Pith Number

pith:4QK2FMLU

pith:2010:4QK2FMLUVOG6MPMQDHREGXOGHT

not attested not anchored not stored refs pending

Density of Zariski density for surface groups

Inkang Kim, LM-Orsay), Pierre Pansu (DMA

arxiv:1009.2258 v1 · 2010-09-12 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4QK2FMLUVOG6MPMQDHREGXOGHT}

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	2026-05-18T02:29:37.160264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e415a2b174ab8de63d9019e2435dc63cebfb7aa5eb322df37e04650df04931ec

Aliases

arxiv: 1009.2258 · arxiv_version: 1009.2258v1 · doi: 10.48550/arxiv.1009.2258 · pith_short_12: 4QK2FMLUVOG6 · pith_short_16: 4QK2FMLUVOG6MPMQ · pith_short_8: 4QK2FMLU

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/4QK2FMLUVOG6MPMQDHREGXOGHT \
  | 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: e415a2b174ab8de63d9019e2435dc63cebfb7aa5eb322df37e04650df04931ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "854763369afa05ad0f089618e47d7d722f0a5fc1c7cc71889f9d0f85d95ef5ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-09-12T18:45:02Z",
    "title_canon_sha256": "ae76ba77d5a850a0adc0a8bf47c092ad46f45425a8c4c7a034774487535d36b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2258",
    "kind": "arxiv",
    "version": 1
  }
}