Pith Number

pith:6UBWZPTR

pith:2015:6UBWZPTRM2QH2T6DNZHMZ3JREQ

not attested not anchored not stored refs pending

Graded unipotent groups and Grosshans theory

Frances Kirwan, Gergely B\'erczi

arxiv:1511.06983 v1 · 2015-11-22 · 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{6UBWZPTRM2QH2T6DNZHMZ3JREQ}

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	2026-05-18T01:26:16.994192Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5036cbe7166a07d4fc36e4ecced31240dc32275dcf3bd138c44e14cdd1270e2

Aliases

arxiv: 1511.06983 · arxiv_version: 1511.06983v1 · doi: 10.48550/arxiv.1511.06983 · pith_short_12: 6UBWZPTRM2QH · pith_short_16: 6UBWZPTRM2QH2T6D · pith_short_8: 6UBWZPTR

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/6UBWZPTRM2QH2T6DNZHMZ3JREQ \
  | 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: f5036cbe7166a07d4fc36e4ecced31240dc32275dcf3bd138c44e14cdd1270e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5639c868a76bc2277dd9a5fd091492c2b705fd1a1d42ad47c131bb7e7fa2671",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-11-22T09:41:17Z",
    "title_canon_sha256": "15547646b4b29ec6a0ee8c4ecc807b1cc5cb3e243b27c308e94beb66731ba6d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.06983",
    "kind": "arxiv",
    "version": 1
  }
}