Pith Number

pith:72TTMRUX

pith:2019:72TTMRUXUPKCPIVTDPQ3CMYQCQ

not attested not anchored not stored refs pending

On planar Cayley graphs and Kleinian groups

Agelos Georgakopoulos

arxiv:1905.06669 v1 · 2019-05-16 · math.CO · 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{72TTMRUXUPKCPIVTDPQ3CMYQCQ}

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	2026-05-17T23:46:01.459595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fea7364697a3d427a2b31be1b13310142a3bb8086e785f1d90580d99f49be760

Aliases

arxiv: 1905.06669 · arxiv_version: 1905.06669v1 · doi: 10.48550/arxiv.1905.06669 · pith_short_12: 72TTMRUXUPKC · pith_short_16: 72TTMRUXUPKCPIVT · pith_short_8: 72TTMRUX

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/72TTMRUXUPKCPIVTDPQ3CMYQCQ \
  | 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: fea7364697a3d427a2b31be1b13310142a3bb8086e785f1d90580d99f49be760

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd6390c280f15f460b8d89d8f50f51031cb358955a2bae9824f4eb25c91a478c",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-05-16T11:42:40Z",
    "title_canon_sha256": "1d8862a00a7ae30c8870bc418ad179c225701ae69f8b196f8797786cb5220daf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.06669",
    "kind": "arxiv",
    "version": 1
  }
}