Pith Number

pith:UMN3ZXDL

pith:2017:UMN3ZXDLDUVHHWCFCJVQ4ZLILM

not attested not anchored not stored refs pending

Hyperbolic extensions of free groups from atoroidal ping-pong

Caglar Uyanik

arxiv:1711.07923 v3 · 2017-11-21 · math.GR · 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{UMN3ZXDLDUVHHWCFCJVQ4ZLILM}

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	2026-05-17T23:44:59.986876Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a31bbcdc6b1d2a73d845126b0e65685b3a283592ac7ff56703540adb7141d78d

Aliases

arxiv: 1711.07923 · arxiv_version: 1711.07923v3 · doi: 10.48550/arxiv.1711.07923 · pith_short_12: UMN3ZXDLDUVH · pith_short_16: UMN3ZXDLDUVHHWCF · pith_short_8: UMN3ZXDL

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/UMN3ZXDLDUVHHWCFCJVQ4ZLILM \
  | 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: a31bbcdc6b1d2a73d845126b0e65685b3a283592ac7ff56703540adb7141d78d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9686aeb5a589d6852fb192aed9b1248bc3f18dfccd6c6a301cb06a3ab7bab11",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-11-21T17:16:49Z",
    "title_canon_sha256": "9a6b5491c09e8b2fca36380eb14cb55bf976642364d2f48da225fcfbcb54a4f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.07923",
    "kind": "arxiv",
    "version": 3
  }
}