Pith Number

pith:GYNOULS3

pith:2011:GYNOULS3JAO5YFD2EC5WSUN4UP

not attested not anchored not stored refs pending

Nine-dimensional exceptional quotient singularities exist

Constantin Shramov, Ivan Cheltsov

arxiv:1110.6782 v3 · 2011-10-31 · math.AG · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GYNOULS3JAO5YFD2EC5WSUN4UP}

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	2026-05-18T04:00:15.525540Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

361aea2e5b481ddc147a20bb6951bca3dc09c02005a2244d480f1b7336974dab

Aliases

arxiv: 1110.6782 · arxiv_version: 1110.6782v3 · doi: 10.48550/arxiv.1110.6782 · pith_short_12: GYNOULS3JAO5 · pith_short_16: GYNOULS3JAO5YFD2 · pith_short_8: GYNOULS3

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/GYNOULS3JAO5YFD2EC5WSUN4UP \
  | 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: 361aea2e5b481ddc147a20bb6951bca3dc09c02005a2244d480f1b7336974dab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c0474288d3c7d11139452df160e84dea130990e79cdeed4e0a5baadc8022f38",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-10-31T13:13:38Z",
    "title_canon_sha256": "640ad6faee60f6776a0c6e8391ff09aa76ca3ccacccb84b8ebf531dc942eb374"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6782",
    "kind": "arxiv",
    "version": 3
  }
}