Pith Number

pith:ZWSHAI3Y

pith:2010:ZWSHAI3YAS2KZAZJ7BPYHUA4VB

not attested not anchored not stored refs pending

Counting Essential Surfaces in a Closed Hyperbolic 3-Manifold

Jeremy Kahn, Vladimir Markovic

arxiv:1012.2828 v1 · 2010-12-13 · 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{ZWSHAI3YAS2KZAZJ7BPYHUA4VB}

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	2026-05-18T04:33:27.658126Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cda470237804b4ac8329f85f83d01ca876ef4fe760097972e9133944c2f6f0da

Aliases

arxiv: 1012.2828 · arxiv_version: 1012.2828v1 · doi: 10.48550/arxiv.1012.2828 · pith_short_12: ZWSHAI3YAS2K · pith_short_16: ZWSHAI3YAS2KZAZJ · pith_short_8: ZWSHAI3Y

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/ZWSHAI3YAS2KZAZJ7BPYHUA4VB \
  | 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: cda470237804b4ac8329f85f83d01ca876ef4fe760097972e9133944c2f6f0da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45b4509974053e2754060c0b4a6c78ed7602c78a5adffcd52fdc04c7cc8ad6eb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-12-13T18:40:17Z",
    "title_canon_sha256": "f96edb295d9bdbb0426fdc53f12d7827ea5e3eebc8b323de21197be1aa3254f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2828",
    "kind": "arxiv",
    "version": 1
  }
}