16: 7BREYV3XP5SK2QN5 · pith_short_8: 7BREYV3X

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/7BREYV3XP5SK2QN5HIEGJPNHAS \
  | 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: f8624c57777f64ad41bd3a0864bda70480b605b513ac14dbaa65ffbb9ae12454

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d38361717de351981a17895810b21a7c0377db3d85a9f8683b88d544869ecaea",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-10-04T19:41:32Z",
    "title_canon_sha256": "09d4246cdd6c2a005b79195c9117b5379d06f7a2e3663ca1139db425bf8e5486"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.1559",
    "kind": "arxiv",
    "version": 1
  }
}