Pith Number

pith:UMNU7ZBK

pith:2011:UMNU7ZBKYGGVZMCZA7IW4DJJVU

not attested not anchored not stored refs pending

Hyperbolic spaces in Teichm\"uller spaces

Christopher J. Leininger, Saul Schleimer

arxiv:1110.6526 v2 · 2011-10-29 · math.GT · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UMNU7ZBKYGGVZMCZA7IW4DJJVU}

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	2026-05-18T03:34:35.774164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a31b4fe42ac18d5cb05907d16e0d29ad335d9c88436eb336314fc43a1aecf191

Aliases

arxiv: 1110.6526 · arxiv_version: 1110.6526v2 · doi: 10.48550/arxiv.1110.6526 · pith_short_12: UMNU7ZBKYGGV · pith_short_16: UMNU7ZBKYGGVZMCZ · pith_short_8: UMNU7ZBK

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/UMNU7ZBKYGGVZMCZA7IW4DJJVU \
  | 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: a31b4fe42ac18d5cb05907d16e0d29ad335d9c88436eb336314fc43a1aecf191

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ece7974883ae4512568a5ef71f68c99adcf5c6c5be1d8c5ef15763780f54d55",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/publicdomain/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-10-29T11:47:24Z",
    "title_canon_sha256": "509c4ff36f7266e56f299cb62846f56e4c9c4dbff2976109d4b1f56c1568e950"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6526",
    "kind": "arxiv",
    "version": 2
  }
}