Pith Number

pith:6R72CFMQ

pith:2018:6R72CFMQBNVPZ2UQ4PKFU3LUQR

not attested not anchored not stored refs pending

A central limit theorem for random closed geodesics: proof of the Chas-Li-Maskit conjecture

Giulio Tiozzo, Ilya Gekhtman, Samuel J. Taylor

arxiv:1808.08422 v2 · 2018-08-25 · math.GT · math.DS · 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{6R72CFMQBNVPZ2UQ4PKFU3LUQR}

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	2026-05-18T00:04:29.352213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f47fa115900b6afcea90e3d45a6d74845da55138b985375c3f702638fa780b70

Aliases

arxiv: 1808.08422 · arxiv_version: 1808.08422v2 · doi: 10.48550/arxiv.1808.08422 · pith_short_12: 6R72CFMQBNVP · pith_short_16: 6R72CFMQBNVPZ2UQ · pith_short_8: 6R72CFMQ

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/6R72CFMQBNVPZ2UQ4PKFU3LUQR \
  | 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: f47fa115900b6afcea90e3d45a6d74845da55138b985375c3f702638fa780b70

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "843de9305bcdaa99191997e9538080d70009739f11a9240ea93d71b774fb9ea4",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-08-25T13:12:37Z",
    "title_canon_sha256": "82592093db0baae0bc168e1c61d771846493215e2ce0b494839ed6e9cd993078"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.08422",
    "kind": "arxiv",
    "version": 2
  }
}