Pith Number

pith:4VBTRWBY

pith:2012:4VBTRWBYXUOML6LALMI27KE2SU

not attested not anchored not stored refs pending

La conjecture des sous-groupes de surfaces (d'apr\`es Jeremy Kahn et Vladimir Markovic)

Nicolas Bergeron

arxiv:1207.3217 v1 · 2012-07-13 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4VBTRWBYXUOML6LALMI27KE2SU}

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	2026-05-18T03:51:03.082345Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e54338d838bd1cc5f9605b11afa89a9534b5787a510b383fe5a0c46194e9ddad

Aliases

arxiv: 1207.3217 · arxiv_version: 1207.3217v1 · doi: 10.48550/arxiv.1207.3217 · pith_short_12: 4VBTRWBYXUOM · pith_short_16: 4VBTRWBYXUOML6LA · pith_short_8: 4VBTRWBY

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/4VBTRWBYXUOML6LALMI27KE2SU \
  | 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: e54338d838bd1cc5f9605b11afa89a9534b5787a510b383fe5a0c46194e9ddad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ee691bb31e8e5ae03663eb50a56d6374336e297c0b7cfff9fa7f4d1947c659b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-07-13T12:27:13Z",
    "title_canon_sha256": "bed1cf849285e173eeb06f1e71b41dbbd1439573ebff21bb953da4eb86a88bfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.3217",
    "kind": "arxiv",
    "version": 1
  }
}